Personal Finance Example Problems Including Time Value of Money – Excel

1. Introduction: Personal finance example problems including time value of money. Excel is a project-based course containing multiple practical personal finance related practice problems, which will contain a time value of money component to them, often needing calculations of present value and future value calculations, which we will do using Excel. Down below, we have some Excel worksheets that can be downloaded. Most of the Excel worksheets will have at least two tabs. One will have the answer key for it. So you can see how everything is structured when it is all said and done and completed. Another tab where we will be working the practice problem in a step-by-step fashion along with the instructional videos, the end result, the final project will be the completed Excel worksheets. 2. Rate of Increase: Personal finance practice problem using Excel, calculating the rate of increase. Prepare to get financially fit by practicing personal finance. We are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example to have the example tab, in essence being an answer key, we have the information on the left-hand side going to populate that into the blue area on the right hand side, calculating our rate of return. Common kind of statistic that we need to get in our mind. One which oftentimes people have trouble with thinking about percentages are kinda scared of ratios and percentages sometimes, but they're really important for many different kinds of measurement things, especially in finance, but with any kind of thing that you're trying to measure performance. Oftentimes with job performance, these types of calculations being important as well, which we can see when we look at a particular and popular type of job that being sports, where we break down to basically statistics, which is basically job performance for athletes. So what we have here, we've got the purchase of a truck and we're going to say the cost at Purchase was $18 thousand. And then we're going to say that years have past five years have passed. The current price of the truck, or a similar truck would be $22 thousand. Note what we're measuring here, we're not saying that we purchased the truck and that particular truck went up in value, that's not likely to happen. Most likely the truck will decline in value due to depreciation. What we're saying here is that similar trucks are going, the current price of a similar truck is at the 22 thousand and that would be one indication that we would think one possibility or reason why that might be is because of the time value of money or inflation taking place. Meaning goods over time might be costing more because the dollar itself is going down in value when we're doing long time projections about our budgeting, we need to take into consideration the cost of the dollar. Typical trend, which will be that the price of things we'll use it usually be going up. In the US. They actually tried to have the price go up by like anywhere between 1, 3% is basically normal rate of inflation. So you've got to take that into consideration. If inflation gets out of control, then it can go up by significantly more than that. It could have a significant impact on your budget and your purchasing power in the future. It's really useful for us to think about this kind of increase in terms of the dollar amount change, but also in terms of the percentage change. Because then we can do things like in this scenario, we can do things and say, well, if the car went up by that much, Is that the same rate? That's a milk is going up or cheese or something like that daily other products, are they going up by similar rates? Can I assume an array greatly increase, such as that? So let's take a look at this. We're gonna say, alright, how would we calculate the percentage increase? We're gonna take the current price, the current price of the truck. I'm going to take the later price, first tier, which is the 22 thousand, assuming a similar truck goes up to 22 thousand. Notice I'm just using keyboard here, equals down, down, down, left, left, left. And we're always taken our data from the, from the information on the left-hand side as much as possible so that if we wanted to change scenarios and run different scenarios, we can do so by simply changing the data that will then populate our worksheet to the right. Then we're going to say the cost of truck in the past. And I'm gonna pick up this information by picking it up on the cell B2. So I'm going to say equals left, left, left, up. And there's the 1800s in cell B2. Enter. Let's go ahead and underline that cell by going to the Home tab font group. And underline, we can look at the dollar difference or the change over time, which will be a subtraction problem, which I'm going to put in Excel by saying equals, use the up arrow, up, up to get to the 22 thousand minus. That brings me back to the cell. Then I'm going to use the up arrow one time to get to that number and enter. So we have a difference of 4 thousand. That 4 thousand is useful when you're comparing things of a similar nature. But like I said, if you're comparing this change or increase in price to something else, like possibly are trying to drive some kind of information from this to think about a change in your grocery list or something like that, then you can't really do it with the dollar change. And the similar kind of thing will happen if you're measuring something like work performance. So if you're trying to measure somebody's batting average, you got to take into consideration that one person batted more times than another person. It would not be fair if you're talking about one person that got 20 at bats versus the other and thick got ten and trying to see how many hits they got or something like that. Or if you're a teacher and you're trying to see how many people are showing up to the course, it wouldn't be fair if you're saying five people were absent from this course versus this course. But one course has 30 people in, the other course has 100 people in it or something like that. You can't, you gotta, you gotta use these. Percentages in order to make accurate comparisons. And these are things like I say, a lot of people don't quite grasp. And when you're looking at finance and even when you're looking at job performance or something like that, people will often not know how to apply statistics and, or purposely manipulate or basically Lie with Statistics. And the way you lie with statistics is not that the statistics themselves are bad. It's just the same way you lie with anything else. You basically give a half truth about the statistics and then you pack up a bunch of lies on top of the half-truth. It's just that people are less good at picking up lies related to statistics. When you do that verbally, you tell someone some little fragment of a truth and then you pack a bunch of lies on it. People are usually more sophisticated with words and they're saying, Hey, look, you're totally lying. You said one true thing and you pack a bunch of lies on top of it. Same. There's nothing wrong with statistics. Statistics are good, but truth needs to be. You've got to find multiple angles to find the actual truth. If someone gives you just one statistic for a complex thing and then gives you a bunch of lives. That's not enough. Okay, So in any case, we're going to compare that to the original cost here. This is how you get the percentage increase, which is gonna be equal to, I'm going to pick up the same 18 thousand, the same 18 thousand. And so notice what we compare it to. We compare it to the original price. We don't compare it to the second price. That's where the confusion comes in oftentimes, and that's gonna give us our rate of increase, rate of increase. I'm gonna go ahead and put an underline under the 1800s by going to the Home tab, font group and underline. And then we'll divide this out. We're going to take the 4 thousand divided by the 1800s. So this will equal, I'm going to hit the up arrow twice, up, up to the 4 thousand, divided by the up arrow once to the 1800s, E4 divided by E5 and enter there, we have it. Now we got to make it a percent so we can see the change. We're gonna go to the Home tab to do that font group. And then you could have the decimals. There's the decimal format. And then I'm going to add it per cent. That moves the decimal place two places over, adds the percent, then add a couple of percentages here. So that's the percent increase over that timeframe, which is five years here. Let's do a similar kind of process and think about, well, what if we had a year-by-year change? And we can think about the percentage change on a year-by-year level. This can give us some idea of trends that are happening over time. So this was a change that took place over a five-year period. Let's bring out these numbers and imagine that these were the increases from years 2345. And we'll do like a running balance type of calculation. Now I'd like to get my data as close to my, my calculations as possible. So I'm going to try to hide some cells to do that. To do that, let's put our cursor on column D. Left-click, drag on over to column F, and then let go, right-click on that selected area and then hide. So there we have it. And now I'm just going to basically do a running balance kind of calculation will have the years, the amount that change, and the percent change. And note the table's already set up for you here. But if you could start to get a picture of the tables, knowing what you're going to have in the columns and the rows is often a skill that is where it's a skill It's definitely worth having and it takes practice to kinda see how you'd set up a table here. So practice setting up a table. So we're going to have year one, year one. And then I'm going to say this is gonna be equal to year two. I'm just going to sit notice I'm going to say equal, even though this is not a number, but a words down here. So I'm going to say equal and I can still pick up the words just like I would with a number. And so I'm going to say equals down, down, down, down, left, left, left, and enter. And I could do that all the way down, equals down, down, left, left, and then equals down, down, down left, left, and then equals down, down, down, left, left. Also note, I could use the autofill to do that as well. And anytime you want to get used to basically just being able to see when you can auto fill. So to show that I'm going to delete these ones. I just did. This one. If I double-click on that is coming from here, if I copy this cell down, it will take the relative cell as I go down, it'll go down each one cell. I should be able to simply auto fill this down, which would be faster. So let's practice that. Putting our cursor on the fill handle, dragging it on down and there we have it, years one through five. So now we're going to pick up the amount in year one. We have the 1800s thousand year two, we got the numbers down here. I'm just going to say equals down, down, down, down, down, left, left, left equals down, down, down, down, left, left, left t equals down, down, down, down, left, left, left. And equals down, down, down, down, left, left, left. Notice you can, you're probably saying, Hey, why don't you use the Auto Filter. I'm hoping you're saying that we serve so you could use the autofill, gets weaker. Let's do that. Let's delete these ones and say, this one is coming from right there. If I copy it down, I should be able to use the autofill. Let's try it out. For our cursor on it, put our cursor on the fill handle, drag it down. There we go. Now this is the same as copying and pasting would be the same just so you know, I'll show you that just real quick. If I copy this down, Control C or right-click and copy and pasting when I paste, I'm pasting the formulas. If I paste the first one, and that'll do the same thing in that instance as the autofill. Then we're going to have to change. Now there's no change in column one. The change in into is simply going to be the second year minus the first year. So I'm not looking at a five-year change. I'm looking at a year-by-year change, and I want to do this in a running balance format. So this is gonna be equal to left once minus left and up. So the 1850s minus 18 thousand, I'll do it again, equals left ones minus left and up. Do it again equals left ones minus left and up. One more time equals left wants minus left and up. Now this one's a little bit more complex, but you can use the autofill with this one as well because everything's within the table. So you would think that if I copy it down, all the relative sales should copy down appropriately. Let's check it out. I'm going to delete these. Put my cursor back on the 750, which is the 1850s minus the 1800s. Put my cursor on the autofill handle right here and left-click, drag it on down. And then I will typically double-check it by double-clicking on one of the cells and see, yes, it does indeed look like it's doing what we expected it to. Then we'll take the percent change. Now the percent change is always the change, the difference that we calculated from period to period divided by the beginning period. So you're always divided by the beginning period. That's where people kind of get a little bit mixed up. That's why I'm saying that loud and emphasizing that point because that's where people get mixed up sometimes. So we're gonna say this equals left once divided by left, left up the 1800s. And then this one, the wallets percent of phi, that one we're gonna go to the Home tab number group. You can add decimals or you can make it a percent and add decimals. Let's do it here. This is going to be equal to the change, which is going to be the 6,600 divided by the year two amount, because that's 600 is a result of the 1850s minus the 1870s were looking at the difference between year 32. So there we have it. Let's go ahead and let's use this time. I'm going to use the paintbrush in order to paint the formatting. So I'm gonna go to the Home tab, clipboard Format Painter, which will paint just the formatting and then put that down here. So it has the same formatting as the one above it. Anytime you're looking at a cell, we don't know exactly what the formatting is. That thing is useful. This is going to equal the 550 divided by the 1850s format paintbrush it, clipboard Format Painter, paintbrush one more time. This equals to 2100 divided by the 199 format paintbrush, the one above it, Format Painter paintbrush it. So there we have it now, we could auto-fill that one down as well. So I'm going to delete these and show that one more time. I'm going to delete these three. Try to simply copy this one down because these are all even though it's a little complicated in the same table. Usually when you're dealing with something that everything's in the same table and not in the dataset to the left. You can copy it down and the relative cell references will do what you want them to. So we're gonna put our cursor on the autofill, drag that on down. Then I'll typically double-click one of the later ones to see if it's calculating the way we expect, and indeed it is. So now we've got our changes. Note that this dollar change is useful. You can see the dollar change and see how it's changing more one year to the other. And you're like, well, four to five, there's a big change there. What happened in four to five? And you can kinda look into that there. But often that change, those big changes stand out more, especially when you're looking at those trends across different kinds of things with the percentage changes here. And I can say, well, that's a big change in the percent. The price of milk grew up by 10.55 or something like that. You can start to ask those questions and you can only do those kinds of comparisons with the percentage change. Okay, so let's do the same thing down here. But this time I want to, I want to see the change compared to the base year, which is often a common type of way. We would want to see this meaning, I want to look at each year we have like we did in year five and compete care each year to year one that we started with the 1800s. Strive at this time, I want the years, the years are gonna be the same as the one up top. You could copy these and paste them. I would rather use formulas whenever possible. So I'm going to use formulas. I'm going to say this equals and I'm going to go up, up, up, up, up to that one. And then notice I can auto-fill it down because these are all relative cell reference. So I'm gonna put my cursor back on this one and then auto fill it down, putting my cursor on the fill handle, dragging down like so. Then we have the amounts. The amounts are all going to be the same here as well. So I'm just going to pick up and do the same method. This equals the one in the 1800s. And then Enter, I'm going to auto-fill it down and I should have the relative cells should, should populate down here as well. Putting my cursor on the autofill handle, left-click dragging down. And there we have it again, bringing those cells down. Now this time, instead of having a change column, I'm going to compare everything to year one. Everything to the 800s thousand. So I'm gonna pick this one up and this time I'm going to say equals the 1800s in my dataset. On the left-hand side. Note that since I'm picking something up from the dataset, if I copy it down, I might need to then make it an absolute reference. In other words, if I want all of these to be 18 thousand, which I do, I can't copy this one down because it'll move the cell down. If I do so to five, I don't want it to do that. One way to fix that is I can double-click on this. See the 100th thousand there, make this an absolute reference by putting my cursor in the b2, selecting F4 on the keyboard and, or just putting a dollar sign before the B and the two. That dollar sign has nothing to do with dollars or a currency. It's just something to tell Excel don't move the cell down when I copy it down. And you only need a mixed references using $1 sign instead of two. But $2 signs is conceptually easier to think about. So absolute reference will work. Then I'll put my cursor back on it, auto fill it on down. So now we've got the 1800s all the way down. Just so you know, there's, there's another way sometimes I will do that. Second method if I have one number sometimes, and sometimes this is useful, I'll delete this. I'll say equals the one above it. And then I'll auto fill that down so I can auto fill that down. And that means every sale equals to one above it. So that if I changed the first one, then it'll change all the ones below it. But I think it's more common to use this one. So I'll copy this back as the absolute reference format. And then we'll have the change here, which is just gonna be the amount divided minus year one. This equals left, left the amount minus the amount in year one. Obviously there's no change from year one to year one. This equals the amount minus the year one. This equals amount minus year one. Then what I say I'm Malthus is your three minus year one. This equals 0 or four minus one equals 05 minus one. And so there we have it. Could we auto fill that one down? We could. So I'm going to delete these. Double-click here. I can subtract that off by just saying the autofill handle, grabbing the autofill handle, dragging that down. I'll double-click it by checking the last one. Looks good. Then we can do our division. And it's always gonna be the change divided by the starting point, which in this case is year one. That's our starting points. I'm gonna say this equals 0 divided by 18 thousand, which is 0. Even if we format it to home tab number group Percent, define it, adding some decimals. Let's do it here. This is going to be equal to the change 750 divided by left, left the starting point here, 118. That gives us, let's go ahead and go to the Home tab number group. You could add decimals or identify it and add decimals. Let's do it here. We're going to say this is going to be equal to the 1350 divided by left, left the 1800s. I'm going to use my paintbrush this time. Home tab clipboard format, painter, paint, brushy it. And then we'll do that again. This equals left once 21900 divided by the 1800s. Let's paint brush that 1750 paintbrush. Put that over here and let's do it one more time. This equals the 4 thousand divided by the 18 thousand. We could paintbrush that Home tab paintbrush. Paintbrush. Could we auto fill that one down? We could have. So let's do that one more time. Deleting these three, selecting this one. This is the calculation. Putting my cursor on it, fill handle, left-click, dragging it down. Then if I double-click this last one, it does look like it's doing what we'd expect it to. Notice that the bottom line number here, 22 to 22, is basically what we got in the first calculation. Meaning if I unhide some cells up top, putting my cursor on column B, left-click, dragging over to column G, Let go, right-click on the selected area and unhide to unhide these cells. We have the 2222. That's gonna be the change that we have here on this last one. But now we're comparing each item to basically the base year, which is another way we can often see this kind of trend type of analysis. And once again, the percentage is often being useful when we're looking at that kind of trend analysis. So like I said, these don't be afraid of the statistics that makes sure that you wanna be kinda comfortable with these kind of basic statistics, these division kind of problems. They are fraction type of problems and they come up all the time, not just in personal finance, just in your job reviews. If you're trying to trying to judge someone else in their performance in some way and you're not using statistics and you're comparing two people about something, you're probably not doing it fairly. You got it. You have to use this statistics. And if someone's judging you based on statistics, in some way judging your performance, it'd be nice if you understood what's, what's happening. So you can kind of determine whether or not you're dealing with someone who's being fair in their assessment, or possibly if they're either not interpreting statistics properly or even intentionally misinterpreting the statistics, which unfortunately is obviously quite common as well. 3. Inflation & Estimated Increase in Personal Expenses: Personal finance practice problem using Excel inflation and estimated increase in personal expenses. Prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, I'd like to follow along note that we're down here in the practice to have as opposed to the example tab. The example tab, in essence being an answer key, we have the information on the left-hand side going to populate that into the blue area on the right-hand side, information saying that we're going to estimate the personal expenses per year, costing us then per year for personal expenses, 66 thousand, we're going to assume that there's a yearly inflation rate of 5%. And then ask ourselves how much we're going to need in two years in order to cover the same kind of personal expenses given the inflation. So we're going to use our same kinda future value calculation to estimate how much we will need. But we're going to use it a little bit differently because most of the time when people think about a future value calculation, as we saw in the past, we use it to basically estimate how much growth there might be in something like an investment, like a savings account, like a stocks or bonds or our home going up in value or something like that. Now we're applying it to something which is going to be the inflation. How much is the inflation is going to be impacting? How much we'll have to typically spend for the same amount of goods in two years. So quick recap on inflation. That's gonna be the purchasing power of the dollar going down. And notice there's gonna be times in the economy. And I'm usually speaking from the standpoint of the US economy, but the same will be true around the world with regards to inflation and the currency and purchasing power of the currency and the US, it can be fairly stable when compared to other countries. Just note that that doesn't mean that you won't have to experience in your lifetime time periods where inflation basically goes up and time periods when inflation goes down. So when we're doing long-term planning, we want to make sure that we're taking into consideration the likelihood that in our lifetime we're going to have to experience increased and decreased inflations. And we might have extended periods of higher inflation and extended periods of lower inflation. Both those two extremes make us feel like that's always gonna be the way it is, like that's the new norm. And as soon as we feel like that's the new norm, something often changes. To change the new norm does something. So note, the Federal Reserve in the US usually shoots for inflation of about one to 3%. Meaning they actually want the purchasing power of the dollar to go down by some systematic component to make sure that there's enough money, currency in the market and the economy in order to meet the needs of kind of like the lifeblood of the economy is cash. So they want to make sure that they have the right amount of cash there, but they try not to let it go too much over that one to 3% and they look at that closely. But again, the fact that we try to do that doesn't mean it couldn't get out of control at some point in time. So we want to account for that. So we're going to assume 5% which is above the norm and the US, which would be 123. But like I said, it's nowhere really out-of-control. 5% is still within the realm. If something got out of control, you can have very extreme interest rates was hopefully it doesn't happen. But that's the idea here. So the idea then being if I'm spending my money today on a basket of goods to things like food and whatnot then, and it cost me 66 thousand. And the money that I have is going down by 5% in terms of purchasing power, then how much will it cost me to live the same in terms of my consumption, to spend the same amount of money. So we're gonna do our future value type of calculation in a similar way as we did in the past. To do that, let's first take a look at our running balance calculation, which is a useful thing to give us more context than simply a future value formula or function. So I'm gonna do are running balanced table. I'm going to start at period 012. We're going to use our autofill to auto-fill the rest of the way down. So I'm going to select these three cells, going to put my cursor on the fill handle and drag it on down to it continues on the series to four periods down. Going to center this by going to the Home tab up top, go into the alignment, and then we're going to center it. So there we have it. I'm going to start with the investment out here in F2. We're going to continue on with our practice. I'm not typing in the 66 thousand at period 0, but saying equals, I'm hitting the left arrow on the keyboard, left, left, left, and up to get to cell B1 and enter. So we're gonna do a same kind of calculation as we saw if I was to think about this as an investment that was going up. But now I'm thinking about it as the expenses that I need to cover and how much I'm going to need in order to cover those expenses. If we assume the purchasing power goes down. So we're going to say, Alright, That means that I'm going to take that 66 thousand times the 5% increase. So let's do that this way. This equals left up times, I'm sorry, that was right and up and then times left, left, left to the five per cent. So F2 times B3 and Enter. Now I'm going to do an absolute reference later so that we can copy it down. But before we do it, let's just calculate it straight away a few times. So that means that we had 66 thousand before and now it's going to cost us another 3,300 after year one. If there's 5%, basically inflation, that means it's going to take $69,300 to purchase the same stuff that we purchased last time, like food and gas and whatnot or personal expenses, cost us to 66 thousand last time. Now remember, that doesn't mean that everything's going to go up exactly the same. Sometimes food will go up more and sometimes gas will go up and they could go up and down. But we're trying to get a broad idea of how much we're going to need in our total basic expenses categorization by broadly categorizing what inflation will be. Also note when you talk to inflation or listen to people talking about inflation, they will often use terms like it's gonna be a short-term inflation are transitory or long-term inflation. And in order to basically lock into what they're really concerned about for the economy. Long-term inflation problems, they often eliminate things that are the things you actually spend money on. Food, electricity, gas, the things that are actually important to most people. Oftentimes will be taken out when you consider the impact of the entire economy because they're trying to find out what the long-term inflation indicators will be in trying to determine if inflation will be short-term. But whether it's short-term or not, if your food costs go up your gas, then that's gonna be a problem. And you want to calculate that and take that into consideration so that the numbers that you'll hear then from the Fed or from news anchors and whatnot will be a kind of, you can't really go off it completely all the time because they're looking in terms of the broader economy. Oftentimes in any case, we're then gonna do this again. This equals to 693 times, and then we'll pick up the 5% again. So now it's gonna go up by another 3 thousand for 65. And then I'm going to say, alright, that means that we have last time equals up to the 69300 plus left wants to the 3 thousand for 65. That means that now it's going to cost us 72,765. And notice this starts to grow up quite quickly at even a modest rate of inflation of the 5%, it's going to cost us 72 thousand, 765, whereas in period 02 years ago, it only cost us the 66 thousand. Let's do it again. This is going to be equal to the 72765 times the 5% left, left, left up, up. Now it's going to be another 3,638. This is gonna be equal to the 727625 plus the 3638. And now it's going to cost us 76403 to get the same amount of stuff, which way back in period 0 cost us 266 thousand. Let's go ahead and do this with a running balance calculations. So I'm actually going to delete these items, do it one more time, this time the easy way so we can calculate it quickly. I'm going to delete these items. This first one, again by saying equals right up to the 66 thousand times left, left, the five per cent. Now that 5% is outside of the table. Anything that's outside the table when I think about copying it down is something I would think that I might need an absolute reference for. I'm not gonna do it yet. I'll do that in a second just to prove that I will need it. And then we're going to say this equals the one above it plus the one to the left of it. And so there's the 693, which is the 66 thousand plus 3,300. Let's go ahead and copy this down and we'll see that we have a problem when we do so. So I'm gonna select these two, put our cursor on the fill handle, left-click on it, drag it on down. We have a problem because that shouldn't be 0, that shouldn't be 0. What should it be? Well, it should be taken that number that looks right, but this 5% is wrong because it moved it down and it should be 5% and it's not. So we need to fix it with an absolute reference. So I'm going to delete these second two here, selecting them, deleting them. I'm going to fix this one before dragging it down again, double-clicking on it. There's the 5% in cell B3. Putting my cursor and B3, we want to absolute ties it, which isn't really a word, but I think it works. I'm going to put F4 on the keyboard to make it an absolute reference, which is the proper phrase, dollar sign before the B dollar sign before the three, you only need a mixed reference, but an absolute references kinda easier to understand because it basically means or telling Excel not to move that cell down. Dollar signs having nothing to do with dollars, simply code for Excel, telling it not to move this cell down. Enter. Then I'll typically select these two and move it down one cell just to double-check that it's doing what I wanted to do. If I'm if I'm not sure that it will auto fill that down, does look right. Let's double-click on it. That looks like it's doing what we want. It looks good. Let's drag it on down to your four then selecting these two cells, putting our cursor on the fill handle, dragging it on down. Year for year four, we're up to 80 thousand to 23 to buy the same stuff. My food, the food I need that I would only cost me 66 thousand like four years or five years ago or something like that. Things are getting out of control. The world's going to **** in a hand basket these days. I remember when I used to be able to buy a hamburger, happy meal anyway. Okay, so now I'm going to hide some cells. Let's do this with just the future value calculation instead of a running balance. To get over there, we're going to hide some cells. So I'm going to put my cursor on column D. We're going to hide the columns, left-click on it. And we're going to drag on over to column G. Let go. I'm going to right-click on those selected areas and hide them practicing are working within Excel so that we have our dataset right next to where we're gonna be working. Once again, let's do our future value this time I'm going to do it just for two years out. So we're gonna say two years out, how much wood, how much would we need if we add 66 thousand to pay for the stuff that we want this time and we want to buy the same food and gas and whatnot. And there's a 5% inflation. How much would we need two years out? Well, we could do is simply the future value calculation instead of a running balance calculation. Although the running balance calculation does give us that more detailed information, I'm going to say this equals the future value FV shift nine. And then I'm going to use my keyboard. So I'm going to go left, left, left. We're looking for the rate, just like it says right here in our little data thing. So we pick up the rate that 5%, I'm not going to type in 5%. I want to pick that up from the data because that's the proper way to set up an Excel worksheet. Because then we can check and we can say, well, what if it was 6%? What if it was 3%? And we can see what's going to happen and run different scenarios with it. Then I'm going to say comma, number of periods. The number of periods we're going to say is two, which I'm going to pick up in our dataset down here as well instead of just typing too. So I'm going to say down, down, down, down on the arrow, left, left, left. There's two comma. Now it's not a payment because this is not an annuity. We're saying it's the same 662 and that's going up. We're not talking about multiple payments. Therefore, I'm just gonna put two comments to move on over to the next argument, which is the present value. Present value is the starting point, which is the 66 thousand. I'm not going to hard code it in there, but rather go down left, left, left, and up to get to that 66 thousand, we could close it up with the brackets here, but we don't need to, because Excel will do that for us. So I'm just going to say Enter. There, we have it. Although it's negative. If we don't want it to be negative, we can flip the sign by double-clicking on it. You can see the brackets are now closed automatically by Excel, you could put a negative before the present value, which is probably the most proper way to do it. But I like to put the negative right before future value on these present value, future value ones, because it's the easiest thing to see, in essence, multiplying the whole thing times negative one, flipping the sign. So that means two years out, we can expect to pay 72765 to eat the same amount of stuff and get the same gas and driving round that we did. Now, We gotta take, obviously, that's important, got to take that into consideration when planning here. So we got the, let's do this with a table format. We could do that with a table down here. So we could do the same thing with a table. So let's say we have the amount in year one. And let's imagine that was the 66 thousand. And let's imagine they took away our Excel and they took away our calculator because it's some kind of test question or they're just mean. And they took away all the stuff that to make the calculation easy. But they gave us this table down here, so we don't have to do it with math, so they're not totally cruel, but they made it a little bit harder. So we're gonna go down here and say, all right, it's gonna be the rate 5% and it's gonna be two periods, two years out. Notice this rate and the periods on this table and meaning also note we have to have the proper table, which is the future value table, as opposed to the present value table. It's not an annuity table, which would be a series of payments, but present value of one or future value of one table. The rates do happen to line up two years here because that's what we're talking about, years and the periods then will be years. But note you can use the same table if you're talking about any other period, as long as the rate aligns up to it. In other words, if you were talking about half years for like bonds or something like that, then you'd have to make sure that the rates that you're looking up here would represent half-year rates, not the typical yearly rate, and then the table who will still work. Okay, so we're taking the 5% 2 years out, that on the table. The table gives us 1.1025. Notice that this is rounded to four digits out, so it's not quite as exact from the table because there could be multiple decimals for the actual number. So we're going to be rounding four digits out. So that's gonna be 1.1025. And I'm going to add decimals here by going to the Home tab number group, adding four decimals, four decimals, decimal wise in it as I like to call it. So we're going to say the table amount, not an actual term desk normalizing. But I think it just sounds good. Home tab, font group underline. And then we're going to say then that's going to be the amount for year two or two years out, which is going to be equal to up to the 66 thousand times up one, the 1.10 to five that gives us our 72765. Once again. Now we're gonna do it one more time. Let's do it with a formula, same calculation, but with a mathematical formula, we're thinking that our instructor now we're out of school, most likely they're making it even there even crueler. That they took away our calculator, they took away excel, and they didn't give us any tables. I still make us do it with a formula like a paper and pencil, like we're cavemen, like it's any case. So we're going to hide the cells to get over to column K, Putting our cursor on H, dragging over two j here so that we can hide these cells and be working right next to the data we're working on, right-click and hide. So now we're going to be putting this formula, future value equals the present value times one plus r to the n. So ours being the rate, N being the number of periods. I'm going to put this into an Excel format to table the same thing, algebraic item into a table. You could type it out algebraically, of course, and just enter the data this way. It would be, the future value would be the unknown, would be, future value is going to be equal to the present value is 66 thousand times times. Where's the times three times? And then one plus the rate, which is going to be 0.05 or 5% carrot to the six carat. Two. We're doing two periods out. So you could do that and then solve it that way. I think it's useful to put it into a table. And a lot of these calculations you might actually start to visualize in a table. So even in a test question scenario, you might start to visualize it in a table format. So if that's helpful, That's helpful. Good to do in practice to work on putting things into tables, because it can be useful depending on what you're doing that way. So I'm going to take this information. I got two major components here that I want to multiply together. So when I imagine putting that into a table, kind of like we would do for a tax worksheet or something like that, or some type of Excel worksheet. I want these two on the outer column. Any other details such as the one plus r to the n, I'm going to bring insight to a sub calculation. So we're going to have then the present value and the outer column. Present value in the outer column, I'm going to pull the data over from our sheets, so equals the 66 thousand. And then I'm going to pick up a subcategory, which is going to be this other side because it has other stuff involved in it. I'm going to make a subcategory of the one plus r to the n periods colon, indicating I'm going to pull that into the inner column. And then the end result will be in the outer column, which we can then multiply it together. This is a similar format that you'll see in financial statements and whatnot, useful to kind of get an idea of how you might structure these things and how you might read these things once structured. So we're going to say one. And then the rate, the rate is going to be, rate is going to be the 5%. I'm going to take that from the table over here, not type it in. So equals left, left, left, up, up, and enter. Going to make that a percent in that cell by going to the Home tab numbers group, you could add decimals. There's the 0.05, or you could make it a percent by moving the decimal two places over, adding the percent. And I do that by clicking this little percent thing. And then font group and underline. And that's gonna give us then the one plus the rate. So we can sum that up. The one represents 100% of course, and the five per cent equals the SUM. You gotta know that some function shift nine. I'm going to do this just with the keyboard. Up arrow once, holding down, Shift up arrow again. And then I can close it up if I want to. You don't have to, because Excel will do it for you. And there it is. Let's make that than a percent. Go into the home tab number group, add some decimals. It could be 1.05 or you can reflect it as a percent, which would be 105 per cent. Then we're going to take that to the number of periods, which is going to be the number, I'm going to say to n periods. And that's gonna be two periods that we're taking it to two years out. We're going to assume, I'm going to take that from our Data tab over here. So equals the two going to underline that by going to the Home tab number group, underline it. And that's gonna be our total here, which is going to be, I'll type that out again, it's gonna be one plus the rate. And then we take that to shift 67 and periods. And then I put in periods here and that's going to be in the outer column now. So this is the final calculation, so I'm going to bring that into the outer column. So this whole half is now outside here. This equals left up, up the 10, 5%. Shift six for the carrot, which is to the power of two or squared and enter. So there we have it. Now we're going to make that add some decimals to it by going to the Home tab numbers group. Let's add some decimals. It's going to add a bunch of them. It could go on for quite some time. We're at the 1.125 and that'll give us the end result of the future value, which we're looking for here. This times this outer column. Now let's underline this first, just to add some more suspense. Font group underline it. And then we're gonna, we're gonna, we're gonna multiply, I'm sorry, multiply the outer column equals up, up, up to the 66 thousand times this number we got to there and enter there it is again, 72765. Let's just do some formatting just to shore this thing up. I would like this colon means that we brought it to the inside for subcategory calculation. Let's go ahead and indent it just so we can redundantly indicate that same thing, that this is a subcategory of that item up top. By going to the Home tab Alignment indent. Then I'll indent this one again, indicating that now we're bringing that to the outer column, Home tab Alignment indent. Again, there we have it. Let's go ahead and unhide some cells between b and k here so we can see all the wonderful work that we have done. Let's go to our b, left-click on it, drag on over to k, and then let go, right-click the selected area and unhide. And so there we have it. So we add the 72765 here. We've got the 727065 there, we've got the 7765 here, and the 727065 here, representing once again, what we really need to take into consideration when we're doing budgeting in the future. The fact that the value of the dollars that we're going to be spending will typically be going down if you're in the US somewhere between 13, possibly one in five. And if we are in a place of higher inflation as the US is subject to, from time to time. Even though you might have long periods without that, then it could be higher than that. And we would just want to take that into consideration, of course, especially when we're taking long-term planning into consideration for our budgeting. 4. Home Cost Estimated Increase: Personal finance practice problem using Excel, home cost, estimated increase, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example. The example tab, in essence being an answer key, we have the information on the left-hand side going to populate that into the blue area on the right-hand side. Our question being that we're thinking about a home price starting at this time period, at the 200 thousand, we're going to have an expected annual increase on the price 2%. And we're questioning how much will be needed to buy an eight years. So this is a question that some people might have in terms of purchasing a home, might be planning out to purchase a home at some point in the future. In order to do that, There's a couple of steps that we would need to keep in mind. One, What's gonna be the price of the area that we're looking to purchase in at this 0.2, what do we expect the price to be in the future as values go up, we would expect generally all else equal over time. Once you have the target, then that should be aiming for. Then you can think about how much you would need to save in order to get there, how much you would have to invest each year. An investment type of calculation taking into consideration loans and whatnot as you do so in downpayment and so on. So here we're just thinking about the value of the home itself. And it's similar to an inflation type of calculation because all else equal, we would expect things to typically go up in value due to the decrease in the valuation of the dollar. However, note that the homes, of course, are gonna be specific to a particular area. So this is another area where you can kinda see the increase or decrease in the homes in a particular area. Measure that possibly to increases in other types of things. To try to determine how much of the increase might be due to, say, inflation and how much of it is going to be due to other factors. But in any case, with regards to the home, a small increase in the value could have a significant impact given the fact that the purchasing value of the home is substantial generally for individual purchasers, there's therefore a small increase is something that you'd want to make sure you're planning in? If we were to if we were to think about purchasing a home and plan for it at some point in the future. So we're going to say it, Let's gonna be similar to our type of calculation for inflation. Note that when we look at our future value calculations, which is what we're going to use most of the time when you were to ask someone what a future value calculation will be, they'll usually have an investment scenario, meaning you're going to say I've put some money down, how much will I have at some point in the future given the increase in the investments? We've been looking here at how we can apply it to basically purchasing in the future, meaning prices go up and inflation type of scenario, or in this case, the home we're expecting to go up at some rate in the future and in our planning component. So let's do first are running balanced type of calculation. We're going to have the number of years on the right-hand side. We'll just list out the eight years and see how much we expect it to increase on a year-by-year basis. And this is a really good calculation because they can kind of give us an idea of where we are at any point. So if we get, if we get above in our plans and we're like, Now I can purchase the home sooner. How much advantageous would it be for me to do so if I'm estimating a 2% increase. So I'm gonna say 12. We will put our cursor on the fill handle, drag that on down. That'll take us down to eight. Let's center that by going to the Home tab Alignment and center. And then I'm going to put the price on the right-hand side. We're going to do that not by typing it in, but rather with a formula saying equals left, left, left, left, and up the 200 thousand and enter. Now we're gonna do our calculation for the increase that we're estimating. A 2% increase will do that with a function once again equals right arrow up arrow. And then we're going to say times left, left, left to the 2%. So F2 times B3 and Enter. So we've got the 400 thousand increased plus the 200 thousand is what we want here. So this is gonna be equal up once to the 200 thousand plus left ones to the 404 thousand, and that gives us 204 thousand after one year. That's what we expect to be paying or would need to pay at that 2% increase. Let's do it again. This time. This is gonna be equal to write up the two O 4 thousand times left, left, left up, and enter 4,080. Then we're going to say this equals the 204 thousand plus the 4,080 given us the 20880. Let's do it two more times and then we'll think about how to do it the easy way, autofill way. So we're going to do it again. This equals right and up times left, left, left, up, up to the 2% and enter 4,162. And then we're going to say this equals the one above the 20880 plus the one to the left of 4,162. And enter, that gives us the 212 to 421 more time. Let's do it. This is going to be equal to right and up to 12 to 42 times left, left, left, up, up, up 2%, enter 4 thousand to 45. And then this is going to be equal to the one above it, 2012 to 42 plus the one to the left, 4 thousand to 45 and enter given us 2006 to 216,486. Price after four years. Let's do it again, this time using the autofill, doing it the easy way. So we're going to select these items. I'm just going to delete the entire thing and do it one more time. Keeping in mind the autofill option, this is going to be equal to write up times the 2%. Now that 2% is outside of my table here. So I'm going to think that I need to make that an absolute reference or a mixed reference. I won't do it yet. I'm going to then go, okay, I'm going to keep that in my mind there. And this is going to be equal to one above it plus the one to the left. And then I'll copy it down to verify whether or not I'm right or wrong about that absolute referenced cell. It's auto fill this down just one set. Double-click on this and I can say, Yeah, that one, move down, it shouldn't have this one's doing what we want. This one's doing what we want. So let's go back up. Let's delete these two and double-click on this 4 thousand. I'm gonna make that one. And B3 absolute, absolute ties in it, which isn't a word, but I like the way it rings, like the way it sounds by hitting F4 dollar sign before the B dollar sign before the three, you only need $1 sign for a mixed reference, but absolute will work. Dollar signs have nothing to do. You'll recall with actual dollars it's just a code in Excel telling Excel do not move that down. Enter. Let's copy this all the way down. Now I'm gonna do, I'm gonna be confident this time and copy it all the way down. Autofill handle, dragging it all the way down. I will then typically double-click on the last one or something like that to see if it does indeed do what we think it should do. And it does indeed do the thing that we did it for. So there we have it. So that means at the end of eight years we're looking 234332, significant increase in the price given the fact that we're only looking at a 2% increase in the value. Remember, inflation could be anywhere from 0 to 3% if they're, if they're not out of control and the Fed too. So That's not certainly not out of a, out of the range of the increase on a home price possibly. So let's go ahead and hide these selfless. Do it a couple of different ways. Let's do it with the formula in Excel. Let's do with tables. Let's do it with a formula. So I'm going to put my cursor on D. I'm going to select over to, I think as g over here, so that we can hide these cells. So we can have our data right next to where we are gonna do the data input, right-click and hide. And let's do that here. So now we're gonna do the future value calculation. This is the easy way of doing it, but you don't get all the detail this way. So we're going to type in future value and we can double-click on this one here or hit Shift Nine, which is the cooler way to do it, or the nerdy or way to do it, which is cooler in the sense that faster. So in any case, we're then going to go left and then down. We want the 2%. So there's the 2% on the rate. And then comma, number of periods, we're gonna go left, left, left, down, down, down, down eight periods. So there we have that. And then comma, and then we have the payment. There is no payment because this is not an annuity. So we're just going to have two commas bringing us over to the present value, which we're going to pick up, left, left, left, and there it is. We could close it up with the brackets. I'm just gonna leave it as is the Excel. We'll close it up for us. There we have it. I think that's the same number, isn't it? Pretty sure. Then it's negative. So I want to flip the sign to positive numbers. I'm going to double-click on it. You could put a negative in front of the present value. Probably the more proper way to do it. But I liked doing it in front of the f over here is I put my cursor in front of the f, put a negative in front of it and enter flipping the sign. Now we can do it with the table. So the table is once again would be used of course, in a situation where some cruel, some cruel school or something took your calculator and your Excel and made you give them, gave you these tables. Like you're in a cave, like you're a caveman. And you had to look at these tables to figure out what you wanna do. If they do that, then we can go, okay, we're gonna take the 200 thousand and then we're going to look at the 2% and the eight years, 2%, 8 years. So we're going to percent and eight years. So we're at the 1.17171.17171.1717. And let's add some decimals by going to the Home tab up top Number group, adding some decimals. There we have it. Notice it's rounded to four digits. So if there's anything more than four digits, we could have a rounding difference there. And we're going to then say this is from the table, this is the table amount. So nothing too unusual with the table this way, by the way, we're using the table in the normal way, get into the end result of the Future Value font group underlying. And this is going to be our amount or future value. Let's call it future value, which is going to be equal to up to 200 thousand times the 1.1717. And so notice it's slightly different than we got up top with the 342. The difference is. Is $8. So notice as you got bigger dollar amounts, that difference could be larger and that could be due to rounding. And remember, if you've got a maniacal test question person that's trying to make you use the tables. They can use that difference of $8 to force you to use the tables. Because if your answer is this, then they're going to know that she didn't use tables because if you did the tables, you would have got that. Now let's do it with the formulas here. So I'm going to hide some cells again, we'll do with the formula by putting our cursor on H. I'm going to drag on over to j and then let go, right-click on the selected area and hide again. This time looking at our formula tabs. So here's our formula. Future value equals the present value times one plus r to the n. Straightforward calculation this time because we're solving for the future value, we're going to put this in a table format, meaning I want these two components to be on the outer side of the table and this component right here to be in the inside. In a similar way as we might see, you know, like a tax return or financial statement format. So I'm going to put them in the present values, our starting point present value. And that's going to be on the outside. This is going to be equal to the 200 thousand. And then we're going to have on the inside, we're going to do this calculation of the one plus r to the n, which I'm gonna do an a sub calculation indicated by the colon here, starting with one. The rate is then going to be rate. And the rate is going to be equal to the 2%, going to pull that from the table equals left, left, left, up, up to 2%. Gotta make that a percent so it doesn't look like a 0 there. Home tab numbers. We could add decimals, by the way, to 0.02 or percent of it, which isn't a word but I like it. Percent of fight, it's been identified in Excel. And then we go to the Home tab font group and underline. And then we got this is gonna be the one plus the rate, which we could do with the trustee. Some function equals the SUM. Got to know this function should be automatic. Shift nine, if it is not, work on it, work on it. Holding Shift Down, Up Arrow, doing it completely with the keyboard as nerdy as possible. And then we're gonna go back on over here and make it a percent Home tab number group. You could add decimals at the 1.02 or you could then hit the Percent button for the 102%. Then we're gonna go to the number of periods. So it's gonna go to n periods. And the number of periods is going to be eight. So I'm going to say equals. And we'll pull this over from the eighth over here, underline it by going to the Home tab, font group and underline. And then that's gonna be our end result for this component. This is gonna be one plus rate, shift or shift six carrot and periods. And we'll put that on the outside now because now we've completed this subsection category. So this is going to be equal to left, Up, Up, shift six carrot left, once, up, once the, and enter. Let's make that a decimal. So we're going to add decimals, Home tab numbers. And then usually if I'm adding a whole bunch of decimals just to see how much I call it desk normalizing it. It's been destined them allies. Which again isn't a word you probably want to type down or anything might not be in the spell check, but I like it. And then we're going to say that this is going to be then the end result. Let's get rid of this year one. That's not necessary, that's not necessary. Then we can multiply this out. So we've got the two components here. So let's multiply this out. This equals up, up, up, up, up 200 thousand times the 1.11.1716594. And that keeps on going on forever in Excel by the way, but we're rounding it, getting us to that to 34332. Let's do some indentation here just to make this nice. So we've got this colon, Let's indent these three to indicate that this is gonna be a subcategory that was brought into the inside by going to the Home tab Alignment indent. Let's indent this one again, Home tab Alignment, indent this kind of indenting in this kind of stuff because probably seems tedious. It does to me, still kinda completely dead to me when I was learning this stuff. Like this is not I just get the answer. I don't, I just get the answer, but you gotta make it nice. Presentation is half the battle because half the people you present stuff to in real life, they have no idea what you're talking about and you just go out and make it look nice. If you make it look nice, then people are normally happy. Then we're going to say, there we have it. And then, so now notice that this amount here should match what's in the table. So if you go to the table down here, at the eight years, we had the 1.171. That's how they get to that amount on the table. And notice this one's rounded to four digits. That's why you get with a different number because this is the actual number which isn't rounded and the table has to round to some number of digits. So let's go ahead and unhide. Now we're gonna put our cursor on B and drag on over to k. So the BK right-click on the selected area and unhide. So there we have it. We got to this to 34332 with our running balance calculation, to 34332 with a future value, we got to the 234340 because it's an estimate from the tables. And then we got to the 234332 with the calculation of the formula for future value. 5. Savings Account Compounding Interest Future Value: Personal finance practice problem using Excel savings account, compounding interests, using future value, prepare to get financially fit by practicing personal finance. And we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key, we have the information on the left-hand side gonna populate that into the blue area. On the right-hand side, we're looking at future value calculations. Probably one of the most common examples of a future value calculation that being related to a savings account. Thinking about what the interest or what the amount will be in the account and the future considering an interest rate that will be applicable. We can have a similar type of calculation with any type of investment, if it was like stocks or bonds or any other kind of investment that we're assuming that will be going up in value like land or a home. Although of course it would not be interested in those cases, but we can still assume an increase in value over time. We did similar problems to this in the past, but we ask the question as to how long it would take for something to double, which is slightly different than just thinking about where you will be at some point in the future. If you have an investment and assume interest rate or annual increase that will compound annually, as we will do this time. We're going to say the savings account has 5 thousand in interest rates are at 4%. Now note 4% could be reasonable depending on the time period in which you have your money in a savings account. If you're in a time period as we currently are, where the interest rates have been historically low for quite some time than 4% might seem high if you put something into a savings account. But if interest rates were to increase, then you might see at 4% whatnot in say, a savings account. And remember that these rates can be applicable to other types of investments as well. In other words, the method being used could be similar to if you have stocks, although it would not be interested in that case, but you could still assume an increase in the value of the holdings. You can do the same for bonds and so on and so forth. So we're gonna say then, how much would you have in years eight? So if you had the money in the savings account, you held it in the savings account, you're getting 4%, which you're compounding annually in our practice problem, how much would you have in eight years? Now, most of the time when you have a question like this, people will pull up the financial calculator or Excel, get right to that bottom line, answer for it. And that's a great tool to have. It's useful to then look at the actual compound. And so we're going to start off with a running balance calculation. Highly recommend getting used to the running balance calculation because it'll show you what's actually happening with regards to the compounding of the interest. So I'm going to start off with 01. Then we're gonna do our autofill function to copy that on down, we're going to select those two cells, put our cursor on the fill handle, left-click and drag that on down. So that's gonna give us eight periods. Let's center that. But I go into the home tab, Alignment Group and center, then we're going to be on the investment side of things. It's gonna be 5 thousand. At our starting point. We're not going to simply type in 5 thousand, but rather take that information from the data. So I'm going to say equals left, left, left, left, and up, there's the 5 thousand. Then we'll do our calculation at the 4%, we have a 4% increase. So 5 thousand times 4% we're going to assume is the interests, the interests that we're assuming we're going to keep into the account and accumulate upwards in the future then applying a growth on the interest rate per compounding. So this is gonna be equal to them, the 5 thousand, right once up, once times left, left, left that 4% and Enter. We're going to copy this down later and we will need an absolute reference to do so, but we won't do that yet. We're going to think about that in the future. Then we have the 5 thousand plus the 200, which we're gonna do this way, equals one plus left one. There's the 5,200. Let's do this a few more times now we have 5,200 instead of the original 5 thousand that we're gonna be multiplying times the rate of 4%. So this is gonna be equal to right once up, once times left, left, left, up, and enter. So now we've got the 208 interests increasing due to the compounding. And this is going to be equal to one, the 5,200 plus left once the 208 given us 500408, Let's do it two more times and then we'll go back and copy it on down using the autofill function. So we're going to say this is equal to the right once up, once the 45408, times left, left, left, up, up the 4% and enter there's the 216. Then we're going to add this up. This will be equal to up once the 500408 plus left once the 216, that gives us the 5,624. Let's do it one more time. This is going to be equal to write one's up, one's times left, left, left, up, up, up 4%, the 225. This is gonna be equal to up once to 5,624 plus left wants to two to five, that gives us the 5,849. Now I'm going to go back and delete what we've done thus far. Do it again, keeping in mind what we need to do in order to copy it on down with the autofill. Let's delete this thing and do it again. And this time it's gonna be equal to write up times the 4%. Anything I'm grabbing on this right-hand side, when I'm keeping in mind that I'm going to auto-fill it down. I'm going to start thinking I need an absolute reference because I don't want that 4% to go down. It's outside the table. I probably need to do that, but I won't do it yet. We'll do it in a second here. And this is gonna be equal to up once plus left once. Now let's autofill it down one time, copy it down. This would be the same as copying it. In this case, autofill handle, drag it down, and then I double-click here. This number doesn't look right. I said, Yeah, I moved it, move that down. I shouldn't have done that. I don't want it to do that. I don't want it to do that, but this one did what we wanted to do. So the relative sales look good. So let's go back and say, okay, let's delete these two and do it again, double-click on that 200. We don't want that 4% to move down. That's in cell B3. Put our cursor in B3, F4 on the keyboard. Or you can simply type in a dollar sign before the B and three, making it absolute, you only need a mixed reference, but an absolute works telling Excel, don't move that cell down, don't you? Don't you don't you move that cell down, excel. Alright, so now we're gonna go and we're going to select these two and will auto fill it on down and putting our cursor on the autofill handle, dragging it down. And I'll be confident going all the way down before I double-check it and then I'll double-check this last one, see if it does what we think it should. It looks correct. It looks correct. Just like I knew it we knew it was going to do. I was totally confident. Okay. So now let's get down to this bottom line would be up to 6,843 at the end of the eight years. And we can see how the interest is compounding, which is useful with regards to the interest table calculation here. Let's go ahead and hide some cells now. So we'll put our cursor on D and let's scroll on over to G here, even though you can't see, I think that's a G. Know my alphabet. What right? Then let go and right-click and hide those cells. So we got, we got the data input right next to the data. And now let's do the same thing with the future value, which is going to jump right to that in number but not give us that nice running balance. That's why you probably want to do this one. And the running balance together in practice would be the ones you'd want to use in practice. And then the tables in the formulas is probably what you would be forced to use from time to time if you're in a test situation, in a school situation, we're then gonna do this. We're going to say this equals the f v. And we can double-click on that or simply say shift nine, which is all the more urine away from the mouse, the geekier you are, which is what we're shooting for here. So left, left, left, down. And then we're going to say comma. And then we're going to get the number of periods. So the number of periods is left, left, left, down, down, down, down eight. And then comma. And the payment, that's going to be, if we had an annuity, this is not an annuity. We don't have a series of payments we're putting into the savings account, but only one payment that we're expecting to compound over periods. So two comments here. And then we got left down, down, we, it shouldn't go and left and then up 5 thousand and enter. I don't need to close it up. I'm just going to say Enter. There it is. I think that's the same number, pretty sure. But it's negative. I don't want it I don't want it to be negative. So let's double-click on it. We could put a negative in front of the present value here. Or we can put a negative in front of the f, which I like to do, which probably isn't as proper. But it flips the sign of the entire function, like so. And I think it's easier to do personally. So now let's do the same thing with the tables. Remember that the tables would really only happen oftentimes they were great before, before we had the computer and the financial calculators and whatnot. But now you've probably used them in a school setting when you have the maniacal teacher that does, takes away your calculator and Excel and acts like your work in a cave with chalk. That you got it, rock that's not even got a good point on it that you're trying to scratch into the side of the wall. Then we're going to say that we got 4% 8 periods. So 4% 8 periods down here, we're going to say this is gonna be the 1.36861.3686, 1.3686. And let's add some decimals. So we can see that number, Home tab number, adding some decimals. There's only four of them. And notice that the tables are limited in that way. They will be rounded. And we go to the Font group underlying amount. And let's multiply this out. This is going to be equal to up, up the 5 thousand times the 1003686. And there we have it. There. This one happens to be exact here. So notice if I add some decimal, I'm kind of curious if I add some decimals and add some decimals. So it's still a little bit off if you add the decimals to it. So remember that. Test question can use that. Like if you're in a school setting, you say, Look, I'm not, I am not a caveman. I don't need to use the tables. I have Excel. And I'm going to, I'm going to use it. And then you do it this way and you get the more exact answer. They can still see that. They can say, Well, you should have got this 6,843 because we told you to use the tables and you didn't you got something different. So we know that you didn't do it the way we told you to do it. And that can be something that they can differentiate on a test question or something like that. So remember you have to use the multiple methods. One, so that she can do the test question properly. And two, so that you can understand what other people are doing if they use a method different, the method that you're using. So let's go ahead and hide some cells again. So we have the column K right next to our data. So we're gonna put our cursor on H, left-click and drag on over two j to j. Let go, right-click and hide. So now we're gonna do it with our formula down here. Straightforward formula, future value equals the present value times one plus r to the n. We're gonna do that instead of just plugging it in algebraically, we'll build our table type of format over here as we do so we're practicing doing financial statements or tax return format, which is highly useful in my opinion. So we're gonna go ahead and these two components we're going to put in the outer column here, sub-categories we want to put inside with a colon and with an indentation possibly to indicate that it's gonna be a subcategory as well and bring into the inner column. So we'll start off with the present value. Present value, which is this term right here. You got to put that in the outside. It's gonna be 5 thousand. I'm not going to type it in here, but rather say equals left, left, left, left, up, and enter. And then we're gonna do the other side, which is gonna be the one plus the rate to the n periods one plus. Notice here I have a colon here, meaning I'm going to pull that into the inside. So I'm going to say one. And in the rate, I'm going to say rate is going to be equal to because I'm gonna pull it from there. The cell over here. I could type in 0.04, but I don't want to type it in there because I want to pull it from the dataset, want to pull it from the dataset. That's good practice, that's good Excel practice. That's how we should do Excel. And so then we're gonna go to the Home tab number group. We could add decimals to make it 0.04 or we could make it a percent, percent ties in it, which isn't an actual word, but I think it should be we should percent ties did in Excel, it's been percentile. And then we have one plus the rate. And we can use the trustee some function. Remember that this one of course, if we made it into a percent, would be number group percentile is 100%. 100% plus the 4% subtotal equals the SUM. Sum function gotta know what shift nine I would do it without, without using the mouse if possible. Up once holding down, shift up again. We have our, we have our items here and then we could close it up, but we don't need to and just enter. There's the one we need to add some decimals, Home tab number of deaths and analyzing or adding decimals, which could call desk normalizing it. Although again, that's not a word, but I kinda like it 1.04%. Or if we make it a percent by percentiles in it, 104%, then we're going to take that to the power of n. So it's gonna go to n in periods of say, periods. And that's going to be eight, which we could type in, but we need to take it from our data on the table to the left. Because that's how we do things in Excel. That's how things are done. Home tab, font group underlying that allows us to run different scenarios if we so choose easily. And this is going to be one plus the rate shifts, nine shifts six to the n periods, shift nine periods. And hopefully I spelled that right. And this is going to go to the outer column because we finished off this thing now. So now this is going to go to the outer column. We're going to take the 104% to the power of eight equals left, up, up 104% shifts gives us the carrot left and up to the eight periods and enter. There, we have it. Let's add some decimals there by going to the Home tab number group and adding decimals. And then I just add a bunch of decimals, I call it destiny normalizing it. It's been destined to mobilized. And then we're gonna go to the Home tab font. That's not a word. I know. I know. But it's still think it should be. So then we're going to say the future value is going to be here. And we can now multiply these last two out, multiply these last two. This is going to be equal to up, up, up, up, up the 5 thousand times that desk normalized thing that we did. And that gives us this 843 adding some decimals. There's, this should be a more exact answer. There we have it now notice that this number right there, the 13685 should be what's on the table. So if I go to the table, what was it? 4484 per cent eight. And we get 4% 8, we get the 1.36861.3, and then they rounded it to four digits. You can see there. And that's what the differences with the rounding difference. This is how they got kind of a table, but they cut it off to four digits. So then we can unhide this by going to the b up top. Left-click, drag on over h or K, that's the K. Right-click and unhide. So now we got the 6,834 from the running balance, 6,842.85 from the future value, which is exact number. There's 6,843, which is a little bit different due to rounding because of the tables. And then the 6,840 to 85, which should be more exact for the actual finance, for the actual formula. And then of course, we've got a running balance to show us the yearly interest that has been accumulated upwards as well. Note the yearly interest is often useful for these kinds of calculations because they might have a tax impact as well. 6. Future Value Annuity Investment vs Non Annuity: Personal finance practice problem using Excel, future value annuity investment versus non annuity. Prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side going to populate that into the blue area on the right-hand side, comparing and contrasting two different investment type of scenarios. One in which we have the one investment that we're going to say is compounding interest annually to see where we will be at some future point. The second, we're imagining we're putting more money in each time period. That would be the annuity type of situation to see then where we will be at some future point. So first one will be similar to what we have seen in the past. We'll probably do it a little bit more quickly. Therefore, as we then move on to the new thing, the annuity thing, the investment of the 1 thousand, the years, eight years, the return we're gonna say is 11% annual compounded. Where will we be then in terms of future value after the eight year time period, then we'll compare that to an investment each year of 1 thousand for eight years rate of return at the 11%. Now note that these two are not comparable in that, in the sense that we're putting much different dollar amounts in for both of them. The first one we're putting 1 thousand in, seeing the growth in terms of interests. The second one we're gonna be putting $8 thousand in over eight years. But we have the comparison between an annuity kind of situation and a future value of one type of situation. Okay, let's start off with the first one. We'll do this a bit more quickly because we've seen this once, a similar one in the past to it. So we're going to have our number of years. We'll do this with a running balance, then with the functions and Excel than using tables and then using a mathematical formula, Let's start off with a running balance. So I'm going to say 012. I'm going to copy that down. So I'm going to select these items, gonna go to the autofill handle down below and drag that down. We're gonna do this a bit faster this time. So bear with me. If you wanna do it slowly, you can take a look at the prior practice problems and will slow it down a bit there. We're gonna go to the Home tab. We're gonna go to the alignment. We're going to indent it. And then we're going to be calculated. And this, I'm going to call this the interests here. I'm going to call it an increase because it could be interested in it could depend on the type of investment as to what that increase format will be looking like. The investment amount is going to be equal to, we're going to pick up the 1 thousand at time period 0. And then we're going to calculate the interests which will be about 1 thousand times the 11% in the first period. So it's gonna be equal to write up the 1 thousand times the 11%. Now that 11% is outside of the table, so I know when I copy it down, which we will do this time, the first time, I need to make that absolute reference. So I'm gonna do that by selecting F4 on the keyboard, putting a dollar sign before the B and three, you only need a mixed reference, but an absolute reference works telling Excel do not move that cell down when I copy it down. All other cells that are inside the same table typically will need to be copied down, which is the default, the default setting when copying and pasting formulas. So this is gonna be equal to the one above it, 1 thousand plus the one to the left, which is gonna be the 110. That'll give us the 100110. I'm gonna go ahead and just copy that down this time. I'm just going to select these two. We're going to put our cursor on the fill handle and just autofill all the way down, autofill it down there, we have it. Double-click on the last one down here just to double-check, see if it does what we think it should. It does indeed do what we think it does need to do. And there it is. So we're at the 2304. If we do our running balance, we can see the increase in the interest compounding as we go. Let's hide some cells and then do it with the other formats here, including the tables and the Excel functions. I'm going to put my cursor on the D drop-down, going to drag to the left all the way to D to G. Let go, right-click the selected area and hide that information. And then we'll do our calculation and the future value calculation. So we're gonna do this with an Excel formula which will take us right to that Indian balance equals the future value FV. We can double-click on the FV or hit Shift Nine. I'm going to try to do this with the keyboard. All with the keyboard. We're going to say left, left, left rate that I'm going to hit comma. And then we have the number of periods which is going to be left, left, left eight on the periods. And then comma, there is no payment because this is not an annuity but a future value of one. Next time we will have an annuity and therefore we'll be using that payment item which you might be asking about at this point. Why don't we ever use that one? We haven't done an annuity. I don't believe yet. If we haven't, then we haven't used that one yet, but we will shortly and you'll get to see that. So there we have it, the 2304. Let's flip the sign. By double-clicking on it, we can put a negative in front of either the present value. I like to put it in front of the entire function. Flipping the sign to 200305. Let's do it with the tables. We should get to the tables. We can do the same thing here. This is what would happen if you are doing it in a school setting. This is gonna be equal to the 1 thousand they might take away your calculator, take away your Excel, and just give you this table to work with. And we'll say, alright, do it this way. If we have two phi half to 11% 8 is what we're looking for. So 11% 8 periods. So 11% 8 periods is going to be down here at the 2.30452.30452.30452.3045. And then we'll add some decimals, Home tab number group, desk and normalizing it, adding some decimals. And then we're going to say Home tab fonts group underline. And that'll give us our future value as FV future value. Let's multiply that out. This equals up to the 1 thousand times, up one to 2.3045 to give us the 2305 matching what we got up top. Let's do it again with the formulas now. To do so, let's hide some cells, let's hide some columns to get our data right next to where we're going to do the input of the data. Putting our cursor on the age drop-down, left-click and drag it over to Jay. Jay, Jay letting go, right-clicking on the columns and then hiding those columns. Now we've got our data right next to where we want our formula calculation. Now the formula bean, future value equals the present value times one plus r to the n. I'm going to put that in a table type of format, as we have seen in the past, trying to get the outer column to be equal to these two components. Any sub calculations on the inside similar as to what you would see in a tax return calculation possibly or financial statement kind of set up. So we're going to say this is gonna be the present value and the outer column equal to the starting point of a 1 thousand will get this sub calculation, which will be then the one plus r to the n periods colon, representing that it will be a sub calculation. We're going to save one. And then the rate is going to be equal to, I'm going to pull this from our data as we've seen in the past, the 11% enter, gotta make that a percent so we can see it Home tab number, you could add decimals, but I liked it, making it a percent Home tab, font group and underlying, let's do a subtotal here which is one plus the rate using the trustee some function equals SUM shift nine up, arrow holding down, shift up again. To sum it up with the keyboard and enter. Let's add some decimals there. Home tab font group coupled decimals to get us to the 1.11 or percentiles it making it 111% will take that to n periods then to n periods. And that's going to be then periods of eight periods up top. Let's underline that by going to the Home font and underline. And that's gonna give us then our whole subtotal here, which would be one plus the rate shift nine, carat shift six, periods, aperiodic. And the outer column. Then this is going to be equal to lift up, up the 111% shifts six carrot to eight periods to the power of eight. And then we're going to add some decimals here so we could see some more detail Home tab numbers, adding some decimals, deaths and analyzing it. And then we're gonna go to the font group and underline. So there we have it and that'll give us our n value. Finally, finally, I thought we were doing this fast. I thought we were doing this. Okay, So this is going to be equal to up, up, up, up, up the 1 thousand times the desk denormalized number. And so there we have it. So there's the 2305 about once again. Okay, so now let's do the new thing, which is to do it, to do this one down here and an annuity calculation as a comparison. So we have the data repeated, repeated on the right. So I'm going to hide all the columns from n all the way back so that we can just work with this data over here. So I'm gonna put my cursor on n, drag all the way back. You don't have to do this by the way, because the data is right here, but it might be a little bit easier to do this. And then I'm going to hide, right-click and hide. So there we have it. Now I have a little bit of a problem. These two, these two calculations that are now on top of each other, but that's okay. We're looking at this annuity calculation here. And so now we're on the second set of data. It's the same as the top set of data, except that now we have this happening every year. So now we're imagining the 1 thousand being a payment that we're adding to our investment each year. So we're saying, okay, I'm going to put more into it each year. Kinda like if you're saving for retirement or something like that and you're adding more money to it. And it's got interests that's compounding on at complex things, making things. More complex, I should say. That's how English, because I was one too. I'm not going to start off at 0 here with the annuity. I'm just going to start off with one and then drag this down. So we'll first think of our annuity with regards to our table. Once again, we're gonna do our table. We're gonna go to the Home tab, Alignment and center. Now note when we think about the annuity, oftentimes the first thing we got to think about is usually like a normal annuity. You think about the payment happening at the end of the period, which kind of confuses things because oftentimes you start the annuity with the payment today. So you got to realize that when you do the annuity calculation that you're talking about, a series of payments that happens at it come at a interval. And usually that interval is at the end of the period. If you're talking years, it would be at the end of the year. So we're not going to start with period 0 here with an initial investment. In this case, we're going to say the annuity happens. And that usually is going to be again starting at the end of the period. So I can put the first payment here in either the payment column or the investment column at period one. And I'm gonna say this equals to 1 thousand. And then I'm going to start calculating the increase or interests if it was an interest bearing type of investment on that 1 thousand starting in period two. Note if you're off, it's probably because you're just kinda mess it up that first interval, the first year. And you gotta, you gotta take that into consideration when you're thinking about your actual calculations and whatnot. And if you have a more complex calculation where you have a starting point that you're putting in and then the annuity on top of it, then you can adjust your calculation. Either saying that you've got that initial investment plus the annuity or you can try to format or just the annuity so that the annuity happens basically, the payments happen at the beginning of the period. Okay? So now we're gonna, we're gonna say then let's do our calculation for the standard annuity starting off here, this is going to be equal to the 1 thousand investment. And then we're gonna multiply that times the rate times left, left. I'm going to bring it down to this 11 down here and enter. So it's gonna be going up your one or two by that 110% again. And then we're going to say this is, but we're also going to have another payment. Another payment which I could pull from the left over here, or I could pull up above, because the payments are always going to be the same. I'm going to calculate this one a few more times before we simply just copy it down. And then this one gets a little bit more tricky when we do our running balance because it's gonna be the prior balance of the 1 thousand we had before, plus the new payment plus the interest. So we can do that by saying the 1 thousand. Let's do it this way. I can show you it could be this plus left, left this plus left, that, or probably more commonly entered. I'm going to delete that as equals the one above it plus the sum, SUM of the two items to the left. The sum of those two. So we're just adding the two to the left and the one above it for our running balance is going to close it up. The brackets. For me, there's the 2110. Then we can calculate the increase again. And now of course we've got another whole, another thousand dollars in there, instead of just the compounding of the interest plus the interest compounding. So now it's going to be equal to the 2110 times the 11%. Plus we got another 1 thousand equals to 1 thousand. We will copy this down later. You can copy it down. So we'll cop, will do that soon. And this will equal the one above it plus the sum of. And then I'm going to say the ones to the left, holding down, Shift, selecting those two, closing up the brackets and Enter. Let's do it again. This is going to be equal to the 3,342 times the 11% Enter. This will be the 1 thousand payment that we're gonna be making on an annual basis, adding to it, This is gonna be equal to the investment we had before plus the SUM some shift nine, left arrow. I'm going to select these two holding down Shift, Control, Zero closing up. Let's do it a couple more times. This equals the 400710 times the 11%. This is going to be equal to the 1 thousand. And this is going to be equal to the one before plus the SUM shift nine, left arrow holding down Shift, Left arrow again holding down Shift and zeros. They close up the brackets and Enter one more time. This equals this two to eight times the 11%. This equals the 1 thousand. This equals the one above it, plus the SUM shift nine left arrow once holding down shift left again, shift 0, closing up the brackets and there we have it. Now I'm going to delete the entire thing and do it again, keeping in mind that we want to basically copy this whole thing down. How could we do that? I'm going to select this whole thing. Delete it. No, it's okay. Because we're gonna do it the fast way this time, the easy way. So this is going to be equal to the 1 thousand times the 11%. Now right away I see that 11% is outside the table. That means I'm. Visualizing that I'm going to need to make that absolute. I won't do it yet. And then this one is going to be equal to the one. That one's not going to change either. I can pull that from outside the table. Again, the fact that it's outside the table means that if I need to copy it down, I'm probably going to have to make that an absolute reference. And then this one is going to be equal to the one above it, plus the SUM shift nine to the left, holding down shift left again, closing up the brackets. That's a complicated formula, but it's all within Excel. So if I copy this down and say, well, what's going to go wrong here? I'm gonna select these auto, fill it down. So if something went wrong here because that moved down and something's going to go wrong here. Because this moved down. I want to keep it up to 1 thousand items outside the table. I need to make absolute, in other words, so I'm gonna delete this, double-click on R 110, that 11% in P7, put our cursor and P7, select F4 dollar sign before the P and seven, you only need a mixed reference but absolute work. And then I'll do the same thing for this one. This one's in the tape outside of our data table here. So we're gonna say F4, saying Don't move that down. I want that whole column that'd be 1 thousand and Enter. Then I'll usually select these three auto-fill at one time just to double-check before I go all the way. And then I'm going to double-click here and say, Does it do what I want? It does, does it do what we're supposed to do here? It does. Does it do what it's supposed to do here? Indeed, it does do the thing that we told it to do. So now let's put our cursor on the auto-fill and drag it all the way down. And there we have it. So we're at the ending result, 115511859. The amount of payments that we put in, of course, are the 8 thousand. So we actually put in 8 thousand every year to get and then we had the interests that increase or whatever. The increase is. At the 3,859, it'll depend on what type of investment we have. Okay, so now let's do that the easy way with the Excel function, which will jump to this dollar amounts down here. But again, doesn't give you anywhere near the detail of a running balance table like this, which I highly recommend being able to do even when you talk to financial people to help you out with it, they're just going to get to this number. And if they probably don't have a good visualization of what is actually happening a lot of times in their mind. Oftentimes, table helps. Let's go ahead and hide these columns by putting our cursor on R to V, the RV. Let's hide that. We're going to hide the RV. It's kinda big to hide the RV will go k. We're going to right-click on it and hide it. Hiding the RV R2 V. Okay, so then we're gonna do the future value of the annuity calculation. Here's where we get to use that payment part now. So it's the same starting point as the last future value. Future value. You can double-click or hit Shift Nine, and it starts out the same. So it starts out the same, which is deceiving. But then there's a twist or a difference. And then we're going to say comma. So this isn't where the twist is yet. Number of periods, this is the same. It's still the same. Here's the twist, here's the difference, the number of payments. Now we use it because the payment means that we have repetitive payments that are happening each time for each of the eight periods that we have assigned. So we're going to say right now we have a payment, we get to use that thing. Then we're not going to use the present value this time because you usually use one or the other here and we have payment's not a present value. So I'm going to just say the payment that we have. And notice this is like a normal standard annuity. There could be variance again, if you had a payment at period 0, which we might talk about in a future presentation, but normal kind of annuity. So we're going to close this up and enter there. We have it. We have the same situation here where it's a negative number. If I double-click on that, you could fix that by putting your payment amount, making it negative, which is probably the more proper way, but I'd like to just put a negative in front of the f. There we have 11858 There, we have it. Now let's do it with a formula, which is kind of a more intense way of doing because the formula gets messy down here. So just note that if you're at a school that makes you use this formula, then there'll be, there'll be an unkind if you have to do that in a test question situation because, but we'll do it. We can do it, we can do it. So I'm gonna go ahead and hide some columns. We're going to be hiding from W to wi, wi, wi, wi. Then we're going to right-click and then hide those. Okay, so now let's do this. So now we've got our formula. So here's a little bit more complex looking formula here it's going to be the future value equals the periodic payment, which is $1000 payment that is now not really the present value as P was determined to be before, but periodic payments times one plus the rate, which is the 11% to the number of periods, which is eight minus one over r, which is 11%. Now you could just type this in algebraically. I'm going to try to build our table with this. Again, noting that this is a complex formula to build in a table type of setting. So I'm gonna kinda make a tax return kinda setting with it. Noting that I want to have this to kinda components that we multiplied together in the outer column. And then I would like to have the numerator and denominator and more complexity happening. On the inner columns. And that's generally how you can basically put a longer kind of function or algebraic equation into Excel in a similar way as you might seem like a tax return or unlike financial statements. So let's just practice that. I know it's kinda tedious, but let's do it because it'll be fun. So now we're going to say we have the payment or the payments which are gonna be in the outer column. This is going to be equal to the 1 thousand. And then I'm gonna pick on the numerator, which is gonna be this item here. So I'm going to pick the numerator. I'll just call it the numerator. And I'm going to say that this is going to be the one plus r to the n. So I'm going to just start off with one. And then I'm going to type in the rate, which is R. I'm going to pick that up by saying equals and make sure we pick it up from our data. I'm going to basically make that will make that a percent Home tab numbers. We could add decimals, 0.11 or percentiles it and making it a percent 11% font group and underline it. Let's put a subtotal in that calculation right there. It looks like a good place for subtotals sub TO tau using the trustee some function equals the SUM, shift up, arrow holding down, shift up, again, hold it and then close up the brackets. We don't really need to close up the brackets, but you can. And then we're gonna go home tab number group. That'll give us 101.11 or percentiles in at 111%. And then we'll take that to the number of periods. Number of periods, which was n, otherwise known as n here. So we're taking that to the power of n. That's where we are in the calculation, to the power of n, n power, which is eight. And then we're gonna go to the Home tab font group and underline. And let's, let's calculate that subtotal. Do the subtotal right there. It looks like a good place for sub subtotal. So we're gonna take the 111% carrot n, which is eight, equals up to 111, Shift six carrot up once and enter. And then we can add some decimals there and the subtotal Home tab numbers, dust animal lives in it. So we can see some detail by adding multiple decimals. And then we're going to say less. Let's just say less one for finally rounding out the numerator here minus one. Then we're finally to the end of this thing. That's gonna be the whole numerator. Numerator for bringing this to the average column is going to be equal to lift up, up this thing minus that one. Let's add some decimals there, Home tab numbers, bunch of decimals, otherwise known as just normalizing. So has been mobilized. And then, so now I'm gonna do some indentation. Let's go ahead and indent these. Let's select these items. Go to the Home tab Alignment indent, and we can indent this one and then this one's going to be indented again. Let's go to the Home tab Alignment and indent this again. So there's the numerator and then we have the denominator, which was simply the rate. Let's pick up the rate which is 11%, equals the 11%. That's this amount right there. There's the rate. Let's make that a percent. By going to the Home tab Numbers Group, we could add decimals. There's the 11 or percentiles it, and then go to the Home tab font group and underline. And that'll give us then, let's call this a subtotal. Subtotal, which is the numerator divided by the denominator, which we're going to put in the outer column so that we can then multiply p times this whole thing that we just calculated. So we'll put this in the outer column. This is going to be equal to the num divided by the denominator, numerator over the denominator. And then we can add some decimals by going to the Home tab number group desks and normalize it. Then that's gonna give us the future value of the annuity. There it is. There it is. Right there. Hold on to say, let's multiply this one up top 1 thousand times, which was p, the number of payments times his desk normalized number that we came to. And that'll give us the 11859 about. That was good times. Good times. So let's do it one more time this time with the tables. So let's hide these cells and do it with the tables. Now I'm going to hide from z to this a D. I think that's gonna be a d over here. Right-click. We're on the double. We've worked so many things that were on two letters. That's when you know, you're doing good work right there. When you're all the way out, all the way out past when you've cleared the whole alphabet of work, we've been clear in the whole alphabet. So then this is going to be equal to the 1 thousand will pull this amount up from the table. Remember that you've got to make sure that you're picking up the right table. That's gonna be the, the key component here, future value of an annuity as opposed to future value of one. And you'll see it because it will of course be compounding a lot more quickly. Down here you'll see bigger numbers in the meat of the table. So we're going to be picking up then our data which was 11% in eight years. So we're still on, the periods are in years and the rate is in years. So we're going to say, I forgot already, 11811, 8% down here, that's gonna be the 11.85911.85911.8591.85911.859. Let's add some decimals, Home tab numbers coupled decimals there, 11.85985911.859. And then that's from the table. And that's gonna give us our future value, future value annuity t, which is going to be equal to 1 thousand times that table amount. And that gives us our 11 859, which is pretty much what we got before. So what's underlying that? And there we have it. Let's unhide this and just recap it. So I'm gonna, I'm gonna select from all the way over and see if I can unhide the whole thing. Right-click and unhide and see if we didn't do everything should come back. We didn't delete it. So it should all be there still. There we have it. So we did our original investments with the annuity calculation. We got to the 23052305 with Excel 2305 with the tables, 2305 with the formula. And then we did the annuity, getting to the bottom line of 11859, running balance, although it's a bit more complicated to do the running balance, I think it's really worthwhile to do. We have the future value of an annuity using that payment cell. Now still get into the 11859. Then we did it with a formula, get into the 11859, and then we did it with the tables, get into the 11859. 7. Investment to Meat Goal Present Value: Personal finance practice problem using Excel investment to meet a goal or objective with the use of present value calculations, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab, in essence being an answer key, we have the information on the left-hand side and a populate that into the blue area on the right-hand side, we're looking at a scenario where we're trying to meet a future financial objective goal. And we would like to see how much we would need to invest at this point in time given a fixed rate of growth to meet our future investment goal. Now, note, we're not talking about a series of payments at this point in time, which would be an annuity type of calculation in which we may talk about in a future presentation, but rather a lump-sum that we would put in to some investment at this point, that if we assume to grow at a fixed amount, will reach some point in the future. So we have our information, how much would we have to invest to have in the future? 2400. So we haven't objective in the future of 2400. We can imagine we're buying something that costs 2400 in the future at some point, how much would we have to put in today if we expect to get a rate of return at 6% and have that grow for five years compounding annually to then get to the goal of the 2400. Again, we're not putting in 2004 we're not putting an amount in annually or anything like that. Just one lump sum today to grow at annual rate 6% to get to the future amount of the $2400. Now of course, the investment could be various investments. We might have it in a savings account, you might put it in a CD. Same kind of calculation for any of them that might be in stocks, it might be in bonds or whatnot. Same calculation, although the kind of income might differ if it was in stocks or let's say a savings account and whatnot. So that's gonna be our objective. Now when you think about this, the first thing you might think about, well, it looks like you're looking into the future trying to get to that 2400. So oftentimes it's a little confusing here. This is actually a present value type of calculation because what we would do is take that 2400 and bring it back to the current point in time in order to basically see how much we would have to put into day to grow to that future point in time. But because we're looking into the future, you might, your first thought might be future value. And if you plug this into Excel, you could use the future value in first, think about that and then say, does that work? Then try to figure this out. So that might be your first step. You might say, let me put that data to say a future value type of Excel function, which will look something like this, equals the future value, shift nine. And then we can pick up the rate. They have a rate argument, we're going to say, yeah, that makes sense. We got to rape comma the number of periods where you're like, Yeah, we've got number of periods. That's gonna be five. Comma the payment. We don't have a payment because it's not an annuity we're making we're just wanted to make one lump sum payment at the beginning. So I'm gonna put two commas there and then we need the present value. And the present value is what we don't know. And this is the area where we'd say whom? That's the piece that I do not know because this amount over here, the 2400 represents the end point. That's where we need to be in the future. What we don't have is the starting point, the current point. So you could use say Goal Seek to then figure that out. We could say, okay, well, I'll just put that component down here, the present value down here. And I'll make that my investment amount, and then I'll populate it. So I'm going to say Enter. And then I can guess my investment amount like a thousand down here to start off with and say, okay, so now I got a thousand, I'm gonna make this number up here, a positive number instead of negative by double-clicking on it, you could put a negative in front of the p, or you could put one in front of the f, like, I prefer to do. Put one in front of the f. Probably not the most proper way, but the way I like to do it. And then I can ask Goal Seek, I could say, well, I could change this cell and say, well what if I made this like 1200 or something like that? And then change this until I get to the proper answer. Or we can ask Excel to do that. We can say, alright, Excel, would you go to the data group? We're gonna go what if analysis, what if Goal Seek, will seek the goal here and we'll say, all right, let's just see if Excel will make this cell. I want to make that cell what it needs to be, which is the future value, what I'm trying to get to, which is that 2400. So I'm going to type in two for down here by changing then what's in this cell, the 1200. So we'll say, okay, and Goal Seek does that. And it says there's the 1793 and there's the 2400. So that's one way you might do it because you might first think of that future value and then you'd say, you know, that kinda makes sense that it's the present value. Because if I'm looking into the future, I'm trying to present value of that back to today. Because if you present value back to today, that would mean that if you started with that value and you earn 6% a year, that's where you would end up in the future. So it's really just a present value calculation. So we could do that same thing here, which you might realize once you see the unknown components who are like, well, why not try a present value calculation where we can say equals the present value shift nine. Rate, once again is the 6% comma, number of periods then is going to be 55 years that we're talking about comma payment. There is no payment because we're not talking annuity here. We're still talking about present value of one, so comma, and now we have the future value, which we have the future value, that's where it is in the future. We're bringing it back to the present. And that's in essence what we're doing here. So I'm going to take that future value. There it is, and enter there we haven't. So yes, the present value calculation to bring it back because if I invested then 1793 at the 6% for five years, then I would end up with the 2400 in the future. That's gonna be the idea. So if I double-click on this, making it a negative by either putting a negative in front of the future value or in front of a P, which I'll put in front of the p. There we have it. Now, of course we can do, now that we know what the present value, we can do the same present value calculations with a formula, we could do a running balance kind of thing to confirm our calculation and with the use of tables. So let's do that to round this out. So I'm going to hide some cells. We can see our formula right next to our data input, putting our cursor on the sea, dragging over to E, letting go right-click and hide, hide those cells. We've got our data input right next to our data. And now we'll take this calculations. It's just a simple present value calculation which equals the future value times or over one plus r to the n, which are going to put in a table format where we want the outer column to be representing the numerator and the denominator. Anymore subcategories like a tax return or financial statement we want to indicate as a sub calculation. So I'm going to say, all right, let's do the future value, FV, future value outside. We don't want to make sure that we're pulling this data from the table on the left equals left, left, left that 2400. Then I'm gonna do a sub calculation which is going to be the denominator, which I'm going to call the one plus r to the n colon, indicating that this is gonna be a sub calculation pulled into the inner column and indented to indicate that sub calculation it's gonna be one. And then the rate is going to be equal to 6%, which we're not just going to type, but rather hit equals. Scroll on over to that 6% and enter, making that a percent. By going to the Home tab up top number group, you could decimal lies it adding decimals or hit the percent, moving the decimal two places over, adding the percent font group and underlying. Let's do a good old subjects here. Subtotal, subtotal. So we're gonna be adding the one plus the R before we take it to the n. So I'm gonna say this equals the sum Trustee some function shift nine up, arrow holding down, shift up again, and enter trustees some function. Let's go to the Home tab number group desk normalized at 1.06, which if we present ties 106%. And then we're going to say that this is gonna go to n periods. Periods taking it to the power of n. We're going to take it to the power of n. And n is five periods in terms of years. So we're going to say this is gonna be equal to five. Taking that from our table up top, Let's put an underline there by going to the Home tab, font group and underline. And this is gonna be our whole thing, which is the one plus r shift 0, shift six carrot to the n periods, pure shift nine. And now we're going to put this on the outside. So this is gonna be then equal to the 10, 6% to the shift six carrot to the power of, in other words, n, which is five. Let's make that some decimals by going to the Home tab number group desk and normalizing it by adding decimals is what that means. And then font group and underlined. It's not a real word by the way, but it is still a good word, even though it's not real. And then present value, we're gonna go over here. And then we're going to say this is going to be equal to the num aerator divided by the denom a nadir. And there we have it, the 1793 about. Okay, so now let's do the same thing with a running balance calculation. So we can, we can, now, now that we have this starting point number we can do are running balance calculation. Notice we couldn't do are running balance calculation to back in from the 2004 into that number. But now that we have that number, we can kinda prove it in our minds by saying, Okay, does that make sense to me that I got that 1793? Let's do a running balance calculations starting there and see if I do indeed end up here, as I would expect to see. So let's hide some cells to do that. Putting our cursor on F, we're going to drag on over to I phi and then right-click, and then we're going to hide those columns. Hide the columns. Let's do our running balance calculation. This balance is running. This is a running balance. Better go catch it because it's fast. So we're going to say this is gonna be equal to 101. We're going to auto-fill that down, selected these two cells, putting our cursor on the fill handle, dragging it on down to five, center in that home tab Alignment and center. And this, I'll just call this the increase in caries, which may be interests. And I may not have done this on all of the problems. I apologize if I have the wrong name up top there and I called it interests when it wasn't, but I'm sure I'll hear about the horrible, horrible error that was made, but it has been corrected now. So note that it's been corrected. Okay, so now we're going to start with our starting point here, which I'll just calculate it again. This was the investment amount which will take as the present value. Let's do the present value calculation again, negative present value, shift nine. And then I'm gonna take the rate which is the 6% comma, and then the number of periods, which is going to be the five comma comma future value, which is gonna be that 2400 and enter. So there's our 1793. I just did the same calculation. I know I did it quickly. You could pull it from the prior presentation or the prior calculation that we just did, but we just calculated it again up top. So that's our starting point. Now, if I calculate the interest at 6% for five years, I would expect the ending point to be that 2400. Let's do that. We're going to say this is gonna be equal to the 1700s, three times the 6% for period one. And there's the 108. And then I'm gonna say this equals the 1793 plus the 108. Let's actually just copy this down. We've seen this type of calculation in the past. So to copy it down, note that if I double-click here that 6% needs to not be moving down because it's outside the table. And I want to just copy this down right off the bat, right away, off the bat Home tab. And then we got, so this is gonna be before putting our cursor and before F4 puts the dollar sign before the B and the four, you only need a mixed reference, $1 sign, but an absolute references easier to think about. So we'll say enter. We'll select these two and put our cursor on the fill handle and drag it on down. And there we have it. So now you've got the interests increasing as we go down. The ending number does indeed get us to that 2400 making us say, I think we did do that. I think we did do it right? I think this is the way you're supposed to do it. The present value is the thing that you're supposed to use. Let's do it one more time with the tables here. Tables are gonna be equal to the two thousand, four hundred, two thousand four hundred. And we'll pick the amount up from the table which you'd only be doing. If you'd, most likely if you're in a school setting where they take away all the other neat and fancy stuff that you want to work with and give you this sheet of paper and like chalk with it. You're supposed to look up on the table. So then we're going to say that that's gonna be six per cent and five years. So we're gonna say 6%, 5 years, which is gonna be 0.7473. So this is gonna be 0.7473. Let's add some decimals by going to the Home tab numbers, adding some decimals underline it, Home tab font group and underline. And this is going to then be our present value. Present value calculation then is equal to the 2400 times the 0.7473. And there's the 179, 41794 approximating this answer up top, it is an approximation due to the tables round into four digits. Let's unhide some cells just to see that. How, how about approximation comes to be? So I'm going to unhide from BTK selected my Selecting be left-click, scrolling over to k bk, right-click and unhide. Getting our, I think I hit, I'm gonna do it again. A to L. I hit the wrong button. I hit the wrong button. You probably did it right. But I'm gonna do it again. Unhide. Unhide. I'm not hiding things, I'm unhide and things. So then if I go over here, this calculation right here could help us to figure out what the table is. Now that you've got to do one more step to figure out the table amount which would be equal to, it would be the 1793 divided by the 2004. Adding some decimals Home tab number. If we add some decimals there, there it is. If I, if I'm going to go ahead and make this a permanent piece of our of our practice problem. So it should be the 0.7747258. And over here we had 0.7473. They rounded it right there, which results in that slight difference. Not, not important or not usually, not usually going to be impacting your decision-making process in real life and practice. But again, a maniacal test person could try to take away your calculator and make you use the tables. And then they would know, they would know that if you didn't do it because of the rounding difference. So you gotta be careful of that and test situations. And again, you really just want to know multiple ways to do these calculations because that'll give you a better grasp of what is actually going on by looking at it from multiple angles and being able to see other people do the same calculations in different ways. 8. Annuity Initial Investment Present Value of Annuity: Personal finance practice problem using Excel annuity initial investment calculation, using the present value of annuity calculation. Now, prepare to get financially fit by practicing that personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side going to populate that into the blue area. On the right side, we're looking at the general type of scenario where we are thinking about wanting to have enough money in an investment type of situation so that we can be taking money out on a periodic basis and thinking about having fixed rate of return for the money that is still in the account. Now this is often one that's gonna be more difficult for us to visualize as to which tool we should be using for this type of calculation because it's something that looks like an annuity is an annuity, but it's something that we're planning for it to be happening in the future. So we might think it would be like a future value annuity type of calculation. But in reality, it's gonna be a present value type of calculation because what we're trying to do is look at the series of annuity payments from a present value standpoint, bring it back to the current date. As of this point in time, think about how much money we would have to put in at this point in time in order to pay out that annuity portion. Let's see if this makes sense here. Here's our information. How much would have to be invested to be able to take out each year, $500. So we want to take out each year $500 for seven years. And the amount that's still in the account we're going to assume is going to be accumulating a 7% increase. So this would be a type of thing you might do when you're doing retirement planning or something like that and you're trying to think about how much money do I need if I was to take out so much per year and the amount that I still have in there is going to be increasing upwards. So that kind of scenario, you might have other scenarios in a similar type of situation. If you're planning for something that's going to result in a series of payments that's going to be happening at some future point. Okay, we're gonna do our present value calculation. Let's start it off with a present value of an annuity in an Excel function type of format. Then we'll prove that by basically running the table, which is often a great tool to kind of verify that we have our mind wrapped around this thing. We're gonna do a present value of annuity calculation equals the present value. It starts off the same as the present value of one. You can double-click on the present value or shift nine. There is our function argument. We're going to pick up the rate which is you could type in there at 0.07. I'm going to point to the cell at the B64, the 7% comma number of periods, number of periods is going to be seven. So I'm going to scroll down, down, right down, down. I'm going a little bit faster in Excel as we get used to using Excel hopefully at this point. So then I'm going to say comma again. This time we are using the payment because this is an annuity calculation as opposed to the present value of one, in which case we skipped the payment and went to the future value. In this case, we have the payment of 500. We're imagining that to be repetitive payment, not just a onetime payment, that will be increasing by 7%, but one in which case we would be putting it in each period. So then we're not going to have any future value. So I'm just gonna leave it there and enter, and there we have it. Let's increase the size of this a bit. We're at the 2000s, 694. Let's make it a positive number by double-clicking on it, we can put a negative in front of the payment, which is probably more proper. I like to put it in front of the p here. So there we have it. So we're at the 2694 now, you might have thought, well, if I would need 500 times seven would be the basic calculation that you would need 3,500. But of course, you don't need exactly 3,500 to be taken out 500 each year. The return is getting 7% return. So then the next step is to say, well, I don't know, let me double-check that this number is correct by basically running that number in our running balanced type of calculation over here. And if it's correct, if I start at that investment point here, take out $500 each year, then am I going to end up at 0 at the end of this time period? That's kinda what we're looking for to see these two things side-by-side. Let's go ahead and hide that some columns here. I'm gonna put my cursor on column D, drag over to column F, D to F def, and right-click and hide those, hide those columns. And let's do this calculation again. I'm going to say 01. I'm going to copy that down to line seven, highlighting those two or selecting them, putting our cursor on the autofill handle, dragging down to seven. Then we'll go to the Home tab Alignment Group and center it. There we have it. Now, I'm going to recalculate the investment again, doing that calculation, again just to practice it. And negative present value, shift nine, the rate left, left, left, left down, down, down 7% comma, number of periods left, left, left down, down, down seven comma, and then the payment left, left, left, left down, down to the 500 and Enter. There's our 2695 about we're going to say that that's going to be an increase for whatever the value is that we're increasing it for. So if it was a savings account, it would be interest if it was stocks, we're going to say the value is gonna go up, we're estimating by 7% and so on. So I'm going to say this is going to be equal to lift, lift up 2695, about times the 7, 7% percent and enter. Now I'm not going to copy it down yet. I'll do a couple of these calculations and then we'll copy it down. And then I'll go back and make the absolute references needed to do so. Then I'm going to make it a negative for the payment. I'll make it a negative here for the payment. A 500 because we're going to take out 500 each year. That's the point. And at the end of this we should end up at 0 if everything worked out the way it's supposed to. So this cell we could be sick equals the investment, the 22695 plus the 189 minus the 500. But because I put it in here as a negative, I'm going to say plus the negative number, which will be a subtraction problem. So the 2695 plus the interest earned minus the amount of we're gonna be paying out in the annuity. And there we have it now, I think it would be better to calculate this one. I'm going to delete that this way. This equals the one above it plus the sum of the fact that this number is negative allows us to do that nice. Some function of these two closing up the brackets and Enter. Let's do it again. This equals to 2383 times the 7%. And then this is gonna be the negative of the 500. And then this is going to equal the amount above it plus the SUM some shift nine left arrow holding down shift left, again holding down the Shift and 0 and enter there, we have it. Let's do a couple more times. This is gonna be equal to the 2050 times the 7%. Then 500 negative at the 500. And then this is going to be equal to the prior balance plus the SUM, the sum left arrow holding down shift, left shift 0, closing up the brackets and Enter one more time. And then we'll do the autofill, doing it the easy way than to take this item times the 7%. This is gonna be equal to the negative 500. This will be equal to the amount above it plus the SUM shift nine left arrow holding down shift left again and enter. See I didn't close the bracket up and it gave me a little error, but that's okay. Then it fixed it. So there it is. So now let's delete it and let's do it again as if we're going to copy it down. I'm going to delete these and do it again as if copying it down. And this equals this 2695 times the 7%. And then the payment is going to be the negative 500. And then this is gonna be equal the one above it plus the SUM shift nine left arrow holding down shift and shift 0 to close it up. Now if I copy that down, selecting these items and using the autofill to copy it down. Then we'll see what the problems are. So this problem here, it moved the 7% down. So we don't want, we want to fix that. And this one got moved down from the 500 down here. So those two we're going to fix. So I'm going to delete these and I'm going to fix it by double-clicking and anything outside of our table that's usually what we need to fix. So this is in B6, I'm going to put my cursor in B6, say F4 on the keyboard. To put a dollar sign before the B and six, you only need a mixed reference, but an absolute reference works. And then I'm going to put my cursor here, double-click on the 500. Once again, select F4 on the keyboard dollar sign before the B, and therefore say an Excel do not copy that down and enter. Now let's copy it down again. I'm going to auto-fill it the whole way down this time because I'm confident I'm confident that we did it right this time. So there we have it and the bottom line number gets to 0, indicating that, yes, indeed this is the proper amount that we calculated. So you can see how that worked. And then if I double-click on this last one, we see yes, that doing what we expect it to do, everything is doing exactly what it's supposed to. Okay, so now let's do this with a formula. Then let's do the present value of an annuity with a formula. I'm going to select the cells from. Let's go from c to k here. I may be larger. I didn't want to make below if I want to go to from C to j, C j, let Glo right-click and hide those cells. Now let's do this with our present value of an annuity calculation. So here it is, down here, this is a long kind of formula. If your instructor or someone forces you to do this, they're kind of mean because it's kind of a long formula. But they might, and it might be worthwhile just to kinda look at, look it over to get an idea of what it looks like. Again, in practice, of course, you'd probably be using the Excel worksheets and I think the running balance, those combination between those two will actually give you the most insight. For what you're normally going to be using these four. Alright, so we're going to start here with the payment amount. So P stands for the payment amount. Obviously you can, you can plug this into this formula. The payment would be the 500 times the one minus one over one plus r, which is seven per cent to n, which is gonna be seven years divided by R, which is 7%. I'm going to break this out into a table format, which I think is good practice just to do and just to build tables with like kinda like a tax return format. And we know that financial statements are similar, similarly formatted. Notice this one is a long, ugly formula with multiple different division components to it. And therefore we're going to have different subcategories. You might set it up a little bit differently if you were to set up a table. But just practicing putting a long formula into this kind of table structure actually is fairly useful oftentimes in practice. So I'm going to say, Alright, the 500. My major thing is these two components. I want to put these on the outer side, outer column, and then I'm going to bring a whole nother inner column for these two. And then this numerator I'm going to bring even further inside for a sub calculation, given them more detail there. Alright, so the payment is going to be 500. I'm going to say this equals the 500. And then I'm going to call this the numerator, which is not an exact Item. I could actually list out the numerator, but I'm going to call this the whole numerator up top. And notice it's one minus this whole thing. So I'm gonna put down here just one in this inner column because once I'm done with this numerator, I'm going to want that to fall out into the outer column. And then I'm going to call this, and I know this is kind of a convoluted item here, but it's going to say numerator to, which I'm going to indicate as this one right there. So I'm just going to indicate that as one. I'm not going to put a colon because it says just gonna be the one. And then I'm going to say the one plus r to the n, which is the denominator of this hierarchy little component here. So I'm going to say this is gonna be one plus r shift to the carriage shifts six, n is gonna be then I'm going to put this on, and I'm going to put a colon on this one because there's, so I'm going to bring it to the inside again. This is going to be one, the rate is going to be then the seven per cent. So let's call this just the rate. The rate is going to be equal to the 7%, bringing that into the inside, Let's make that a percent go into the home tab numbers, making it a percent font group. And then underline, I'm going to call this a sub calculation. So this is a sub subtotals sub TO tau. I'm going to use the trustee some function equals the SUM shift nine up arrows holding down shift up again, and then closing that up, making that a percent Home tab numbers per cent to find it 107% that I'm going to take that to the power of n. So I'm going to say this is going to go to the periods n period in periods, in other words, which is gonna be seven periods. So this is going to go to seven periods, seven. And let's underline that by going to the Home tab font group and underline. And that's gonna be this whole subcategory calculation which was one plus r, and then shifts to the n, which I'm going to put it in the outer column now. So now we're pulling this to the outer column. This is going to be equal to the 10, 7% shift six carrot to the seventh power, power of n. Let's add some decimals there. We're gonna go to the Home tab number, group and desk denormalize it, just adding a whole bunch of decimals. And so there we have that. Then we could indent this whole thing. Let's go to the Home tab Alignment, indent, indent, this whole thing. Home tab Alignment, indent, and then indent this one again, Home tab Alignment and dent. And so there we have that. And then we've got, I'm going to call this a subtotals sub, subtotal, which is gonna be this whole thing right here. And I'm going to pull that into the outer columns, put an underline here, font group and underline. And now I'm going to subtract this column here. So subtracting this out, notice I'm only doing something to the left or right above in our calculations, this is gonna be equal to the one divided by now the 1.605 and so on. Adding some decimals Home tab number group, Let's destiny symbolized that number. So it's been desk normalized. So there we have that. And then we can pull up the denominator, I'm sorry, then we can get the full numerator. So this is going to be the numerator torr, which is gonna be this whole thing now one minus that thing underline here, I'm going to go to the font group and underline, subtract this out. Notice I'm in the same column. This colon might indicate that I could have one more column, but we'll do this in the same column. This is going to be equal to the one minus one minus the 0.622750. Adding some decimals there, Home tab number, group desks and normalizing. So there we have that. And then we can take the denominator, which is R here. So that's gonna be the rate. So let's pick the denominator, which we'll just say, let's call it denominate torr, or the rate. With the brackets around that, that's gonna be equal then to the 7%, again, 7%, making that a percent by going to the Home tab numbers, group per cent ties in it, font group, and underlining it. And then we have our subtotal here. Let's call this a sub total, and we'll bring that to the outside. And we'll divide this out. This is going to be equal to the 0.37725 and so on divided by the 7%, making that a percent or adding decimals Home tab numbers desk normalizing it. So there we have that and that'll give us the present value of the annuity. Finally, by taking this component times this whole thing here, underlining this one before we do Home tab, font, group and underlying, multiply this out. This equals the item way up top 500 times this 5.389. And so on. Adding a couple of decimals there, Home tab numbers coupled decimals. So there's our 2694 once again. So again, I know that was kind of a long table type of worksheet and whatnot. So if you were to calculate this in practice in a test question, it's can be kind of cruel again to make you do that multiple times. And the Excel functions are useful to do that. And of course you could plug this into the formula here as well. So I'm going to hide this. Let's look at the tables now. I'm going to hide from L to Q. Right-click on the selected area and hide those cells. And let's do this with a trustee table. So we're going to say the payment, payment is going to be equal to 500. Now, make sure you've got the right table. We are talking about the present value of an annuity table. And once we have that, we're simply looking for 777, 7% periods or years, yearly percent yearly years and periods. This is gonna be 775.38935.3893. Adding decimals Home tab, the number group, add four decimals there. And this is gonna be from the table. And let's underline this by going to the Home tab font group and underline. And this will give us the present value of an annuity t. Let's just keep it and knew at T, this will be equal to the 500 times the 5.3893. And we can add a couple of decimals there. And there we have it. Let's unhide a few tables here or unhide some of these columns. And then just recap what we've got on hiding. And we're gonna put our cursor from our column to be right-click on the selected area and unhide. Then we can see that we got this calculation at the 2694 with the present value of an annuity. We double-checked it by starting there and then having the annuity payments ending at 0, which gives us verification that it was done properly. We then look at the present value of the annuity. We get down to that 2694 as well, noting that this amount is in essence the amount from the table. This is the amount that she could build the table from. Its more than four digits long, which means we have a slightly different number here, the 2.65694, fairly, very close, but slightly different due to the tables rounding to four digits. 9. College Savings Calculation: Personal finance practice problem using Excel, college savings calculation, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side, going to populate that into the blue area on the right-hand side looking at a college tuition saving type of scenario. So there's a couple of types of things that we would commonly need to take into consideration when thinking about college savings. One is we want to think about how much money we're going to need when the college basically starts. And then two, we've got to think about the idea that the college is kind of like an annuity. You would think that we can estimate how much it's going to be costing for the time period that we will be there, which would be like four years that we'd basically be planning for. So we have two things that are involved here. We've got once the college years start, we have an annuity type of situation where we would assume set cost that it's going to be costing for, let's say, a four-year time period. And then two. Once we know that annuity amount, we can think about how much we would need to be investing at this point in time in order to save enough to get to that to that annuity amount, to get to the college years point in time. Then of course, we can take into consideration student financing and other kinds of things that would go into into play at that point. So at this time, were trying to figure out how much would basically college costs at the point in time that college would start using our annuity type of calculation. And we're going to be assuming that the costs for college are gonna be the 25 thousand per year for four years with a rate of return at the 6%. So in other words, if we had a series of annuity payments then for four years that are going to cost us the 25 thousand, how much would we have to invest in order to cover that? And of course, the first calculation you'd say, Well, we would need then we would need the 25 thousand times four, which would be the 100 thousand. And I'm gonna make that blue here, that 100 thousand total. But if we have money in the savings account and during the annuity and it's getting the 6% increase, then we don't need the full 100 thousand at the starting point. So first we want to think about how much we would need at that starting point, the next step, and that's what we'll work on here. The next step would then think about how are we going to get to that, to that starting point number in terms of our savings as of today and or any other financing that that could be taking place. Okay, so we'll do now, this is a similar kind of thing with this annuity type of calculation, which seems a little bit one of the more difficult ones to visualize in your mind because your thing, you're saying, this is an annuity kind of thing because this is, we're going to assume it's a 25 thousand for four years even payment. But it's something that we're planning to happen like in the future. So you might say that it should be a future value. Annuity might be your first guess, but it's actually a present value of an annuity because we're trying to figure out the annuity payments and then bring them back to the amount that they would be at the start of the annuity. So to prove that, then we'll do a present value type of annuity calculation, and then we'll prove it with a running balance type type of calculation. And then we'll do the other methods of calculating a present value of an annuity. So let's start this out. We'll do this a little bit quickly because we've seen some similar problems. The difference here is the scenarios that you want to keep in mind that you can use these different calculations for and be able to understand when you look at different things that you're planning on that are gonna be in the future and need to take into consideration time value of money that you know, you can figure out which tools to be using. We're going to say this is gonna be equal to the present value, shift nine. We're going to pick up the rate which I'm going to type in there at 0.06. But take that from the table. At the 6% comma, we're now at the number of periods, which is going to be four. We're going to say for bringing that from the table here and then comma, the payment, the payment is gonna be the 25 thousand for each of those years. And we are using a payment because we're talking about the annuity point in time. Once in college, we don't have any future value. So I'm just going to leave it at that and enter. Let's go ahead and make that a positive number by double-clicking on it. And then I'm gonna put a negative. We could put it in front of the payment. I like putting it in front of the present value. So I'm going to put a negative here, flipping the sign to the 8667, six twenty seven, sixty four. So if if at the start of college we plan on taking out 25 thousand each year and we're generating six per cent. We should not need hopefully the 100 thousand, but the 86627, given the fact that the amount that's in the savings account, hopefully we will be making around that 6% of of interests or increase or whatever value that we have, whether it be a savings account, where it would be interest or it would be stocks or something like that. Let's go ahead and hide some cells and kinda prove that by doing a running balance calculation, we're gonna put our cursor on column D, drag over to column F. Let go right-click on the selected area and hide them. And then we'll do our running balance calculation. I'm going to put our periods here by saying 01 and so on. Selecting those two cells, put our cursor on the autofill handle and dragging that on down to four periods, going to go up top to the Home tab, the alignment group and center that. Now our starting point, I'm going to recalculate just to practice this again, this is gonna be our starting point. And then we're going to imagine this annuity playing out and the end result should be 0 at the end of this process. So let's, let's test that out and see if that is indeed the case negative. Present value shift nine. We're going to pick up the rate over here at the 6% same calculations. So I'm gonna do it a bit quicker here. Comma, number of periods is gonna be the four periods and then comma and the payment is going to be the 25 thousand, That's it. And enter there is our starting point at the 86628. So if we had that at the beginning of college and then we're saying that this is going to be, I'm just going to call it the increase instead of interests because it might not be a savings account, we might have it in some other format. But whatever format it is, we're going to assume a 6% increase. Now I'm going to try to do this a little bit quicker. I'm going to plan as we go to copy it down. And so any absolute references, I'm gonna do that on as we go here. So this is gonna be equal to the 86628 times. And then the 6%. Anytime I pick up something outside the table, I'm going to think and say, what am I going to need to make that an absolute reference to copy it down? Do I want that cell to move when I copy this down to the relative Cell Below, the answer is I do not want it to move, and therefore, yes, I do need to make an absolute reference, selecting F4 on the keyboard, putting a dollar sign before the B and eight, you only need a mixed reference, but an absolute reference will work. Then we'll do the payment here. The payments are all going to be 25 thousand. I'm gonna make that a negative. And 25 thousand so that it'll show up as a negative number, allowing me to use my sum function when we sum them up on the, on the outer column here. So this one again is picking up something outside the table. When I copy it down, I don't want it to move down. Therefore, I need an absolute reference here too. So I'm going to select F4 on the keyboard, dollar sign before the B and the six. So there we have that. So now we want the 86628 plus the increase for the gains that we're going to have as this is still in an investment minus the 25 thousand, which is the actual cost we're going to have to pay for the college on a yearly basis. So this is going to be equal to the one above it. And then I'm going to say plus because and use the sum function. And then as I sum these up, it's going to be adding one and subtracting the other due to the negative number. Closing it up, shift 0 to close it up. And hopefully we've done everything we need to do to now copy it down. So I'm going to select these three cells, put our cursor on the fill handle, drag it on down. And there we have it at 0 at the end of the day. So that kinda proves that our present value calculation is correct. We have 86628. If everything goes well, we can spend the 25 thousand each year and still have enough instead of having 100 thousand due to the fact that whatever still in the account's gonna be generating that 6%. When you're doing a retirement type of calculation, you typically have a similar kind of thing in mind. You've got a big chunk of money that you're trying to and nibble at over time without having it go away and still earn interests so that she can live on the thing. So now let us do it in the calculation with the formulas over here. So we'll do the same calculation with the formulas. And this is more of a complex formula to do so hopefully they don't make you do this too much in a classroom, but they probably will at least introduce it to you. So we'll do that by putting our cursor on column C, dragging over two j, C j. And then right-clicking, we're going to, we're going to hide those cells were doing this calculation. So you could simply plug the information into this formula, which would be the payment, which would be the 25 thousand times the one minus one over one plus r, which is 6% to the number of periods, which is n, or four divided by r, which is 6%. Again, we're going to use this opportunity to make a complex table, given the fact that this is a complex formula with two division components in it. And see if we can build basically a table. On. The table doesn't need to be perfect. But practicing putting something into a table format like this is good practice. And so that's what we'll use it for. This is the format. You might see a tax return in. The format you might see financial statements in just building the table can be useful. It's also something that you can use if you're basically having a similar calculation that you want someone else to use. And you want to make the data input screen an easy data inputs grand or something like that. So we're going to say we have the payment up top, picking up a payment. I'm going to put that in the outer column using our strategy of having the two major components in the outer column and then the inner column. I'm going to take the two major components here, numerator, denominator and the inner column. And then this numerator, I'm going to have to break this thing out as well given the fact that it's somewhat complex two, so this would be a fairly complex thing to put it into a table. And so if you look at tax returns, you have complex things in tables that are in a similar format like this, right? So this will be the 25 thousand. Then I'm going to call this just the numerator. Numerator, and this is the whole numerator, this whole apart. And notice I have another numerator kinda subcategory here. I'm gonna put a colon bringing this to the inside. I'm going to put over here starting with just this one. I'm just going to put one here because I got to have one minus this whole thing. And then I'm gonna put another subcategory which I'm going to call the numerator 2s. I'll call it numerate toward tour, to which I know is a funny name. But you can then I'm going to say this is gonna be one because now I'm in here in this subcategory calculation. I'm just going to put that on one line. I don't need a sub category for it because there's only one number in it. And then the denominator, which I'm gonna call, I could say denominate torr, which is one plus r to the n, something like that. And so that's gonna be the denominator. I'm going to put a colon for a subcategory on the denominator, which is gonna be one plus the rate, which is going to be equal to the six per cent. So now I'm in here one plus the rate 6%. I'm gonna make that a percent Home tab number group per cent to fight it. Font group underline it. Then we'll put the subtotal here. So subtotal, subtotal and sum that up equals the good old SUM shift up, arrow holding down, shift up again. Let's make that 8% by going to the Home tab, font group, or number of group percent define app. The 106 per cent will take that to the number of periods or n. So I'm going to take that to the periods, periods. No one as n, which is going to be four periods. Four periods. Let's underline that home group, font, Home tab, font group underline. And that's called that another subtotals sub total TO tau, bring that to the outer column. So this is going to be the outer column. This equals the 106% shift six carrot to the power of four. Let's add some decimal so we see some activity there by going to the Home tab number of group desk and embolize in it, adding bunch of decimals. And it could keep on going, but we'll keep it there. And let's actually call this, this should be the, we're going to call it the denominator here. So that's, this whole thing. Is Indian this kind of process. So I could indent these selected this whole thing, Home tab Alignment and dent and possibly indent this again, Home tab Alignment, indent again, we're going to pull this to the average column, Home tab, font group and underline. So now we've got this division problem we'll do here. We'll pull that in the outer column. So this is gonna be equal to, notice we're only working in one column at a time. So I'm gonna be in this column and then divided by this. This is standard kind of financial statement formatting, oftentimes where you work in one column at a time. And then we're gonna go to the Home tab. We're gonna go to the numbers and some decimals destiny analyzing that. So there we have that. So now we've got this whole piece done. And now we're in this outer column where we have one minus that whole piece, which will be the end of the numerator calculation, which indicated by this colon, would think that we would put it into another column, but I'm gonna keep this in the same column here. So this is gonna be the whole num, num or eight torr, which is going to be equal to the one. We're working in one column again, minus this thing which just came to that decimal number. We need to add decimals there so we can see it. Home tab number, group, desk and normalizing it. Let's put an underline under this one, where we go font group and, and underline. So there's the numerator, then the denominator, which is the rate. So that's this denominator, the rate we can put right underneath here, and that's gonna be the 6%. So we're going to say 6%, they're adding that to a percent. Home tab numbers per cent define it, font group underlining it. Then we'll call this a sub tote, subtotal, putting that in the outer column, this whole thing divided by this. So now we'll have this whole thing done, which we can finally multiply times the payment. Putting that in the outer column, this will eat the num array ptr divided by the denominator on nature, adding some decimals Home tab numbers, desk minimizing it, underlining it by going to the font group and underline. And finally, that'll give us our present value of the annuity working in the outer column. Now, we're going to multiply the 25 thousand, this whole thing, this thing times this whole thing that we just calculated, the 3.46 and so on. This equals then the 25 thousand times. 3.46 and so on gives us about the 86628. Let's add couple of decimals, Home tab number, coupled decimals. Finally, there we have it. Okay, I tried to correct some spelling here and I tried to do the indentation is a little bit, make sure we got those lined up. But now since there we got it, we have that there. You can double-check that on the answer key if you want to look at it a little bit more detail, okay, and that's the green tab. Let's do this one more time with the tables. So I'm going to put my cursor on K here. And before we do just note that this cell right there represents how you build the tables. Notice it has more than four digits, which will result in the tables which are limited to four digits being somewhat off in terms of rounding, which will not be too bad for what our purposes are here for decision-making, given the fact that it is an estimate. But in practice or in a test situation, they could use that. Remember, to distinguish what you're, what you used to calculate. Okay, let's hide some columns. Put in our cursor on column K, dragging over to column P, let go, right-click the selected area and hide those columns and do it one more time with the tables. So we're going to have the payment, which is going to be equal to the 25 thousand. We're going to look for the tables now, 6% for year, 6% for years. So there's the 6% for years. Is that, by the way, make sure you have the right table. We're looking at the present value of an annuity table here. Typically you have four tables to pick from present value of an annuity, 6%, 4 years, 3.4651. So we got 3.4651 adding some decimals, Home tab number, group, desks, animals. And then we're going to say this is from the table. And this is gonna be the present value of an annuity. We're going to say multiplying this out 25 thousand times the 3.4651, putting an underlying Home tab font group and underline, we get the 86628. Let's add a couple of decimals Home tab number group, a couple of decimals there. He's got the 86, six, twenty seven, fifty. Okay, Let's unhide some cells and just recap here, putting our cursor on column B, dragging to our right-click unhide. So we had the 25 thousand that we want to take out each year, which if we didn't have any other earnings on it would be the 100 thousand. We calculated that if we have a 6% earnings in the beginning amount, we would need only the 86, we'd only need 86627, 64. And then we prove that by basically starting that and having a running balance which brings that down to 0, proven, proven the annuity. Then we've got in this calculation, we've got the 86, six, twenty seven, sixty four using our formula. And then we've got slightly different number using the tables of the 86, six, twenty, seven, fifty due to the difference of rounding, because of this number is rounded to four digits. That's the number that came from the table. And if we look at the actual number that we calculated or closer to the actual number going more digits out. It's going to be different due to the rounding of the four digits. 10. Retirement Savings FV of Annuity: Personal finance practice problem using Excel retirement saving calculation with the future value of an annuity formula. Prepare to get financially fit by practicing personal finance. And we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side and a populate that into the blue area on the right-hand side, we're looking at a retirement savings type of scenario. Note that there's two general kinds of scenarios that you'll set up in your mind when you're thinking about the retirement savings. So in other words, if you're thinking about saving over your earning years and thinking about how much you would need at retirement. You might phrase that one way to say, Hey, look, I'm going to save as much as I can at this point in time on a yearly basis or periodic basis, and assume some rate of interest on that increased amount that I'm going to put into a savings account or some other retirement account and then try to determine, given an average rate of growth, how much we would have at retirement, which we're going to say in 40 years at this point in time. You can compare that and contrast that to the other view you might look at, which would be, how much money will I need at retirement in order to support my needs at the point of retirement after I'm done with my earning years. Meaning you might then do an annuity calculation at that point in time to determine how much of a basically a nest egg, what big chunk of money that you're going to need to be generating revenue if you were to eat away at it as you consume that revenue over the retirement years. And then you would be thinking about a goal, an end goal to get to that lump sum of money that you would need at the retirement point. So in this case, we're going to start off with the first of the two scenarios thinking about we're in our earnings years, we're going to try to save as much as we can and think about what if we were able to put away just say $5 thousand for the next 40 years and get a return. We're going to estimate an average return or an even return in this case, which is one of the limitations of our present value, we're going to kind of estimate a nice even returned of the 7% over that entire time period. Note, of course, you can get more complex with these kind of scenarios. You could then increase in C, I'm going to put 5 thousand in for the next ten years. And in the next ten years I think I'm going to earn more money and I'll put 10 thousand in, in the future and so on and so forth. But to do that, you'd have to get a little bit more complex than simply just an annuity, right? You'd have to then make some adjustments because your payments into the retirement plan would not be even. But you can use these tools for similar calculation as that as well. So let's look at this. We're going to say the investment each year is gonna be 5 thousand that we're going to put it and we're gonna say it's gonna be for 40 years. We got 40 years to save this depths, and then the rate is going to be 7%. So we're going to say a rate of returns seven per cent. So let's first do this with our running balance calculation, which you might think that's a tedious thing to do given the fact we're talking about 40 years here, but not hard to do with Excel. You can go out. You can even do it on a monthly basis if you needed to, because you could just simply copy and paste this thing out. So let's do that. So we're going to start off at period one. Note that when we think about an annuity calculation, we're typically not starting at time period 0. We're going to start because the annuity happens, you assume kind of at the end of the period. And that's how the calculation works. So if you have an initial investment at this point in time and then are adding to it, then you got to account for that basically initial investment and then the annuity component to it. So note we're starting at one instead of 0. Then two, we're going to select those two cells. And then I'm gonna put my cursor on the autofill handle and drag all the way down. Notice it gives me that nice little number range that tells me where we are at all the way down to 40 periods and then let go. I'm going to center that by going to the Home tab, the alignment and center it. There we have it. And then I'm gonna put the investment and the outer column, and I'm going to have this as the initial payments. The investment is the initial payment that we're going to have as we consider it to be our annuity, which we're going to say happens in year one. So we're gonna say this is equal to the 5 thousand. And then I'm going to have the investment just simply be the same, 5 thousand. Now, I'm going to do this fairly quickly because we've seen this calculation in the past. So I'm going to copy it down and I'm going to populate this assuming that it will be copied down from here. Meaning any cells that need to be absolute reference, ties are into an absolute reference, those typically outside the table from our dataset. We will do so as we go. So we're going to say that there's gonna be an increase which will be equal to the 5 thousand. And then we're gonna multiply that times the rate, which is gonna be the 7. 7% is outside the table. So that's something that I do not want to move down when I copy the cell down. Therefore, I'm going to make it absolute. I'm gonna do so by selecting F4 on the keyboard and, or put a dollar sign before the B and five, only a mixed reference is needed, but an absolute reference works and it's easier to think about the payment then is always going to be the same. So I'm going to say the payment equals. That 5 thousand this time I'm going to make that an absolute reference by selecting F4 on the keyboard, putting a dollar sign before the B and the three, and then Enter. And then we've got the initial investment, which is gonna be the 5 thousand plus the increase, which might be interests. It might be increased in value if it's in stocks and whatnot are index funds, different types of investments that we have. But we're going to say the increase in value is going up by the 350. So I'm going to say plus the SUM, shift nine of these two, and then we're entering another or adding another 5 thousand into it, we're saying each year. So then I'm going to close that up. And there we have it. So now we've got the 5 thousand plus another 5 thousand that happened in year two plus the interest that is accumulating as we go. I'm going to select these three cells and I'm just going to auto fill it all the way down now. So I'm gonna put my cursor on here now note, if we're not confident that this was going to work, you might auto fill it down simply one cell, double-check these cells that they are doing what you expect them to, and then copy them the rest of the way down. Selecting these three, putting our cursor on the fill handle, dragging all the way down to 40 time periods down here and there we have it. And so we're down here at after 40 years, we're at that 998176. So almost at the million there in the 40 years that just the 5 thousand per year. And we could see, we could see how the increase in the interest is happening here as we go. Fairly small amount of increase with a gain on the revenue that we're generating. As we go through here, you can see how much we put in, in terms of total payments, the sum of this column, we would be putting in 5 thousand, that'd be 200 thousand that we put in over 40 years. And how much we earned, which would be this column, which would be income from it. This would be the 798176 over and over those 40 year time period. So hopefully you can see the running balance table really useful to get a better grasp of what, what happened. Now if you were to ask them when they are even work with a financial analysts to on this or something like that, they probably wouldn't graph it out like this, but would rather just do a future value of annuity calculation. So let's do that now and note the contrast between the two. You probably want to do both of these things in practice, the annuity calculation in Excel, and then show it to yourself by actually calculating, calculating the payment to confirm what is in your mind and then get a better visualization of what is happening. So this is gonna be equal to the future value shift nine. We're going to pick up the rate, which is going to be the seven per cent over here, comma. And then the number of periods is going to be for T periods. And then comma, we do have a payment this time because we're talking about an annuity instead of a present value of one. In other words, we're not just talking about 5 thousand and the interests that will accrue on that or increase on at or be earned for it over 40 years, but having another 5 thousand that will be inputting every year for the 40 year time period. So Enter and there we got our 998175. Let's make that a positive number by double-clicking on it, you could put a negative in front of the B here, or in front of the f, which I choose to do in front of the f. So there we have it. So again, this would be the first thing that most people would probably do, or the simplest thing to do. But notice how much more information, how much better you get a grasp of it if you actually graph it out here and then put the table together for it and you can determine how much your payments will be, how much the interest will be. You can look at the yearly interest as well. You can take into consideration the tax impacts on different types of savings accounts, whether you put it into an IRA account or for one K or outside of the IRA or Roth IRA and all that fun stuff that you can take a look at with the savings account on a yearly basis and consider the tax impacts related to just to note also, you might be thinking, well, if that's 7%, that's gonna be my rate of, of revenue or gain that I'm assuming. What about inflation? Because you might think, well, the purchasing power is gonna go down over 40 years, around one to 3% as well. So when you think about the actual purchasing power you're going to need, you're also thinking about where, where's that endpoint going to be? You're going to need more money, in other words, to retire 40 years from now, you would think than today. If the economy does, hopefully it goes well and that there's gonna be some kind of inflation that will happen. So when you play and how much money you're going to need at the end. Is that going to need, is that going to be enough money? In other words, in 40 years, it might be enough money. The starting point, if you look at it in 40 years, you're going to have different purchasing power related to it. So you got to take into consider Asian inflation. So let's do this a couple of different ways. We'll do this with the formula now, which is less likely to be needed in when you go to a financial planner, they're not going to break out this, this future value formula most likely, and putting it together that way. But when you're in a school setting, they might do that and then we'll use the tables. So let's go ahead and put our cursor on. Let's go to column C and drag over to column J and hide those cells. Right-click on those cells and hide them. And now we'll put this formula into a table over here and do that and try to build our table with it, which is good practice in Excel. So we have the future value equals of an annuity. That's gonna be the P, which is the payment, the 5 thousand times one plus the rate, which is 7% to the n, which is the number of periods, or 40 minus one over r, seven per cent. So you can type, you can write that down and solve it algebraically. We're going to put it into our table. The practice putting things into a table, into a tax return kind of format, into a financial statement format. To do so, I want these two primary components to be on the outer column. And then I would like these other two primary numerator and denominator to be an inner columns. And then this more complex numerator, I might break out to another inner column. So we've got the payment, that's going to be easier, that'll be in the outer column up top. The payment is going to be equal to 5 thousand. Then I'm going to pull it into the inside of this thing and I'm going to try to get to the numerator first because it's gonna be more complex. So let's pick up the numerator. I'm going to indicate a colon that this is gonna be pulled inside. And then I'm going to say that this is going to be one. And then the R, which is the rate, is going to be the 7% or something right here. That's gonna be equal to the 7%. Let's percentiles that by going to the home Tab Numbers, Group per cent ties it, font group underline it. Then we'll have a subtotals sub TO tau sub tote, which will equal the SUM shift up, arrow holding down, shift up again, making that then a percent Home tab number percent times 107%. Then we're going to take that to the number of periods, number of periods or n. And so that's gonna be right here in our calculation. That's going to be 40 periods. 40 periods. And let's underline that by going to the Home tab font group and underline. That's gonna give us another, let's call it a subtotal, subtotal, sub total toe, toe, toe. And that's gonna be in the outer column here. Actually, I'm not going to bring that in the other column that's in the inner column. This is going to be equal to the 107 per cent shift, six carrots up one and Enter. So that's gonna give us our 15. Let's add some decimals, make it more specific Home tab number, decimal lies in it. So 14.19744 and so on. So that brings us to this whole piece, minus one here. So I'm just going to say less one. And that'll give us our whole numerator. So that'll give us the numerate torr. Finally, that'll finish up this calculation. So let's indent this whole thing. Go into the home tab Alignment indent, and then I'm going to indent this again, Home tab Alignment, indent again, let's underline this one. Home tab font group underline. Bring this to the outer column and this is going to be equal to that 14.97. So on minus the one gives us around 14. Let's add some decimals. Home tab number, destiny symbolized, Dustin normalized it. And then we're going to say this is gonna be the denominator. So that's the whole numerator. Now that this whole thing is done, denominator is simply going to be our or the 7, 7% percent percentiles in that home tab numbers, percentiles, font group underline. And then that's gonna give us, Let's call this a sub tote, subtotal. And that's gonna be in the outer column. Now that's this whole thing. We've now got this whole thing that's going to be in the outer column, which will then multiply times p. Notice we're only doing calculations in one column at a time. In other words, I'm not jumping from a calculation from one column to the other. That's common practice in financial statement type settings. So this is gonna be that divided by the 7% then num divided by the denom, adding decimals Home tab numbers destined to mobilize in it. And then underlying font group and underline. And that'll finally gave us the future value. Finally give us the future value, which will be this times this or the outer column. Now only doing things in one column at a time, the 5 thousand times that 199.63, whatever and so on. Let's add a couple of decimals here by going into the home tab number coupled decimals. So when 99817556, Let's do it one more time this time with the tables, this time with the tables. So hopefully a school doesn't make you do that. Algebra too much on it. And they might give you the tables which is slightly nicer, which is just going to take this 5 thousand and multiply it times the amount from the table, which would be at periods 40, rates seven. So we're looking seven on the rate 40 all the way down at the bottom of the table, way down here, 199.635199.635199.635199.635, adding some decimals, Home tab number group decimals. This is from the table. Let's go ahead and underline that by going to the Home tab, font group and underline. And that'll give us once again the future value of an annuity. Multiplying this out, this is the 5 thousand times the 1.63599. Add a couple of decimals there, Home tab number group coupled decimals. We're up to 998175, slightly different than the 9.5698175 due to the fact that this number right here, which is the number that is used to build table, is really more than three to four digits out. So they rounded it on the table, resulting in a slightly different number, which can be somewhat more distinct when you're talking about larger numbers, but as often or when you're looking at retirement type of accounts. So just notice that that rounding difference could be larger as you deal with larger numbers depending on the circumstances. Okay, Let's unhide and recap. So I'm gonna, I'm gonna put my cursor on l, drag on all the way back to B and unhide those cells, right-click and unhide. So there we have it. I should probably run a spell check. Let's just did I misspell anything enumerators spelled wrong? Okay. Got it. And then so now we've got this 5 thousand all the way down, gives us that 199998176. So notice this table very useful. Then we've got the future value. This is probably what someone would give you if you talk to a financial advisor. And then it's really useful to plug that into a table so you can visualize it. You can get to that same 9.5698998175 with the formula. And you can get to a close number with the use of the tables which you might see in book problems, mainly in the school setting. 11. What if We Saved Our $5 a Day Coffee Habit: Personal finance practice problem using Excel. What if we saved our $5 a day coffee habit? Prepare to get financially fit by practicing personal finance. Now before we go into this in much depth, I do want to point out something that many people are probably thinking. So we can address that first. Many people are probably thinking, I know what would happen if I cut my $5 a day coffee habit, I'd fall asleep at work, I'd get fired. I wouldn't have any money then I'd have to spend all my time in the coffee shop because that's the only place I get decent Wi-Fi. And if I didn't buy any coffee, then the baristas were all get mad at me because I'm sitting there using the Wi-Fi and not buying any coffee and so on. If not buying coffee, in other words, would cause you a problem, then you don't have to do this. But the general idea would be that if you can cut out a little bit of money on a daily basis and save it. It could kinda go a long way. So here we are in our Excel worksheet. We have the practice tab on down below, and then the example tab, the example tab, in essence being an answer key, we got the information on the left-hand side. We're going to populate that into the blue area. On the right-hand side. We're going to imagine we have a cost per day of the $5. We're going to imagine that we saved that $5 in some way, shape or form, possibly buy coffee, possibly in some other area. So then we're going to say that how much would that be on a yearly basis if we were to add that up those days, a yearly basis, I'm going to use that 360 day year, which is often done in finance because it kind of evens out the months. Meaning it's nice to be able to assume 30-day months. So it's all nice and even 12 times 30 would be the 360 as opposed to the more close to accurate number in terms of actual days, which would be around 365. I'm going to take then five times 360, that would be $1800 a year. And then let's assume just on a yearly basis. And again, you could do this on a daily basis, but let's say we take that $5 and spend it on a yearly basis of the 1800 and put it into a savings account. What would that do if we could over ten years, if we're assuming compounding yearly at eight per cent in whatever we're investing in, whether that'd be stocks, that savings account or so on, in terms of our average investment returns at the 8%. So this would be a future value of an annuity type of calculation. Let's first do it by just doing a running balance type of calculation, just listing out the number of years and assuming that we're depositing or making another deposit yearly of the 1800s. Now this is an annuity calculation. So we're not going to start at 0. Usually we start at the end of each period, which is going to start at period one, period one, period two, and so on. Let's copy that on down with the auto-fill. I'm gonna do this a little bit quicker because we have seen this in the past or similar problems just as a different kind of scenarios to take a look at here. We're gonna go to the Home tab up top alignment and center this. Now the first payment is going to happen in year one and our assumed annuity, and we're gonna do it on a yearly basis. We're going to assume that 1800. Now, note that you could do this. You could think about, well, I'll save that money on a weekly basis or a monthly basis and so on. You can adjust your calculations accordingly. We're going to keep to the yearly basis here. We might do that in a future presentation to look at the compounding that could happen or the annuity that could happen if you're putting more money in on a basis other than basically a yearly basis, then we're gonna have the investment which is going to be equal to the 1800s starting point, then the increase that we're going to have from the investment, which could be from stocks, could be interested in a savings account, and so on would be equal to the 1800 times. We're going to pick up the 8%. I'm gonna make that an absolute reference because we're outside the table. I want to copy this cell down. I'm going to do that by selecting F4 on the keyboard, putting a dollar sign before the B and the six, I'm going to select tab this time, which will take me right to the tab to the right instead of Enter, which will take me to the tab below it. Then we're going to pick up the payment which is gonna be that 1800. That once again is something outside the table. I want to make it an absolute reference selecting F4 on the keyboard dollar sign before the B and four, I'm going to say tab now taken up to the cell to the right. Then I'm going to say equals the one above it, plus the SUM shift nine left arrow and then holding down shift left, again, closing up the brackets shifts and Enter. Now I'm going to select those three cells and auto fill it down, putting our cursor on the fill handle, dragging it down. And we can see the increase resulting that we'd be saving on a, on a earning on a yearly basis, we would be having 26,076 the payments that we put in place. You can select this column and see the sum calculation, 18 thousand over the ten years. And the increased meaning the earnings and interest or whatever format we have, 8,076. Let's do that same thing with an annuity calculation. Now, let's hide some cells from C onto G. Let's go from Right-click and hide those cells. We're gonna do this with an annuity calculation. Once again, I'm gonna do this a little bit faster since we've done this a few times, I'm going to say negative this time instead of equals, which is a little bit faster. And we'll flip the sign so that we do not have to basically put, go back in and put a negative number. It will then result in a positive end result. Notice I can still type in future value here and it still gives us our functions down here, just like if I typed equals. So if you want to flip the sign easily, instead of putting a negative, instead of putting equals, you could just start with negative and then type your function like you normally would shift nine. The rate is going to be equal to this eight per cent comma. The number of periods is going to be ten in this case comma, and then the payment is going to be because it is an annuity, we will be using the payment that 1800 and enter. There. We got the 2675. Again with the $0.81. We could do that same thing with the calculations for a table and the calculations for the mathematical formulas. Two ways you probably wouldn't be doing this so much in practice, but can do oftentimes for test questions. So we're gonna put our cursor on H, drag to j. Let go, right-click that selected area and hide. We're gonna do this formula now, future value of an annuity, which is the payment, which is gonna be the 1800 times one plus r, which is going to be the 8% to the number of periods, which is ten, and then minus one divided by R, 8%. Practicing putting this into a table format, a format you might see in a tax return or similar to a financial statement format. We're gonna put the payment up top outer column 1008. Then we're going to have the numerator. I'm just going to call this the numerator, which is gonna be this whole thing, which I'm gonna put in the inner column or inside and indicate that with the colon up top. I'm going to bring that inside here. This is going to be equal to, let's say one right here, that I'm picking up the rate, the rate which is going to be equal to the eight per cent, making that 8% by going to the Home tab number per cent ties in it, underlining it, Home tab font, group and underline. That's gonna give us a subtotal. We're going to call it sub total. Summing this up using the trust, The SUM function, SUM shift up, arrow holding down, shift up. Again. Let's make this a percent by going to the Home tab numbers and percentiles it 108%. We're gonna take that to n Now, which is gonna be the number of periods. Here we odds, and that'll be n periods, which is gonna be ten equal to ten. Underlining that we're gonna go to the Home tab font group and underlying, we don't really need the decimals here. Removing the decimals, then we'll have another subtotal. So this is going to be a subtotal. And we're going to take this as equal to the 108 per cent shift six or carrot to the ten periods. That's going to give us two, but we're going to add some decimals going to the Home tab number group desk, normalizing it. And then that's going to be this whole piece right here. Then we're subtracting one from it. So I'm going to just say less one. Underlining that by going to the Home tab font, group and underline. And let's give us That's going to be the numerator, torr. Torr. Let's put that in the outer column, and this is gonna be equal to the 2.15. So on minus one. Let's make that eight per cent or add decimals, I should say Home tab number, group desks and normalized. So there we have that. And then we got the denominator. The denominator. So we've got this whole thing here. Now we're going to take the denominator, which is simply R, put that in the same column, that's going to be 8% the rate making that a percent Home tab number group per cent ties and then font group and underline. And that'll give us, Let's call this another subtotals, sub total. Putting that in the outer column, this being equal to the numerator divided by the denominator, making that then a desk animal eyes number adding decimals, in other words, Home tab number, group, desk normalized, then font group and underline. And that'll finally get us to the future value of the annuity. Future value of the annuity. Now, multiplying these two components, the outer column, that being the 1800, times the 14.48 and so on. We get about 2676. Let's add some decimals Home tab number group, a couple of decimals. Let's do some indentations here, selecting these items and indent them home tab Alignment, indent. And then we'll take the numerator and dent that again. We could do some spellcheck, see if I misspelled anything. Yeah, of course. Of course you did misspelled stuff. Okay, so there we have it now let's do it with the table one more time with the table time. And this is gonna be a payment. And the payment is simply going to be that 1800 picking them out from the table, making sure we got the proper table. This is the future value of an annuity table. And we're looking 810810. Here's the eight. Here's the 1014.48714.48714.48714.487. Add a couple of decimals, Home tab number coupled decimals underline it font group underline. And there's our FV future value annuity. Multiplying that out equal the 1800s, that 14.487. And so we're at the 2677, 60 close to the twenty six, seventy five, eighty one. Not exact due to rounding. This being the actual number that would be on the table if they took it out more than three to four digits, this being where it is at. If only taken out three to four digits, resulting in a slightly different number between the table and our other calculations. Let's go ahead and unhide ourselves by going to the be to L column. Let go right-click unhide. We're going to say if we save that money, we would be totally tired and our whole life would fall apart. But we would have we would be able to save $26,076. All the baristas would hate us, give us mean looks in the coffee shop because we never buy anything. But we would save $26,076 or an urn that over time. If we saved it, then we'd have the future value of the annuity also twenty-six, seventy-five eighty one. If we calculate it with our function, we calculated it this way. Twenty-six seventy-five eighty one with a formula and then slightly different twenty-six seventy six, sixty. If we use the tables. 12. Option to Receive Money Today vs a Series of Payments: Personal finance practice problem using Excel option to receive money today versus a series of payments in the future, prepare to get financially fit by practicing personal finance. We are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tap the example tab in essence being an answer key, we have the information on the left-hand side. I'm going to populate that into the blue area. On the right-hand side, we have our general type of scenario. The general circumstance being that we have a lump-sum that we can either receive now or received a series of payments in the future. This type of problem often represents something like a lottery type of situation. So if we won the lottery, you get the question as to whether you want to get the money upfront now or if you want to get them in a series of payments in the future. This could also apply to other scenarios such as like winning a lawsuit settlement or something like that, or insurance settlement, you could possibly have a similar option of either receiving an upfront some, or a series of payments. So for example, here's our situation. We have the option to receive 45 thousand today for whatever reason that might be might be some type of settlement, might be the lottery. We want some prize or something like that. Or we can get $7 thousand payments for nine years, which would be better to 7 thousand payments for nine years or the $45 thousand today? Well, the answer will depend on our discount rate that we will be using. So for example, if I just look at the dollar amount, of course, comparing the two, the 7 thousand here, I'm just going to equal to 7 thousand times nine would mean that over nine years we would get 63 thousand. Which would of course indicate that this one would be better because we're gonna get more money than the 45 thousand. But of course we're going to get that over nine years. And the option, the other option means that if I had the money today than I might be able to do something with it today. And the common response, oftentimes it's well, I don't maybe I don't need the 45 thousand right now. So I'm okay with getting at 7 thousand a year or something like that. But still, even if you've got the money today and you didn't need it, you could put the money to work and have it earning a return on it. So there's at least two factors that are involved here. One, time value of money will typically go down. So if I get 7 thousand a year later, the purchasing power of that 7 thousand will typically be less than if I got it today. But above and beyond that, if we got it today, we could put it to work with something today, either spending it on what we want or by investing it and getting a return on it. Whatever that return is, the thing we're losing. That's the opportunity cost of us choosing the other option. So that'll be more than just generally inflation if we think we can get a return higher than inflation. In other words, if I thought I can get that 45 thousand today, invest it in some way or use it in some way where I'm getting a benefit that I believe is worth a 7% return on it, then that, then that's the return will have to take into consideration. So the biggest problem with these types of calculations is where do you get that 7% return? It is not simply the interest rate, because the interest rate in the US might be around one to 3% if the Fed or the government shoots properly for what they want. But it's also the opportunity costs that you're losing for what you think you could have gotten with that 45 thousand if you had it today? Again, either through the pleasure of simply using it if you needed it or if you don't need it, then where you could have invested at what return are you losing by not having it upfront? And that's gonna be the discount rate that will have to use here. If we, if we assume that then to be the 7%, we'll do our calculations. So if we get a series, obviously if we get the lump-sum payment that happens at time period 0, we get the money today, we do whatever we want with it. We might invest it and get some return on it at that point in time. If, on the other hand, we're gonna get a series of payments of 7 thousand. Then we're going to discount it. We're going to discount that series of payment using the present value calculation to try to get a number that is equivalent to this time period 0 numbers. So we can do our comparison. Let's start that off with a formula. Excel formula equals the present value is going to bring it back to the present Shift, Nine, left, left, left, left. We're going to pick up the rate. So we have the right here and then comma, we're then gonna go left, left, left number of periods, which is gonna be nine comma. And this will be a payment instead of skipping the payment to go to the future value because this is an annuity. We're dealing with series of payments, so we're gonna go left, left down to the 7 thousand and Enter. I'm going to make that a positive number by double-clicking on it and then flipping the sign. So I'm gonna put a negative in front of the p. You could put a negative somewhere else, banker put it in front of the p in my case, and that's gonna be the 45605. So that's pretty close to what we had before. So if we got the lump-sum payment where we're at the 45 thousand. This one is slightly more so the annuity, it looks like it's gonna be slightly more even if we present value it at the 7%. So we're comparing, of course, 0 period $0 to getting the money today to the period $0 equivalent, assuming the discount rate at the 7%. Let's do the same calculation with our mathematical formula. Before we do, we're going to hide some cells. I'm going to put my cursor on column C, drag over to column E, let go, right-click, and let's hide some of those cells. So we're gonna be working here on the table. I'll make this a little bit larger so we can see our information. Okay? So now we're going to do this calculation will do this fairly quickly because we've seen it in the past. I want to jump to the running balance calculation next, which I think is a useful thing to look at. So if you want to skip forward to that one, you can't hear if you don't wanna do this calculation, but I think it's worthwhile to look at the running balance. So it's going to be p equals the payment. The payment is gonna be the 7 thousand times one minus the one over one plus r 7% to the n, nine periods over r seven per cent. I'm gonna plug that into our table format, putting these two primary components and the outer column and any sub calculations inside in the inner columns. So we're going to start off with the payment and the outer column here, and this is gonna be the 7 thousand, so this will be the 7 thousand. And then I'm going to take the numerator, some sub categorizations, this whole thing on the numerator. And then I'm going to do another subcategory, which is simply going to be this numerator or the one on the full numerator I'm going to put on the outside, this one is solo one. And then I'm gonna put this calculation in the inside. So I'm looking up the other numerator, which is this one on top, which I'm gonna call numerator two, which I know is not the most descriptive name. Enumerate tore too. And that's gonna be then one, this one right there, one. And then I'm gonna put that over the denominator here, the one plus r to the n. So I'm going to say the one plus r shift to the n, going to put a colon indicating that this is gonna be a sub counter calculation of that inside here one. And then I'm going to say the rate is going to be r or seven per cent per cent. To find that by going to the Home tab number group, making that 8% font group and underlining it. Then that's gonna give us a subtotal, which I'm gonna call sub TO Tau. Use the trustee some function equals the SUM shift nine up arrow holding down, shift up again and enter, making that then a percent Home tab numbers percent define it 107 per cent. Taking that to the periods and periods which is n, that's gonna be nine years. So that equals then the nine years. Let's underline that by going to the Home tab, font group and underline. Then that's gonna give us our whole thing, which is one plus r to the n. And let's get rid of the colon though, removing the colon, putting this into the outer column because we had the colon indicating a subcategory. Now go into the outer column. This equals left up, up, shift six carrot, left up to the power of nine. Enter. We're going to add some decimals to give us a bit more detail there by going to the Home tab number, group, deaths in the Molas, did destiny symbolized? Then that's not a real word, but remember, but it's fun to say, there we have it. So now we've got this, this whole thing, bottom part, and now we can divide these two out. I'm going to call that then a subtotal. Subtotal. Put that then in the outer column. This is going to be, I'm only working one column at a time. So now I've got this one right there divided by this desk, the normalized number, adding some decimals there, Home tab number group. Yes, in normalized. Then go to the font group and underline. Then we can say now we've, we've got wherein this outer thing. So now we're gonna do this as B, the whole numerator. Now, put this in as the numerator. And I'm going to keep this in the same column, even though it's, keep it in the same column, this is going to be equal to one, This one way up top minus this desk normalized number, which also needs to be desk normalized Home tab number, deaths in them allies. And then we're going to take that divided by the denominator. So we'll say denominate torr, which is the rate. And that's going to be equal to the 7, 7% percent. Making that up per cent by going to the Home tab numbers group per cent to find it font group and underlining it. And then that's gonna give us a subtotal, again sub TO towel in the outer column, which is going to then be that's going to be equal to the num array ptr divided by that denom and adding some decimals there, Home tab number group, yes and no lies. And that'll get us finally to the present value calculation down below present value. Which is gonna be these two components multiplied together the thing way up top, which was the seventh thousand times this 6.51 and so on. Let's add just a couple of pennies. Home tab number group couple of pennies, do some formatting. Let's underline this one, home tab font underlying. Let's add some indentations to this whole thing right here. Indentations to this whole thing. I'm going to say Home tab Alignment, indent. And then let's indent this thing again. Let's do another indentation here, Home tab Alignment and dent that again. And let's indent this one more time. Uno vase mosque. Poor or five or that was my attempted Spanish. Sorry about that. Indicates here we have it. So now we're going to then lets unhide some, let's hide some columns. And let's do this again with the, with the running balance. So I'm gonna put my cursor on column F, left-click and drag over to k. Let go, right-click the selected area and hide those columns. Note I've made an adjustment here from the table to another kind of concept that might make this a little bit more clear of a decision. Note when we have a decision between these two items, something like this, what we will typically do with bring things back to the present, present value them so we can compare them both in present value terms. It might make sense to or help to solidify this by thinking about them in future value terms as well. In other words, if I had this 45 thousand upfront, the assumption of this discount rate is that I can get value of that 45 thousand at a 7% return. So I could think about, okay, where, where would I be in nine years if I got a value, some kind of return of a seven per cent on that, and compare that then to the future value of the annuity payments, assuming I can get a 7% return as we basically get the money for nine years in an annuity. So let's do that and I'll just do this one with basically the Excel functions here. So I'm gonna say this is gonna be the future value of a lump-sum. So I'm going to say this equals the future value shift nine. I'm looking at the rate which is going to be that 7% comma, the number of periods is going to be nine. And then I'm going to have two commas because I'm not going to put a payment here. But look at the present value of the option of getting the money upfront, the 45 thousand. So we'll start with a 45 thousand and Enter. And that'll give us the AD2, 731 about. Now let's think about the future value. If I was to get 7 thousand for nine years and be able to invest that 7 thousand when I get them each time period at the 7%, where would we be in terms of future dollars? We would be at the negative future value shift nine rate will be 7%. Comma, number of periods, I'm gonna say is nine. And then comma. Now we will use the payment because this is an annuity calculation. Let's take the 7 thousand and enter. So there we have it. So you can see where a difference between the two. Let's see what that difference is. As far as future dollars, this would be equal to AD2, 731 minus the 83846. That's a difference of 100115 in terms of future value dollars. So we brought these both out nine years into the future and we have a difference in future doubt value dollars of the 1015. Let's now think about bringing that future value amount, that future value difference back to the present by basically discounting it back to present value, present value of one calculation, which would be negative present value shift nine. The rate would be the 7% comma, number of periods would be nine. And then comma, comma because it's not a payment, we're gonna, we're gonna present value, this future value amount Back to the current point, and that would give us these 607. Now note, if we unhide some cells here, I'm going to unhide from m, from B to M. Putting my cursor, I will be selecting over two m. Let go, right-click and unhide. I think I did the wrong thing I hit. I'm gonna go from a to N, right-click and unhide. I don't want to hide it. I want to unhide it. So notice when we did the present value here, we had a difference. Let's put a difference column here. And I know this is jumping around, but I felt that this might be more beneficial. So we've got the 45607 minus the 45, there's our 67 seven, right? So when we present valued it, we had a difference between the two options of $607 are pretty close when we future value it and think about it in future value terms, you have a difference of 100115 in future value dollars way out into the future, and then we can present value that. And again, you get down to the 607. So you can kinda think about it both ways. The traditional way to look at it, of course, is to try to take whatever's in the future, bring it back to a time period 0. But notice the point is of course, that you're trying to measure things as of apples to apples, they say or the same thing to the same thing. So if you put both things out in the future, you can do that too. But again, if you want to see it in terms of current dollars, you would then have to discount it back to the present. Okay, Let's do the same thing with the tables here. During the tables will pick up the table and that's going to be equal to the 7 thousand. I'll just pick it up right here. Pick up the amount from the table, which is making sure that we have the proper table, which is going to be the present value of an annuity. We're back to the present value thing. Present value of an annuity table. We're looking 7%, 9 years, 7979, which is going to be these 6.51526.5152, 6.5152, adding decimals by going to the Home tab number group. You decimals there. And then that's gonna be our present value of an annuity at T equal to the seventh thousand times the 6.5152 gives us about the 45606. So let's just recap what we've done here. The two decisions going all the way back to the left. We can either get the 45 thousand upfront or the 7 thousand over a series of nine payments. If we got the 7 thousand over a series of nine payments, it looks better at first glance, of course, because that would be $63 thousand versus 45 thousand, but it's over nine years. If we were to discount that series of payments were at the 45607, It's still better, but only slightly than the 45 thousand by the 607 difference. We then present valued using the formula to get that 45607 about again. We then compared it and said, well, what if we future valued the two options? And we found that we got the difference between the two options in future value terms nine years from now, 100115. And if we present value that, we get that 607 different again. And then we did it with the tables. And we got this 45606 again, let's go ahead and put an underline under that one. 13. Loan Payment Calculation & Amortization Table: Personal finance practice problem using Excel loan payment calculation and amortization table, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along now that we're down here in the practice have as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side going to populate that into the blue area on the right hand side, looking at a loan situation where we have an imagination of our borrowing, the 11 thousand, the interest is going to be 5%. Now, obviously, if we are borrowing, interest is in essence, you can think about it as the rent on the purchasing power of the money. So we're borrowing money. It's similar to as if we were using basically a place to live or for using basically a place to work and renting that place where borrowing the use of it and have to pay basically rent on the use of it, interests. You can basically think of as the same thing we're borrowing the purchasing power, have to pay rent for that purchasing power. That's going to be called basically interest. We're going to repay in years, seven years. So we're gonna be making installment payments will be paying yearly. And usually when you're looking at a fixed kind of setup for a repayment of a loan, which is quite common for a personal kind of financing options. Although note, you could have different financing options when you look at basically like business financing options. But most of the most common things we think about on the personal side of things, we have a fixed set of payments that we repay. Oftentimes we don't repay yearly, we repay monthly. We will take a look at monthly repayments, but that's a little bit more of a twist in our calculations. So we'll take a look at that in a following presentation. We'll start off here with yearly repayments. This would be applicable if you're thinking about like a home loan or something like that, which is often paid off in installments, once again, monthly usually. But similar concept. Or if you're talking about any kind of financing like a car or something like that. Now first, we're gonna be thinking about the payment option, which is often something that you would be thinking about if you're the loan, if you're the one that's granting the loan. But clearly, if you're if you're kind of budgeting yourself and you're trying to think about how much money you would want to borrow, then you would want to do a calculation such as this. So think about what the payments would be if you could get borrowing at certain terms and whatnot. So that's gonna be the kind of concept with it. Once you know what that is, then it's useful to make an amortization table to list out what the actual payments will look like. So that's gonna be, that's gonna be the idea. Now, you have this information. We could use the payment calculation, which is a function in Excel, but it's kind of, it's related to, once again, the present value calculations. So oftentimes you might first the most comfortable with the present value calculations. And you might say, how about if I'm going to back into this payment situation? Is there some way that I can use basically the present value calculation to do so. So let's, what we might start doing then is to take our data, start plugging it into the present value calculation and see if we can use that with the help and use of the Goal Seek and then get a better idea possibly, if there's another function related to which there is, which is the payment function here as we go, we might say, okay, let me see if I could start plugging this into like a present value. Shifts nine, we're going to say the rate would be this 5%. So we're going to pick up the five per cent and B2 comma, the number of periods would be seven. So we know that we know the number of periods would be seven, the payment amount comma then we have the payment amount. And we should have a payment amount because this is basically going to be a series of payments kind of situation and that's what we don't have. So if I look at the present value, I'd say, okay, I don't have that. I'm going to put that in a, in a cell down here and say That's gonna be my unknown. And then the present value, the end result of this thing we actually know should be basically the 11 thousand, that should be the starting point. So if I say Enter here, we can kinda back in and use our Goal Seek. And we can also say, okay, I can either use Goal Seek or I can see that that payment thing right there. The PMT is what I'm missing. Maybe there's an Excel function which is called PMT, and we can do that directly. But considering I know the present value more clearly, I'm going to use it first and use the Goal Seek to kind of back into what I need and then we'll verify it with a payment calculations. So I'm gonna, I'm gonna type in a payment of 1 thousand down here just to test it out. And I know the end result should be 11 thousand now I would like the result to be a positive number. So I'm going to double-click on it again. I'm gonna put a negative in front of the P to flip the sign. And then I can start to adjust this. I can say, well, I know what the end result needs to be that 11 thousand. If I make this like 2 thousand or something like that, I'm getting closer to the 11 thousand. I can ask Excel to do that for us using the Goal Seek feature, which would be in the Data tab up top. And the what if in the forecast group, What If Analysis Goal Seek. Let us seek the goal we want to set then this cell up top to be 11 thousand by changing then this data input cell right here we can say, OK. And there we have it, the 19011901. So in this instance then we would have to make payments, repayments if we're paying them on a yearly basis of 100901 for the borrowing of the loan. Now we could also think about that and say, okay, well, I can get there more quickly with just a payment to calculation down here. Let's use the trustee payment calculation. This is equal to the PMT payment shifts nine. The rate is going to be over here at the 11% comma number of periods then is going to be the seven periods and then comma the present value. That's our starting point. That's, that's gonna be our loan amount. So present value is gonna be the loan amount, that's the money we're getting now and enter and there we have it. The 100901. I'm going to flip the sign of it again, making it a positive, double-clicking on it. You can do so by putting a negative in front of the payment, which is probably more proper, I like to just put it in front of the p, flipping the whole thing, multiplying by negative one in essence. So now that we have that, we can then do our calculation with our loan, with our loan over here and do basically an amortization type of table. This is really useful to be able to do and this will give you once again a better understanding. I'm going to make these cells a little smaller here so we can keep all this stuff together. A better understanding of the pictorial picture of what you're basically doing and the interest in the loan balance as we go. It can also help you to record the payments accounting system. If you're trying to track what's your current loan balance is, what your interest is. So you can deduct the interest for taxes and all that kind of stuff. So let's go ahead and say we got, we got year 01. I'm going to select those two cells. We're going to put our cursor on the fill handle and auto fill that on down, auto-fill. Then let's go to the Home tab. Let's go to the alignment for some reason it's shaded out here. I want to center that. There we go, center it. Then we're going to say that we have our starting point, which is the loan balance, which I'm going to put at period 0 all the way in column K, which is going to be equal to the 11 thousand, that's our loan. And we're going to think about, well, what if we had payments on that with the 9% interests and we're going to make payments on it. This is a common kind of format to set up an amortization table you might want to practice if you're doing this in a school setting or something like that. Or if you are calculating loans for a home or purchasing, purchasing equipment or a car, you might want to set up a table like this and just practice setting up the columns because that can be a little bit tricky once you know how to set them up. It's fairly easy to do this. And again, in Excel, even if you're doing a loan with 30 year payments and whatnot, even if you're doing it by month, 30-year payments and you gotta go down to 360 cells. That's okay. You can copy it down. You can figure out what the yearly interest rate would be and whatnot. That's why spreadsheets are nice. Spreadsheets are nice. So then we're going to say to the payment that we're going to make each year is going to be equal to the amount was pulled it from here. We already calculated the payment. So there's the payment. Then we know what the interest is going to be. The interest is going to be the 11 thousand balance times the 5%. That's the rent that we're paying on the borrowed money. So this is gonna be equal to the 11 thousand K3 times left, left, left, left, left, up to the 5% Enter. So that means that we're gonna be paying the 1901 about. There might be pennies involved here, we've rounded it. The interests related to it is 550. So that means of the 100901550 is like go into rent, it's gone. We're not getting any decrease in the loan balance from it. The difference between the two is the decrease in the principle that we will have. So we're going to say the loan decreases the amount we pay minus the rent on it, the interests. And so that 1351 about is what the loan balance actually goes down by. So this is going to be equal to the 11 thousand minus that 1351. So now the loan balance is going down to here. So if you were to record this in an accounting ledger or something, decrease cash or the 100901 interests would be like rent, it would be an expense, and then the loan would decrease by 1351, there would be three accounts affected. In essence, bringing your balanced loan balance down to nine, 1649 and record the interest expense at the 55050, which would bring down your net income. Okay, So let's do it again. The payment would then be once again, 100901. Now, in a future presentation, we'll do this with monthly payments, which will be a bit more complicated because we'll have to deal with the added periods. So we will do that in a future presentation. It's not too much more complication. Once you get this down, this is gonna be equal to the 9649 times the 5%. Notice that the interest will go down because that's how the loan was set up. So most loans are actually set up in this format. So you can have nice even payments that's easy for individuals and companies to budget. But the sacrifice on that is the fact that you've got this funny business happening between the interests and the decrease in the loan balance as it, as it goes down has a different amount each time due to this. So the payments the same, but now the interest is different. So now I got to take the payment minus the interest. That means the decrease in the loan balance is now different. So the interest will always be going down because we borrowing less money at this point in time. So we're paying less rent on that money, and that means we're paying the same amount. So that means that we actually have a bigger decrease in the principle as the loan continues on into the future. So this will be equal to the 9649 minus the 1419. Let's do it a couple more times and then we'll use our auto-fill feature to copy it down. This equals the 1901, this equals the eight to 30 times the rate of the five per cent. And then we have the difference. The 1901 payment minus the interest, which is now at 412, gives us the decrease in the loan balance of the 1489. That means the prior loan balance of the 8230 minus the 1489 gives us the new loan balance that we still have outstanding is at the 67 for one about. So we're going to pay once again that 1901 and year four. Now the interest is going to be these 6741 times the rate, which is 5%. And so we paid the same amount 1901, but the rent or interest has gone down 337, meaning the decrease in the loan goes up. And our prior loan balance was the 6741 minus the 1564 new loan balance, 5177. Let's do it one more time and then we'll go back up and do it the easy way. Instead of this way I'm going to hit this one then say tab instead of enter. And then equals. That takes us to the cell to the right, equals the prior balance times the five per cent tab. And then this equals the amount we paid minus the interest tab. And this equals the one above it, the 5177 minus 1642. And that gives us the new loan balance of the 3535. Now, before we end this thing off, because we should be at 0 at the end and we would get there. But we're going to start over the suspense just to maintain the suspense. And then we're going to do it again, this time using autofill to make it, don't do it easy, do it the easy way. So I'm gonna delete this whole thing. No, all that work was wasted. Okay, we'll do it again. It's okay. Okay, so we're gonna say this is going to equal the payment which is over here. Notice that from somewhere outside the table, when I copy it down, I don't want that cell to move down. So I'm going to say F4 on the keyboard, dollar sign before the E and the five, you only need $1 sign or a mixed reference, but absolute works. Then we've got the interest calculation, which is going to be equal to the 11 thousand times the rate. Note that the rate is outside the table, which once again means that I don't want it to move down one when I copy it down. So I'm gonna make that an absolute reference, hitting the F4 on the keyboard. Or you can put a dollar sign before the B and the two, you only need a mixed reference again, but absolute is easier to think about. Then we can subtract these two out. This is going to be equal to the 1901 minus 255. Oh, those are both within our table and I do want them to copy down relatively when it moved down properly like they normally do. So I don't need to do anything to them. Then this is gonna be equal to the one above it minus the one to the left. And I want those both to move down relative nothing is outside the table there, so that one should do as we want it to. So let's go ahead and then select these and auto fill it down, grabbing fill handle, dragging it down. If you do this properly, the bottom-line number should be 0. That's your indication that you've, that you've done this correctly. This can help you to actually record your payments, breaking out the proper amount of interest in principle and double-check what's your principal balance will be as, as well as give you help in terms of what your interests payments will be. Interests is gonna be something that's going to have an impact on your income statement. And you could have tax impacts on that because it'll typically be deductible portion of the payment. Alright, now, let's do this one more time with a table over here. You might say, how can I do this with a table? Because the tables are usually used to give us basically the the present value calculation. So now I'm going to use a present value of an annuity calculation to back in to a number on the table, which is something you probably wouldn't need to do in practice because you do it in Excel. But some nefarious teacher or something school might make you use the tables in this odd way. And so we can say we can do it, It's not hard. We just do our same table thing. We're going to say payment. You got the payment than the amount from the table. And then the present value of the annuity. This is how we usually use the tables. What we're gonna do is now we know what the end result is. So I'm not going to rework the algebra. I'm going to say, Well, the end result is gonna be that 11 thousand. And then I'm going to get the amount from the table and then I can back into the payment from it. So we're just gonna that's why it's yellow. That's why I made it yellow because we're going to back into the payment. So I'm going to say the amount from the table, we gotta make sure we get the right table. This is an annuity table, present value, same thing we did up top present value of the annuity. So we're going to use a percent and the number of years. So five per cent and seven, here's the five. There's the 75.78645.728645.78645.7864. And then we can back into this. So if this times this equals that, I should be able to take then this, the 11 thousand divided by that. And obviously you can write it down and work it out algebraically. You can double-check it and say, did I do it right? If I take this times this, I should get 11 thousand. I did do it right. Okay, so there's that, so we can do that. We can use those tables and again, be aware that the tables can be used in such nefarious ways. If for test purposes and then know how to do it. The easy way for actual practice when you're figuring this stuff out. 14. Monthly Loan Payment Calculation & Amortization Table: Personal finance practice problem using Excel monthly loan payment calculation and amortization table. Prepare to get financially fit by practicing personal finance. And we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tap the example tab in essence being an answer key information on the left-hand side and populate that into the blue area on the right-hand side looking at a loan scenario, once again, similar a prior presentation, but this time we're looking at monthly payments as opposed to a yearly payments, making it a little bit more complex to do our calculations. So we're going to say that we're gonna be borrowing the 11 thousand for the borrowing, the interest rate this time is going to be 12%. And we're going to say that we pay repaid in monthly payments for three years. So in other words, we're gonna be paying it back for three years, but we're gonna be paying monthly, as is often the case for many kind of loan situations, like a mortgage or loan for financing a car or something like that as it is typically going to be set up. Now note, as we look at this payments calculation, if you were to get a loan for financing the car and whatnot, normally the person that's calculating the loan will just give you the payment information. You would like to be able to calculate it yourself so that you can go into a situation and practice different kinds of payments and interest rates settings to see what would happen and also get a better determination through the creation of an amortization table of the payments and interest in what the relationship will be to the loan. So let's calculate this out. We got our information, we're going to calculate the payment then. Now first, you might first be most familiar with that present value calculation as opposed to the payment formula, there is a payment function, in other words in Excel. But when you're first looking at this, you might say, look, this looks like a present value of an annuity kind of thing because the payments are all the same. Let's try with the present value, see what the unknown is, and possibly use our goal, seek to figure it out and then see using the present value function whether or not there's another function that we could then use called the payment function to then rework the equation and solve using that function. So in other words, we might first start off and say, let's, I know this is a present value kind of things. So let's go Present Value Shift Nine and say that we have a rate. The rate is gonna be the 12 per cent. Now, note this is where it's confusing that 12% is a yearly rate. And normally when you're talking to people, they will quote a yearly rate, because the yearly rate will be somewhere between 1, 100% generally. But we're gonna be paying monthly. And therefore we got to have the rate that's going to be equal to the payment. So I need to take the yearly rate and divide it by, divide it by 12 in this case. So that's gonna be the kinda twist involved here. Note that no one really quotes the monthly rate, which in this case would just be 1% per month. Because although 1% is fairly easy to say, if it was 1.05432 or whatever, something like that, then obviously that becomes much more difficult to to be dealing with them. The yearly rate, which would be just simply 12 years or the convention. And then you have to basically make the adjustment to whatever you need to adjust it to use in your calculations. Then I'm going to say comma. We have the number of periods. Now the periods were given in years. Once again, it's going to be paid off in three years. But just like if you had a 30-year mortgage or something like that, but you know, you're gonna be paying it off monthly. So you're going to take that three years and times 12 because there's 12 months in a year. So we'll take the three years times 12. And then we're going to say comma and the payment amount. That's what we don't know. That's what we don't know. I can do two things. I could say, well, I think the end result here should actually be the 11 thousand, the amount we're borrowing. That's the present value. I can then use goal seek to figure out the payment. Or I can go to another function and see if Excel has a function called Equals PMT, which it does, which is the payment function. So we're gonna start off here pointing to this cell and try to use Goal Seek to back into this first, because we might first understand the present value calculation best. And so there we have it and then we can guess at a number. I could say, well, what if this was 500? We'd get a result of 1545. We want a result of 11 thousand. That's what should be in the end result. I would like it to be a positive number, however. So what I'm gonna do is double-click on this 11 thousand. I'm gonna put a negative in front of the p, which will basically take the entire thing multiplied times negative one, flipping the sign to that 15,054 positive, then I can adjust this number down here to like 400 and so on until I get it to what it should be at, which is that 11 thousand. We can then ask Goal Seek to do that for us by going to the Data tab up top, go into the forecast group, the What If Analysis and say Goal Seek. We're going to seek the goal and we want to set then this cell to be 11 thousand hardcoding that in other words, typing it in there. Then we want to do that by changing this cell. So we're asking Excel to make that cell whatever it needs to be the payment so that that cell up top gets to the answer. We know what should be, which is 11 thousand. There we have it where at the 365 about there might be pennies, but we're going to keep it there. Let's add well as look at the panties. So they're gonna be pennies. There are pennies, so it could go on here, but we're going to round it to two pennies, which is gonna be 3.36650 to get the pennies Home tab number group. Adding the decimals. Then we could do it the other way with the payment formula because we saw that there's a payment thing here. So let's see if Excel has a function for the payment thing. We're going to say I think they do. I'm pretty sure I've seen one before. I'm pretty sure I've seen that before somewhere. So there's the payment. There it is. Let's go shift nine. We're going to pick the rate. The rate is 12%. Once again, that's a yearly rate. So we've got to divide that by 12 to get the monthly rate comma. Then we got the number of periods, which is three, but those are years and we're doing this monthly, so I'm going to take the three times 12 to get the monthly periods comma. And then the present value is the amount we're borrowing at the current level, the current 0.11 thousand in B1 and enter there, we have it. Once again, let's add some decimals, Home tab number group coupled decimals. And then let's make it a positive number by double-clicking on it. I'm just gonna put a negative before the PE flipping the sign of the whole thing. There we have it. So there we go. So now, now we can do an amortization table. So note the number of periods we have is actually going to be equal to three times 12. So we're looking 36 months in terms of the periods. So keeping that in mind, let's build our table out here. And I'm going to say, let's bring this up from 01, and I'm going to bring that down to 36 months by selecting these two, grabbing the autofill, it doesn't matter how long this is. You can do this for 360 months, which would be like a 30-year loan. That's fine because you can just drag it down like this. That's what Excel is four. That's what Excel is here, four. And then we can go to the Home tab Alignment and center it. And then we're gonna go to the loan balance and the outer column, this is going to be equal to the eleven thousand, eleven thousand on the balance. And then we'll just do our calculations once again, the payment we already calculated, that's going to be equal to this payment amount. And then we're going to take the interests. And the interests is a little tricky because we got it. We got to take into consideration months instead of years, and they gave us the yearly rate over here. Let's do this real quick. And the trusty calculator over here, just so we can see it. We're going to say, we will take the 11 thousand times. You could say that 12, which will be the yearly rate. And that will give you the 1320 for a year's worth of interest. But then we're only talking about a month here. So I take that divide it by 12. That's how I would normally calculate it with a calculator, because that's the way that you're not going to get these decimal number. The easiest way to do it typically if you're doing that, but when you calculate it in the formula, as we saw, we could do something like this. 0.1 to the rate divided by 12 gives us the monthly rate, which happens to be 0.01 here, which is conveniently given the problem, of course, we set it up conveniently nicely so it's one per cent. But that can be a little bit confusing. That's a monthly rate and then we can multiply that times the 11 thousands. So either way you want to think about it, it's useful to think about it both ways when you're calculating, depending on whether you're using a calculator or Excel. Okay, So let's do that. We're going to say this is going to be equal to the 11 thousand. We're going to say times the 12%. And that 12% would give us the result per year. And then I'm gonna take that and divide it by 12 to give us the monthly result. And there we have it. So let's then decrease it. So this is the amount we're paying threes. And by the way, if you didn't divide by 12 and you came up with this, you'd say that doesn't make any sense because the interest is more than what I'm paying. That doesn't make an, oh, I didn't divide it by two. And then you're going to divide it by 12. So that might happen. And then we've got the 365 minus the 110. So we're paying 365 minus 110, which is the rent portion, which we're not getting back. So we're going to reduce the principal by only the 255. So then we got the equals the 11 thousand prior balance minus the reduction of the principle. That's gonna give us the 10745. So if we were to record this, like in an accounting system, we'd have the loan balance at 11 thousand, we pay cash goes down 365, but 110 of it is interest expense, and the loan is only going to be decreased by 255. So once recorded, the new balance would then be 10,745. Alright, let's do it a couple more times and then we will auto fill it down. Don't worry, we won't do this the whole way down. We'll just do it a couple more times here. So this is gonna be the 365. The interest is going to be equal to the new balance of a 1074 or five times the 12%, but that's the yearly rate. So we've got to divide that by 12 to get to the monthly amount. That's gonna be the 107, it being less than the prior balance. We're going to take the same payment of the 365 minus the decrease interest amount that gives us an increased loan decrease in which is going to be equal to the prior loan balance minus the decrease in the loan. We're now at the 10 thousand for 87. Let's do it again and we're going to pay the same amount, which is the three sixty-five thirty-six, the interest is now gonna be the new loan balance to 10487 times the 12 per cent, but that would be the yearly rate. So we divide that by 12. And then we're going to subtract this out. We're paying the 365 minus 2102 interests, gives us the 2.6D. That means the loan balance, which was privately at 10 thousand for 87 minus the 260, gives us the new loan balance of 10 thousand to 26. Let's do it two more times, two more times, and then we'll do it the easy way. 365 payment interest is going to be the 10 thousand to 65 times the rate of 12%, but that would be for a year, so we divide it by 12 for the monthly rate. Then we're going to take the amount of the payment which is still the same 365, but now the interest is going down to the 1A2, so the decrease in the loan goes up to 263. So now we've got the new loan balance, which is was at ten to six to ten to 26 minus the 263 new balance, 99631. More time and then we'll do it the easy way. One more time. We're going to say this is gonna be equal to the 9963 times the 12 per cent up top. We will take that divided by 12 to get the monthly amount. We're down to a 100. We've got the 365 payment minus the 100 down means the decrease in the principles at the 266, the prior balance at the 9963 minus 266 gives us the 9697. Okay, now i'm, I'm gonna go back and delete the whole thing so we can do it the easy way. This is painful to delete it, but it's okay. You don't have to delete it. I'll do it, but delete it. Let's do it again. So this is going to be equal to the 365. Now this time I want to copy it down. That number is outside my table. So I'm going to have to absolute ties it because I don't want it to move down. So I'm gonna select F4 and the keyboard dollar sign before the E and the five, you only need a mixed reference, in other words, $1 sign, but $2 signs is easy to think about. So that's what we'll do. This is gonna be equal to the 11 thousand on the interest times the 12%. That 12% outside the table, again, don't want it to move down when I copy it down. So I'm going to select F4 on the keyboard dollar sign before the B and two. Then I'm gonna divide by 12, which is a hard-coded number. It will copy down as we go as we want it to. So we're good. Move. This then is equal to the 365 minus the ten. Both of those are inside of our table. Both of them are wanting to be moved down. No absolute references necessary. This is gonna be equal to the 11 thousand prior balance minus 255. Again, both those inside of our table, both of them need to be moved down to relative when I copy down. So nothing special needs to happen there as well. Let's go ahead and select these three, will copy them down. Now if I wasn't confident and I am confident, so I won't do this, but if I wasn't, I'd copy it down just one cell and see if it does what we want it to do. But since we're totally confident, I'm going to copy it all the way down. And the confirmation number here should be that this last one should be 0 if we did it right. 0, just like I told you, I told you it would. If I, if I double-check these, is it doing what we expect it to? This is pulling that cell all the way up there. Yeah. That's what we wanted. This is pulling that cell all the way up there. Looks good. Looks good. And this end result is 0, making me think that things have been done properly. So you can see the payments the same, the interests goes down over time. The loan balance than more of your payment is then a decrease in the loan balance over time. And this becomes quite significant, especially when you're looking at deductible kind of things like a home loan where the interest portion is deductible and it's important to be able to figure this out. You can then do because you can then say, Okay, for the next year, this is the interest we would be paying, which would be the 1146 and so on. If it was a deductible loan for a business, same kind of thing. You might, might have tax implications that you have to be taken into consideration. It's also just useful to see what is actually happening in terms of how much you are paying for rent interests, in essence, and how much is being paid back with regards to the loan principal amount. Okay, let's do it again. Or one more thing with a tables. Remember this is a table. The backing into the table, you got to do the reverse format to get to the table amount, but I'll set it up in the same format here we would say this is gonna be the payment, which is what we're looking for times the table. This is what we usually do. It gives us the present value of an annuity. Now we already know what the end result is. That's the 11 thousand. We can find the amount from the table and then back into the payment. So the new twist, however here is that we're not looking for years and yearly rate. We're looking for months, which is gonna be 36 months. And that's why we don't often use the tables or y book problems, avoid monthly rates because three years already has you almost to the end of the table. The end of the table only goes so far and I don't even have a table Hold on a second. It's over here because I see why. Okay. So it only goes down to 50 and then it starts skipping periods down here. And the rate or even rates and they don't go below, below 1%, which is also a problem which we made conveniently to be 12%. So the monthly rate is simply one. So it's nice to have nice even rates. In other words, if you're using tables. But in real life it doesn't really matter because Excel can take care of uneven rates. So in other words, we're looking for then 36 periods and we're looking for 1%. And so when we go down to the table, note that we've gotten you've probably gotten used to the periods, meaning years and the percents being yearly percents. But what you got to keep in mind is that it doesn't matter what the two are as long as they match. So if I'm seeing these periods as months, that's okay. As long as I see the interest rates as the monthly interest rate, if I was to look at these and months, looking up 36 months, and then use the yearly rate of 12, that would be a problem. But if I convert these two months using the 36 months and I use the monthly rate of one, then I'm okay. So that's gonna go down here to the to the 30.10830.10830.108. And then we can back into this amount now because I can say, well, if the yellow number times this is that, then I should be able to say that this is the 11 thousand divided by the 30,000.108, giving us that three sixty five thirty-five. Again, we could double-check it down here by recalculating that 365.35 times the 3D, 0.108 equals 11 thousand. Let's blue a fire that one just to double-check it. So there we have it. So we've taken this, we've basically got our payment amount on it. Very useful, very useful to this number note you can find a lot of tools to help you out to figure out the payment. But using Excel, I think, is the easiest, most transparent thing to do that you can understand it with, then take that payment, prove it in your mind, and get a better understanding of it by putting in, into an amortization table where the end results should be 0, which should give you some confident that you set up your table correctly. And that'll give you a lot more context on which to make decisions related to car loans, home loans, and that kind of thing. 15. Annuity Due or Annuity Beginning Period: Personal finance practice problem using Excel annuity due or annuity where the payment is due at the beginning of the period, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side, we're going to populate that into the blue area. On the right hand side, we're looking at an annuity situation which is a series of payments on normal annuity, usually assuming the series of payments happens at the end of the period. Now we're going to basically assume the payments are happening at the beginning of the period. We got the payment amount, which is gonna be the $1 thousand. We've got the rate at the 5% that yours are going to be six years. We're gonna do a future value calculation of an annuity and we'll do one for the standard annuity and look at the difference. If we were to calculate the annuity due or the series of payments happening basically at the beginning as opposed to the end of the timeframe. So let's first do that with just simply the Excel functions, normally the normal standard annuity. If I'm looking at the future value of annuities, meaning I'm going to make a series of payments every year, assuming at the end of the year for six years at a 5% rate, where will we be in terms of future value? We're going to say this is, I'm going to start with a negative to flip the sign at the start, which is going to be future value shift nine will pick up the rate, which is going to be the 5% comma, the number of periods is going to be the six periods, which is going to be the years, and then comma, and the payment is going to be the 1 thousand. So this is what we have seen in the past. Notice that we haven't been using these other two components here because by default we're at the standard annuity. But notice if I hit a comma, again, I'm going to say comma, that gives us the present value. We don't have one comma. Again, that takes us to the type. Now the type says here, the default is basically end of the period versus the beginning of the period. So by default, typically having this end of the period or 0 calculations. So in other words, if I was to hit the 0 calculation here, we then have the type added and then Enter. That'll give us this 1008 O2. If I double-click on this again, and I remove the 0 and just remove these last two fields which are not required. It will by default give us the same calculation of the 68 O two. Now, if I want to change that, then I can use that type field to make the adjustment away from the default, which is two, which is to say it's at the beginning of the period. Let's see what that would look like. So it's going to be a same starting point. This will be the future value shift nine, the rate once again at the five per cent. Then comma, we got the number of periods. The number of periods is going to be six comma and then the payment, the payment is going to be the 1 thousand and then comma, I'm not going to put a present value here. I'm going to put another comma and note the present value is typically there when you're not doing an annuity where you would skip the payment and use the present value. This time I'm going to skip the present value to get to the type calculation, which I do want to use because I want to remove myself from the default and go to this one, which is indicated with a one, the beginning of the period. So I'm going to select that one that'll put a one for the type. Now, we could close it up or we can leave it as is and then say Enter and we get them to a different result, a larger result, because we're assuming here then that the payment went in at the beginning of the period. Let's see if we can make some more sense of this by basically putting these two into the table. We'll start at our first table doing the standard kind of annuity and then compare it to the one of the payments happened at the beginning of the period. So note with a standard annuity, I'm not going to put a time period 0. I'm going to start at 12. I'm going to select those two cells, put my cursor on the fill handle, drag it on down for our six periods, Home tab Alignment, center. And then the payment is going to be equal to the 1 thousand at period one. Notice that no interest is going to happen, no increase in the value due to the fact that we're assuming that happened at the end of the period one, end of the year. In this case, the investment at the end of the year will still be the 1 thousand. Then we're going to calculate the increase which would be interest to whatever the increase would be increased in value if it was stocks or something like that. In the next period, which would be the 1 thousand times, we're going to save the five per cent. I'm going to select F4 on the keyboard because I will copy this down since we've seen this one in the past. So F4 dollar sign before the B and the two before the B and the two. And that would mean it's absolute, it's not going to move down. You only need a mixed reference, but an absolute references easier to think about. About 50. Then we're gonna be seeing the payment is the same at the 1 thousand. That's also something I don't want to move down. So I want to make it absolute by selecting F4 dollar sign before the B and the one. Once again, you only need a mixed reference but an absolute works. Then we're going to have then the investment, which is gonna go up by both the 1 thousand and the $50. And that's gonna be calculated as the 1 thousand we started with. And J2 plus, I'll say plus the SUM, the sum shift nine, left arrow of these two items to 50 plus the 1 thousand plus 1 thousand closing the brackets. And there we have the 2050. I'm simply going to copy those cells down. I'm going to select these three, put our cursor on the fill handle, auto-fill and copy that on down, dragging it on down. That gets us to our end result of the 6,008 O two, we would have put in six payments given us the $6 thousand over the six years and the amount of increase we had if we sum this up, would be the $802. Now, this one will be a little bit more confusing if we think about the payment that happens at the beginning. So I'll set the table up two different ways so we can look at that. The first way, we might do the same kind of process. We're going to say we've got 01. I'm going to start at 0 this time instead of out1. And copy that down. I'm going to copy this down to six periods that I'm gonna go to the Home tab, Alignment and center. And then I can think about periods 0 as basically the starting point, meaning the end of period 0 would be the beginning of period one. So the payment happens at the beginning of the year. You're thinking, which I'm going to say is that the end of period 0. So you got the same kind of starting point. So I'm gonna say this will then IQ actually let me put that in the payment. The payment here is going to be equal to the 1 thousand. And that means the investment is gonna be the same at the 1 thousand at that point in time. And then I'm going to say in period one, then, now we're actually going to be calculating interests in period one because we're assuming that we had it at the beginning of the period. And therefore interests will be calculated for the year of period one. And we're indicating that by having the investment amount at the beginning of the prior period so that we can have a similar table formatted. So let's see what that would look like. This would be equal to the one thousandth times. I'm going to scroll up and pick up the 5%. I don't want that cell to move down again. So I'm going to select F4 on the keyboard, dollar sign before the B and to making it absolute so that when I copy it down, it does not move down. Note you only need a mixed reference, but the absolute works. Then the payment is going to be equal to, and I'll pick up the 1 thousand. I want to make that absolute. So when I copy it down, it doesn't move down. F2 for on the keyboard, dollar sign before the B and the one. And then we have a similar calculation here. We've got the prior amount, 1 thousand plus the sum of shifts nine left arrow holding down shift the 50 and the 1 thousand shifts 0 it up 1 thousand plus 1 thousand plus 50, given us the 2050, then I can copy this down. This is a similar format, just kind of a different starting points selecting these three cells. We're going to copy that on down. Let's do the good old copy down here. And so there we have it. We have the similar layout. Now, you can say, well, this doesn't quite make sense because now I've made seven payments here of 7 thousand. And so what we're gonna do is basically delete this last one. And that'll give us two are balanced of the 7,142. So it's a little bit staggered in the format, but hopefully that might be clear to you. You will do, we'll try it a different method to, so that might click a little bit more. But remember that this period 0 actually represents the beginning of the year. So we put it at the beginning of last year of the 1000s so that we can have the same structure and then calculate this the same way. And then the $50 is being calculated on the 1 thousand that we put in period 0. But we're kind of assuming happened at the beginning of period one, earning the 50 thousand in period one. And then we had another 1 thousand, which is a little confusing given the fact that, that 1 thousand would be there at the beginning of basically period two. So in other words, at the end of period one, you really got the 1050 that would be in there as you accumulate it, the interest, this payment then what basically happened at the beginning? You can think of these two days at the same day, right at the end of the first year, the first day of the second year, the next 1 thousand going in, bringing the amount up to 2050, calculating the interest on that would be at that one oh, three. And that would be what we would have at, at year two, then the 1 thousand would be put in. Again, we're really, what would happen is that the beginning of year three, you put the 1 thousand in at the first day we got up top kind of imagining the end of year two and the beginning of year three being basically the same, and so on and so forth, until we get to your six here, which once again does not have a payment because we put the payment at the end of last year, at the end of year five. We can calculate the interest on it and then we get to our ending balance. So this structure is the same format. We can come up to a little bit more complex of a table, which might give us a better grasp of this. So let's make a little bit more complex of a table and see if that makes it a little bit more. This time we're going to start with year 12 and so on. Same kind of format at the starting point. And I'll pull this down. And then we're gonna go to the Home tab Alignment and center it. Then we could say, okay, let's let's start the payment at the beginning of the year. So I'm going to say this equals the 1000-dollar payment. I'm going to select F4 on the keyboard, F4 to put dollar signs and Enter. Then we're going to stay at the start of the year. And we'll say the start of the year balance versus the Andy the year balance of the start of the year balance, which will be that $1 thousand. And then we're going to calculate the increase for that time period, which would be from January 1st to the end of year December 31st, all in the same year, we're saying this is gonna be equal to the 1 thousand times and we'll scroll on over to the 5%. I'm going to select F4 on the keyboard to make that absolute. So that times the 5%. And then we have the end of the year balance. So we now we've got two year balance, beginning and end equals the sum of the 1050, then we can say, alright, the payment for year two is going to happen at January. It's going to be the same. I'm just going to say equals the one above it this time. And then the year start balance will then be equal to the 1050 plus the 1 thousand we put up in the beginning. So that's our January balanced, January 1st balance. It's going to increase during the year January through December by this equals the 2050 times. I'm going to scroll all the way over to that five per cent. Again, the five per cent, and enter. So there we have that. And then the year-end balance would be equal to the sum of the beginning balance plus the three oh, one, oh three. About getting us to that 2153. And then we have another payment which would be 1 thousand. The starting balance would then be equal to the to the 2153. I'm sorry, hold on a sec. The starting balance yeah. It would be equal to the 2153 plus the 1 thousand. And then the increase would be equal to that 3,153 times scrolling over the five per cent up top. And then we'd have our ending balance equal to the sum of these two numbers. And there we have it. Let's do it one more time. And this time we'll figure that we're going to copy it down. Note that I didn't use an absolute reference here, I'm equally in the one above it. That's also another method if this whole column will be the same that you can do instead of using the absolute method, absolute value. So I'll keep that the year start balance is going to be equal to this number, the prior year-end balance plus the 1 thousand payment, that's the January balance. They're both within the table. There's nothing I need to do for absolute references there. Then the increase is going to be equal to that 400110400310 times. I'm gonna go all the way left and then up to that 5% that is outside the table. So I'm going to make it an absolute reference selecting F4 or putting a dollar sign before the B and the two. And then over here, the year-end balance is going to then be equal to the sum of these two. There's no nothing outside the table, so I should be able to copy that down. Then if I select these four columns and put our cursor on the fill handle and drag that down. Then we get to that 7,142. Once again, this one might make a little bit more sense, but obviously we had the structure, the table a little bit differently than we had over here. Or how you might structure the table in a normal type of annuity and just want to point out that obviously they're the same kind of thing that's happening is just basically when you're calculating the payment to be made, be made at the beginning or the end of the period. 16. Present Value Monthly Periods: Personal finance practice problem using Excel present value calculation with monthly periods, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along note that we're in the practice tab as opposed to the example tab. The example tab in essence being an answer key, information on the left-hand side get to populate that into the blue area on the right-hand side, the question says, how much would we have to invest to be, to have in the future 25 thousand rate of return at 24% years, three years, but this time not compounding yearly, but rather compounding monthly. We want to have in the future, 25,024% is the rate of return. That then is the yearly rate of return, not the monthly rate of return. When we look at the tables, you'll be able to determine why we picked 24%. And if you're working in a school setting, you can get an idea of the limitations that a school might have if they're trying to limit you to the use of the tables in the way that they format their problems. And then we've got three years that we're going to have to break out into months. So let's first do that. We're going to say, okay, we're not compounding this yearly, we're compounding monthly. That means we have to calculate how many periods we have, which is going to be three times 12 or 36 periods. Now that already when we do our running balance calculation, you could see how much more complicated that will be, because we're going to have to compound it 36 times as opposed to three times if it was compounded yearly. That then again, is one reason that many practice problems we'll focus in and 0 in on yearly calculations, even though many kind of real-life settings compounded monthly. So if you're in Excel, once you have the concept down, not really a problem to be able to copy and paste this information down for longer periods. Let's do the present value calculation. Note that this 25 thousand, the future, what we want to do with bringing it back to the current time period to see how much we can put in today that would be earning 24% compounded monthly for 36 period or three years to get to that end period. That's why it's going to be a present value calculation. I'm going to do it fairly quickly because we've seen it before, but I'm going to highlight the new things that will be involved. The major things you want to keep in mind is that that rate that's been given twenty-four percent is usually a yearly rate. And that's gonna be similar if you're talking about like a loan for a home loan or something like that, which you know, is a monthly payment. Generally, they're going to quote it as if it's a yearly rate. They're not going to give you the monthly rate because the monthly rate to be quite small and confusing and whatnot. So they'll give it to you in a yearly basis. But when you do the calculation, you need the monthly rate, which means it's going to be that 24 divided by 12, in essence. Now, again, the software can do that quite easily. So let's see what that will look like. It's gonna be negative to flip the sign present value shift nine, then we'll pick up the rate, which is going to be that 24, but that's the yearly rate and we're doing monthly periods. So now I got to divide that by 12. That's the new thing that we gotta do in terms of an Excel function comma number of periods. Now it was three years. They might give you three years, in which case you would take three years times 12. Or we already did that here, which is 36 periods. So 36 periods, comma, and then the payment that would be for an annuity. This is not an annuity present value. This is a function of one, present value of one, so two commas bringing us to the future value. The future value where we want to get to is the 25 thousand, picking up the 25 thousand and enter. So we're at the 12 thousand to 55 or 56 about, Let's add some decimals Home tab number group coupled decimals. So we're at the 12 thousand to 5558. Okay, so then let's do this with a formula basis. Same kind of thing. This is what you would probably do in practice. And then you would probably wanna do a running balance in practice. But before we get to the running balance, let's do the table that we're gonna do in Excel. But it'll be similar to an algebraic format, meaning we'll do the formula down here. So let's go ahead and hide these cells up top. I'm going to put my cursor on C, drag on over to E, right-click on those cells and hide them. We're gonna look at this formula which you could plug in algebraically, it's still just a straightforward present value. The future value over or times one over would be the future value of 25 thousand over one plus r. But now are, is not 24% but 24 divided by 12. We need the r that matches the number of periods. And then to the periods of 36 periods which are monthly periods, making sure that the periods then 36 periods match the rate, which is not the yearly rate, but the monthly rate. So in a formula it would look like this. We're going to say, all right, here we got the outer column is the 25 thousand. We're going to bring inside this inner calculation, as we have seen in the past, for the denominator, which would be one plus the rate. But now the rate, There's the new thing is gonna be equal to the 24 divided by 12. I'm going to make that a percent Home tab number. We're going to make it a percent. We can add some decimals and obviously rounds to two nice and evenly. Now note that I used 24 per cent in part so that it does round, nice and evenly to two. You can see that if we had a yearly rate of 5% or something like that, then the monthly rate would be something kind of ugly, something ugly to basically talk about, right? That's why a book problem will be limited to something like a twenty-four percent. If you're going to use the tables, obviously, you can still calculate this in Excel without a problem, no matter if it was an ugly number or not. But also note that when you're talking about rates, that's why we don't use monthly rates when we talk about them, even though will be compounding monthly. Because again, the yearly rate makes more sense, It's easier to deal with. So let's go ahead and underline that will go to the Home tab font group. And underline, There's our 2%. And then we've got the, we're gonna call this the one plus the r. One plus the r. And this is going to be equal to the SUM Shift Up Arrow, adding those up, making that up per cent Home tab numbers, obviously that would be 1.02 and a decimal or percent ties in it 102%. And then we're gonna take that to the power of n periods, periods to the power of n and n. Another new thing here is not three years now, but rather 36 months. And so as long as these months match up with the rate, same thing, rate, the monthly rate. In this case, we're good and we're gonna go home tab font group and underlined. And that's gonna give us then the result of the 1plus, our shift six carrot to the n periods. And that's going to be in the outer column, which is gonna be equal to the one or 2% shift six carrot to 36, and that's gonna give us two. Let's add some decimals. Home tab numbers, destiny symbolized. Then we're gonna go to the Home tab font group and underline it, and that'll give us our present value, present value. Finally dividing this out, this equals to 25 thousand divided by that desk normalized number, adding a couple of decimals, Home tab numbers coupled decimals, there we have it. So we've got that same 12 thousand to 5558, again, that we'd have to put down up front compounding monthly for three years or 36 monthly periods at 24% the yearly rate, which would be 2% monthly rate to get to the 25 thousand after that time period. Okay, so let's go ahead and indent this, selecting these items Home tab Alignment, indent. Let's indent this one again. Alignment and dent. Okay, now let's do this again. This time. Let's do a running balance table, which again it's a longer period because it got monthly periods. But that's okay because we have what's known as a spreadsheet in Excel, makes it easy. So we're going to then put our cursor on F, drag on over to I, right-click and hide, right-click and hide. And then let's do this one. I'm going to say this is just going to go from one to start at 001 to selecting those three. And then we're going to auto fill it, fill handle, dragging it all the way down 36 periods, no problem. Because, because Excel, that's why. And then we're gonna go to the Home tab, Alignment and center. And then we're going to say that the investment that we're going to start with, which I'm going to recalculate again to start at the starting point and prove that we will end than at the 25 thousand. So I'm gonna do it again negative, do it with our formula present value shift nine rate is the 24, but then I got to divide it by 12 because I need the monthly rate comma number of periods is going to be not three years, but 363 times 12 comma. And then the payment is going to be no payment. What am I doing to two commas because it's not an annuity, future value 25 thousand. And there we have our 12 thousand to 56 again. And now let's do our interests calculations and we'll do just a couple of them here. We won't do it 36 times. And then we'll drag it on down with the autofill. So this is gonna be equal to, and I will do it a couple of times because again, this one will be a little bit different due to the twenty-four percent needing to be monthly rate. So in other words, if I took that 12 thousand to 56 times 24, that would be the rate for a year and I got to divide it by 12. And that'll give us the monthly. I think it's worthwhile to kinda look at this two ways. Note that if I was to do this in a calculator for a problem, I would do it this way, 12 thousand to 56, about times 0.24. And that would give us about this. There's rounding involved and then that would be for a year interests if that was for a year, but it's only for months. So divided by 12, that would be the monthly amount. Or, and this is how you think about it in Excel. You can take the 0.2 for the monthly or a yearly rate divided by 12 given you the monthly rate, 2% then times the 12 to 56. And you'll get to that same result about rounding involved. Alright, so then that means the investments can be equal to 12 thousand to 56 plus T2 45. Let's do it a couple more times and then we'll go back in and auto fill it. So we're going to say this is now that 12 thousand to 1200502 times the twenty-four percent and then divide it by 12. And then this is going to equal the prior amount, that 12,005 over one plus d 250. Let's do it two more times here. This equals the 12,751 times the twenty-four percent, But then divide it by 12. This equals the amount above it plus the amount to the left. Now we're at the 13,006 and this is gonna be equal to 13,006 times the twenty-four percent divided by 12. This will equal the 13,006 plus 260 and so on and so forth. Now, I'm going to delete this and do it again, but this time keeping in mind that we're going to auto fill it down and making any absolute references that we have to do it. So we'll delete this, selecting this item. No, don't delete it. Don't let God all that work on. Okay, let's do it again. This is going to be equal to the 12 thousand to 56 times the Twenty-four. Twenty-four is outside of where I want to be here. I don't want it to copy down when I auto fill. So I'm going to select F4 on the keyboard, putting a dollar sign before the B and four, you only need a mixed reference, but an absolute will work, then divide it by 12. That is a hard-coded or typed in number. That one will continue on when I copy it down as well. And then this one is simply going to be the one above it plus the one to the left of it. It doesn't have anything outside the table. Therefore, I want them both to move down relative, so I don't need to do any absolute references there. Then I can just select these two. And once again, I don't care how many periods there are because I can just grab the fill handle and drag it down. Doesn't even matter. You can have we can do a whole mortgage, 360 monthly payments for a 30-year mortgage, which we might do later. And whatever. I don't care why, Because Excel, that's y. And then we get to the bottom line here, that's gonna be the 25 thousands. So we get to 25 thousand proven to us that we do indeed start at the 12 thousand to 56. If we compound monthly using this calculation, we get to the ending 0.25 thousand there. Let's do it with our tables. So if we do the tables here, we got the investment. The investment is going to be the 1225 thousand that we're gonna present value. Now again, this is another one where you look at the tables. We've been using the tables. And I'm sorry, I'm saying again a lot. I notice I'm saying again a lot. So if that's annoying anybody I'm working on, I'm trying I'm trying to stop. I'm trying to stop. But we got the percents up top and the periods on the left, the periods before we've always thought as years and the percents as yearly percent. So as long as those two things match, we're okay. But this time we need 36 periods, which are monthly periods. And therefore we have to match the related percent, which needs to be a monthly percent, which would be the 24 divided by 12, which would be two. Now, note that if this was something like five or something like that, you wouldn't be able to find the percent here because one, it wouldn't be even and they only have even percents. And two, it would be smaller than one. So if because it's a monthly percent, so notice how severely limited the tables are when a practice problem starts dealing with monthly time period compounding as opposed to yearly compounding. That's why most book problems will simplify problems that might often be monthly in real life to yearly. So they can force you to use the tables. That's not a problem when you're, when you're using Excel, but if you're forced to use the tables, that is a problem. So you'll see percents like twenty-four percent, because if I divide that by 12, that gives me a nice two per cent, which is nice and even that I can then use in the tables, don't let that limitation make you feel like that's a real limitation on in life. Because normally people don't take your calculator away or your Excel worksheet when you're doing stuff. And so it's not a problem, therefore, but when you're in a book problem tables, that's it. Okay, so we've got the 236, which is way down here. Notice I'm limited to like three years. I can't go too far over that because it only goes to 50 payments and it's separated, kind of weird down here because five years would be 60 months, right? And a monthly period and whatnot. So in any case, we're limited to the number of years if it's a monthly as well with the table. So 36 I said it was thirty-six point 4.4909020 to adding some decimals Home tab numbers destined to moles. And this is from the table. And then we're gonna go to the Home tab font and underline. And that's gonna give us our present value. Present value, which will be equal to the 25 thousand times the 0.4902. Adding some decimals by going to the Home tab numbers coupled decimals. Notice this number slightly different, of course, than what we got here. Well, let's unhide some cells. Double-check this due to rounding tables, rounded to four digits. Okay, let's put our cursor on, be dragged on over to k b, k, right-click and unhide. So now we've done it this way. We've got the 12 thousand to 5558. We did it this way with the formula 12 thousand to 5558. This is basically the amount that should in essence be on actually, that's not the amount. If you want the amount on the table, you could calculate it this way. It will be the 12 thousand to 5558 divided by the 25 thousand. Adding some decimals, Home tab numbers. Decimals, that's the amount that would be on the table. Notice it doesn't stop at four digits. When we look at the table, it does stop at four digits. That's why we have this rounding difference between the calculation and the table calculation. Note that's not a problem in real life due to it being an estimate in any case. So it won't affect our decision-making process most of the time, but it will be some difference that a school could use to force you to see that you use the table. And if you don't, they can say See you didn't even, you didn't follow the directions. F. And so you don't want that to happen. So be aware of that. 17. Present Value Annuity Monthly Periods: Personal finance practice problem using Excel, present value of an annuity using monthly periods, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side going to populate that into the blue area on the right-hand side, the information says, how much would have to invest to be able to take out each month? $1500 for three years. So for three years, we would like to take out monthly $1500, the rate of return is going to be 12%. Now note what we're looking for is a lump-sum that we can then have that's going to be generating interest on it as it's in there, but then we're gonna be pulling out 1500 from it. So this is actually a present value type of a calculation of an annuity. So we're thinking of the annuity, which would be a series of payments of the 1500s over the three years, but on a monthly basis. So we do this on a monthly process that we're taking out 1500 each month, present value them to the starting point at this point in time. And then think and then we can basically prove that with our running balanced type of calculation. So in other words, the number of months that we're looking at is going to be the three times 12 or 36 months. So we want to be able to take out $1500 for 36 months. Let's do our present value calculation. It will be the present value of an annuity type of calculation, now slightly different. So we've seen these before. If you want to do this a little bit slower for a yearly present value, take a look at prior presentations. We're going to focus in on the new thing. So we'll say negative to flip the sign instead of equals present value shift nine, the rate is gonna be the 12%, but that rate is a yearly rate. Notice we generally assume that we're given the yearly rate unless told otherwise, even though we're gonna be working with something that's gonna be on a monthly basis. And that's generally what will happen. That's just the convention of how we use rates. Because if I was to give monthly rates, oftentimes you would have a small, ugly looking rate, although this one would be 1%, 12 percent divided by 12 months, which is nice and even, which is why we picked it. But in practice, if it was like a 5% yearly rates, you can see the monthly rate would be a problem. So we're going to divide that by 12 in our calculation. That's the new thing. Comma number of periods is not gonna be three years. But if that was what we're given, we would be three times 12. Or we can just we've done that here, it's the 36 periods then making sure that the periods matches the rate. And then comma, now we are doing an annuity, so we're looking at payment here. So the payments are gonna be 1500 and Enter, that'll give us the 45,161. So the idea then being that if we had the lump-sum of 45,161, then we should be able to take out 1500 for three years each month of those three years or for 36 monthly periods. If we're earning a return on everything that's still in there at the 12% yearly rate, which would be 1% monthly rate. So let's do a running balance calculation to kind of prove that to ourselves. Now I'm gonna go ahead and hide some cells. I'm going to put my cursor on column C, drag on over to E, let go and right-click. Let's hide these cells. Right-click it doesn't want to, right-click, isn't staying there and then hide. Okay? So then we're going to say 012 and we're going to drag this all the way down to 36 periods, noting that we have more periods here, But if we're using Excel, not a problem, it should be okay. So we're gonna put our cursor on the autofill handle. Left-click, drag it on down to 36 periods. Look how easy that is to do. And then we're gonna go up top Home tab, Alignment and center that. It's just incredible, just incredible the ease at which we could do that with the tools at our disposal. So then we're gonna, and I'm gonna call this the increase. This is the increase. And then I'm going to say the investment, I'm going to recalculate it again just to practice it. It's gonna be negative. Present value shifts, nine, rate 12%. But then I got to divide that by 12 because I'm looking for the monthly rate which would be 1% comma number of periods is not three years, but three times 12 or 36 periods because their monthly periods, comma payment 1500s, and enter. So there it is, again, about 45161. Let's go ahead and then calculate our increase. So whatever still in the annuity would be the 45,161 times the rate of 12%, but that 12% is the yearly rate. So I got to divide that by 12. That's the tricky new thing. That's the tricky new twist. Note that when calculating that you might do it this way. 45161 times the 0.12 or 12%, that would be the interest for a year. That's what I would first do in a calculator if I had a paper and pencils usually, and then take that and divide it by 12. That would be the monthly amount about or you can basically take than the rate 0.12 divided by 12 to get the monthly rate, one per cent, which is kinda what you do when you think about an Excel function as we just saw usually. And then multiply that times the 45161 and you get about the same number. So let's go then. We have a payment, so we're going to be taken out each time. I'm going to make this a negative by saying negative instead of equals and point to that 1500. And then we had the prior investment equals the one above it. Plus, and I'm going to say the sum of using the trustees some function shift nine, and I'm going to add these two together, summing them. That's what somebody means. Even though this one will basically subtract because it's a negative number of closing up the brackets. The 45161 plus the 452 minus the 1500s gives us the 44113. Let's do that a couple more times before we use the autofill to do it the easy way we're taking now the 44113 times the 12% down here, but that's the yearly rate. So we're going to divide it then by 12. That's the monthly amount. We got the same negative 1500 were taken out each month. So we're increasing or earning 100 or 441 each period, but we are taking out more than we're earning. Of course, bringing down the investment amount, which means that our earnings are gonna go down as we go on each period, although we still have earnings each time we compound. So this is going to be equal to the 44113 about plus the SUM shift nine left arrow holding down shift left again shift 0, closing up the brackets and Enter. Let's do it two more times here. This equals to 4554 times the 12%. That's the yearly rate dividing that by 12 for the monthly amount. This is gonna be the negative of the 1500s. I'm going to select tab to go to the next cell. This equals the item above it plus the SUM, the sum shift nine left arrow holding down shift left again, closing up the brackets Shift 0. Let's do it one more time. This equals to 45985 times 12%. That's the yearly rate divided by 12 to get to the monthly amount Tab to go directly to the cell to the right, negative to make it a negative number of the 1500s, this is going to equal the amount above 4585 plus the SUM shift nine left arrow holding down shift left again, shift 0, closing it up. There, we have it. Now let's do the whole thing again, but the easy way so we can auto fill it down. So I'm going to delete what we've done thus far, selecting these atoms. No, don't, don't, don't do. Yeah. Oh my gosh. I can't believe you delete it. That's okay. We'll do it again because we're gonna do it the easy way this time. This is going to be equal to the 45161 times, times the 12%. Now that 12% is outside of the table here, so we want to make it an absolute reference by selecting F4 on the keyboard dollar sign before the B and the eight, you only need a mixed reference. But an absolute reference is easy to think about. Then we're going to divide that by 12. That's what we call a hard-coded or typed in number that will also copy down as we auto fill down. So this is going to be equal to the payment, I'm going to say negative of the payment. That payment also outside the table. Therefore, we want to make it absolute because we don't want it to move down when we copy down. So I'm going to select F4 and the keyboard dollar sign before the B and four. Then this one is going to equal the 45161 about plus the sum, SUM shift nine left arrow holding down shift left again and shift 0. And we'll close that up. Now there's nothing here that's outside the table. So although this is our most complex formula, all within the table, I want it all to move down relative when we copy it down, so no absolute ties in necessary. Let's go ahead and select these then. And we're just going to copy it all the way down, putting our cursor on the fill handle, dragging it down 36 periods. Right on, down, there we go. And the end result at 0, indicating that it looks like we did it correctly. So that's going to give us an indication. So that's basically what you'd want to do in practice. Now let's do a book problem types of things where we will do with a formula and then we'll do it with the tables. So we're going to put our cursor on column F. Let's drag on over to j. Let go right-click, and let's hide those cells. Let's hide those sales. My right-click, it keeps doing something funny like that. I want to hide those, want to hide those cells. Okay, so then we're gonna do this. You could do this and just plug it into the formula down here, which is kind of an ugly formula. So it would be the present value of an annuity equals the payment, which would be the 1500 times one minus one over one plus r, which is gonna be the 12% divided by 12, or one per cent to the number of periods, which would be three times 123 years times 12 or 36 periods. Those are the new things. That's why I'm saying it kind of emphasis like with an emphasis on it, because that's the new thing from the light. So that's the new stuff. So the 37 next period's divided by R, which is the rate, which is 12 divided by 12 months, or 11 per cent. So let's put that into our formula as we've done in the top, making a table out of it. Because that's always good times. And then we'll emphasize the new stuff again in our table. So this isn't new stuff. This is the same stuff that 1500, but making sure that's our monthly amount though. And then we have the numerator. And I'm going to put the calculation of one here. Which is that one right there. And then I'm going to call this numerator to numerate, numerate Tor to, which I'm just going to put one here and that's gonna be this one right there. And then we're going to put this as the denominator of one plus r shift nine shifts six carrot to the n periods colon because we're pulling up to the inside. One is gonna be here. The rate is going to be our right there. Here's the new thing. Here's where the new thing happens. It's going to be equal to the 12%, but that's the yearly rate divided by 12. Let's percent defy that by going to the Home tab number group percent of phi. It's 1%. That's why we made it nice. And even again here with the 12 per cent yearly rate, obviously if it was something like 5% or something, we have some small, less than one decimal monthly percent, which is okay for Excel, but it can be a little confusing to discuss and talk about. Then we're going to go to the Home tab up top font group and underline, this is gonna be what we'll call our subtotal, subtotal, a SUB TO Tau, which is going to be equal to the SUM, the sum of these two items. And we'll make that into a percent Home tab number per cent defy were at the 10, 1%. We're going to take that to the number of periods. We're down here at the number of periods now, That's going to be to the number of periods, which is n, and our calculation which was 36. This is new, not three years, 36 months, 36 months for three years. And we're gonna go to the Home tab, fonts group underlying. And then that's gonna give us then our 36. That'll give us our total here, which was the one plus r shift nine to the end but without the colon, because this is the end result which we are going to bring into the outer column, which will be then the one-on-one percent shift six carrot to the 36th periods. And that gives us one, which we're going to add some decimals to Home tab number, cinema lysed. It's been destined to mobilize. So there we have that. Let's do some indentations here. Let's go ahead and indent this whole thing. Home tab Alignment and dent. And then let's indent this thing by going home tab Alignment, indent, and then let's indent this and go home tab Alignment in den, that looks way better, that looks way better. So then this is gonna be the numerator. And then I'm gonna say this is a subtotal, so SUB TO tau. And we'll bring this to the outside. And so now we're going to go ahead and divide this out. This is going to be then the one over that desk normalized number. We're going to add decimals it by going to the Home tab numbers. We're going to normalize that one. Let's bring that one out too. So I'm going to indent that Home tab Alignment and indent that all the way out here. I'm going to underline this number, font group and underline. And now we've got the numerator, which so the end of the new moraine torr, which is now going to be one minus this whole thing represented in this column, one minus that whole thing. Let's underline here, Home tab font and underline. This is gonna be equal to the one minus the destined them allies number, adding decimals to it, Home tab number, deaths and normalizing it. And then we're going to have the denominator, denominator, which is gonna be the rate. And that's simply going to be equal to the 12th, but that's the yearly rates. We've got to divide it by 12 to get the monthly rate or 1%. Home tab numbers per cent define to that 1%, underlining it by going to the font group and underline that's gonna give us another and we'll call it a subtotal, bringing that to the outer column, and that'll be this whole piece here now. So we're gonna, we're gonna divide this out. This equals the numerator divided by the denominator, which is gonna be 30 about, Let's add some decimals Home tab number, desk and hemolyzed. And then we're going to say that's finally going to give us to the present value of the annuity at the bottom of the line, the bottom line, which is gonna be these two things multiplied together, which are represented in the outer column here. That's the 1500s times the 3D 0.107 and so on. Let's add a couple of pennies here by going to the Home tab number a couple of pennies, we're up to 45.26161. Let's put an underline here while we are at it. Home tab font group underlined. So there we have that again. Now let's do it with the tables. Let's do it with the tables. So let's go ahead and hide some cells here from K on over to P. K to P, right-click. And let's hide those cells. Don't delete them, just hiding them. And then we're going to say this is gonna be the payment, payment. And this is going to be equal to the 1500s. Now when using the tables, note the limitations of the tables. We had to limit it to three years to make sure that we had 36 periods. If you go much over that, you're going to have limitations on how many periods are in the table. And we picked a nice even 12% because if you divide that by 12, you get 1%. So in other words, when you look at the table, the percents in our past problems have been always percent per year because our periods were a yearly period. But if you have something other than yearly periods like months, then the periods represent months now instead of years. And you have to have the matching percent up top, which means that if you're given a yearly percent, if it's a small yearly present like 2% a year than the monthly percent. You got to divide that by 12. It's not gonna, you're not gonna be able to use the table. We used 12%. Because if that's a yearly percent and you divide it by 12, you can have the monthly percent, which is 1%. In this case, we used 36 or three years, which adds up to 36 periods. Because if you use something like five years, you're gonna be at 60 periods. And again, you're limited to the table. So just note the limitations of a table. Those are limitations in a school kind of setup. If they're going to force you to use tables in a setup where you don't, you're not forced to use tables. You're not limited by them because you're simply going to use a calculator or Excel to do the calculations. So we've got the 30.108. So this will be 3.1080 adding some decimals. And we're going to say Home tab number adding a couple of decimals. Let me double-check that. This was at 36.108130, 30.108. That's right. So then let's multiply this out. This is gonna be 1500 times the 30.108. And so there we have it. Let's say this is from the table. This is a present value of annuity underlining here, Home tab, font group underlying. Let's add a couple of decimals to note the rounding. Notice that this is rounded to three to four digits here, typically from the table. Let's go ahead and unhide some cells now, putting our cursor on column B, dragging over to our H-Br, let go and let go. Right-click on the selected items and then unhide. So now if I add a couple of decimals here, Home tab numbers, we got the 45, one, sixty one, twenty six. We got that with our running balance and then we kind of proved it by going down to 0. And then we've got the same thing here, the 4545, one sixty one twenty six here. And then with the table, we got the 45162 slightly different due to the rounded a four digits. If you were to see the actual number, it would be closer to this that we saw when we did our mathematical calculation. That difference is due to the rounding from the tables. 18. Future Value Monthly Periods: Personal finance practice problem using Excel, future value calculation, using monthly periods. Prepare to get financially fit by practicing personal finance, we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side going to populate that into the blue area. On the right-hand side, we have the information of an investment at 50 thousand, the rate of return thirty-six percent, we're going to say that's a yearly rate, the years, two years, but we're going to be compounded monthly. So in other words, the question is, where will we stand in the future if we have an initial investment of the 15 thousand of the 50 thousand rate of return, 36 thousand per cent per year. And it's gonna be for two years, but we're going to be compounding monthly. Note that the Thirty-six percent will make more sense as to why we chose it when we look at the limitations of the tables when you're using that format of calculations. So we're gonna be looking at our future value type of calculation. There's a couple of different ways we can do this. Sometimes this is a type of problem where it's kinda easiest. Oftentimes to just run the table and think about where we will be in the future as we do a running balance type of calculations. So let's start off with that this time. Note that we have two years. We're not going to be compounding yearly, but rather monthly. So that means the number of periods is going to be equal to two times 12 or 24 periods. Obviously, when we compound monthly, we have a whole lot more periods. So when we do a running balance, it can be somewhat more tedious. But when doing it in Excel, not really a problem because we can just copy it down, use our autofill type of calculations to do So let's do that first. I'm going to start with period 01, and then select those two periods. Put our cursor on the fill handle, drag it on down to 24 periods. And then let's center that Home tab Alignment and center. Then we're gonna have our initial investment which is going to be equal to the 50 thousand. And then we'll do our calculation with the interests or it could just be the increase. Let's call it for whatever type of investment that we have at that thirty-six percent, which is probably not interests if we've got thirty-six percent, but in any case this is gonna be equal to the 50 thousand. And then we're going to say times the 36 per cent, but that's the yearly rate. So when we go to the monthly, we have to divide that by 12. That's gonna be the new thing that we're taking a look at. So we're at that 1500, which is our darn good Monthly returned typically. So let's see how we can calculate that a couple of different ways. You can take the 50 thousand, you can then multiply it times 0.36. That would give you the yearly return and then divide it by 12 to get that 1500. Or you can take the 0.36 divided by 12 to get the monthly rate, which would be 3%, which is nice and even which is the reason we chose thirty-six percent because that 3% is something that we can easily look up on a table, even though we're looking at monthly rates, then you can take that and multiply it times the 50. And that'll give you once again that 1500. Let's do this a couple of times. This is going to be equal to the 50 thousand plus the 1500s. That's going to increase the investment to 515. Let's do it a couple more times and then we'll do the autofill. This is gonna be the 515 times the Thirty-six percent divided by 12. That's the new thing. And then this is going to equal the 515 plus the 1545 gives us the 5345. Let's do a couple more times. This equals the 5345 times the 36 per cent, then divide it by two to get us the monthly percent or monthly amount. However you want to think about it. This equals the 53,045 plus the 1591 given us the 546. Thirty-six, let's do it one more time. This is gonna be equal to 54 to six Thirty-six times that thirty-six percent divided by 12, given us the 1 sixth 39. Now we have the balance of the 54636 plus 1 sixth 394, 56 to 75. Let's do it again. Keep it in mind and setting it up as we go so that we can auto fill it down, adding absolute references when necessary. I'm going to delete what we've done so far. Really, you're going to delete it. I'm going to undo know. We're gonna do it again here. We're gonna, we're gonna think about basically auto-fill When we do at this time, this is going to be equal to the 50 thousand times the Thirty-six percent. Now that is outside the table. So that's typically something that we want not to move down when we copy it down. So we're going to use the absolute reference, which is F4 on the keyboard, or dollar sign before the B and three, you only need a mixed reference, but an absolute one works. And then we need to divide that by 12. The 12 is a hard-coded or typed in number. Therefore, it'll copy down as we go to. So then this is going to be equal to the 50 thousand plus the 1500s. Although this is a more complex calculation, nothing is outside the table. Both of those cells we want to move down relative when we copy it down. Therefore, no absolute references necessary here. We're then going to select those two cells, put our cursor on the fill handle, left-click on it and drag it on down 24 periods to get to the 101640 about. There's that. Let's do it again. Let's do it this time. Let's do it with the future value calculation in terms of an Excel worksheet formula or function. This is probably the two ways that we would do this most commonly in practice. And then we'll move on to the table and the mathematical formula. Two ways that you might do this in a school typesetting more likely. Let's go ahead and hide some cells first, I'm going to put my cursor on C, even though it's really skinny over here. And then scroll on over to F. Let go, right-click the selected area and hide those items. And then we'll do our calculation here. I'm going to do it more quickly than in the past because we've seen these in the past, but I'll kind of emphasize the new areas. So I'm going to say negative future value shifts nine. This is all the same, but then the rate is that 36% and we got to divide that by 12 because we're looking for the monthly rate. So divided by 12, that's the new thing. Comma number of periods would be two years if compounded yearly, but now 242 times 12, which we already have down here. So I'm just going to pick up the 24 comma. This is not an annuity, so we don't have a payment commas that brings us to the present value, which is at the 50 thousand and enter. So there's our one-to-one six forty. Again. We can also, of course do that with the tables. So we can say that we have the tables, which is the payment, let's say, which is gonna be the 50 thousand. When we look at the tables, then we're not looking at the periods no longer represent years to us. They have to represent months. And the percentages need to represent them to relate it. Monthly percents, not yearly presents were given the yearly percent. So we'd have to take that and divide by 12. So if we take 36 divided by 12, we would get three. So the monthly percent is three, which you can see why we're chose that percent if we're working on a book problem where we're forced to use tables. Because if I use a percent that's uneven or less than one, then we're going to have a problem with the tables. So remember, if you're in a school setting where they're going to force you to use tables, they will often be limited in these ways and you can kinda keep that in mind as you're working through the problems. So we got three and then we're also limited to the number of periods. That table only goes down to 50 periods. So we've got two years here, which in months would be 24, which is still pretty far down on the table even though it's only two years, so 24 and then three on the percent is going to give us that too. 03282.03282.03 to eight, adding some decimals, Home tab number group a couple of decimals or four of them. This is the amount from the table underlining that Home tab, font group and underline. And that's gonna give us then our MT, which we'll call future value. Let's say this equals to 50 times that 2.03284101640. Let's add a couple of pennies Home tab number, a couple of pennies, even there. Now, let's do it again this time with the, with the mathematical formula pointing out the differences here. If we were to do a mathematical formulas such as this for the future value, let's hide a few cells. Hiding this cell I can't see what it is but that skinny sell on over to, I let go and right-click and we'll do this again. Don't delete it, hide it, Hide it. And then we've got the future value equals the present value, which would be the 50 thousand times one plus the rate. The rate would be the Thirty-six divided by 12 or three to the number of periods, which would be two years times 12 or 24. Those would be the major changes as you plug it into your algebraic equation, which we will do in the format matt of a table of top. We're going to save. We'll start off with the present value in a similar way as we've seen with prior presentations at the 50 thousand. And then we're going to say that we have these sub calculation, which is going to be the one plus the rate to the n periods that we're going to pull that into the inside, which is one. The rate is going to be equal to the 36th, but we got to divide that by 12. This is the new thing. That's the new thing here. Home tab number per cent define that gives us a nice even three, which is not likely to happen. Oftentimes when you're really doing that in real life because you won't have a nice even present. But we're going to go to the Home tab, font group and underlying. Let's give us subtotal here, which is going to be oral. Just call it one plus the rate, which is our subtotal, equals the SUM, sum of those two numbers, making that a percent Home tab numbers, we could add a couple of decimals, 1.03, or make it a percent 103 per cent when we do. And that will then be taken to the number of n periods and periods, periods. So this is going to be not two years but 24 periods because we have monthly periods now, that's one of the new things. Home tab, font group and underline. And then that's going to give us, we'll call it the one plus the rate shift to the ships six periods of n periods. And we'll put that into the outside. This equals the 103 per cent shift six carrot to 24 periods. Adding a couple of decimals Home tab numbers. Deaths in a more lies in that cell. Fonts group underline. And that'll give us our future value. Let's call it the future value. Future value, which is going to be equal then to the 50 thousand times the 2.032 and so on gives us our 1011, 40, adding a couple of decimals there, Home tab number group coupled decimals, and make it a little wider so it can handle the decimals that are added. There we go. Let's do some indentations selected in these cells. And let's indent them alignment and indent, alignment group indent, and then alignment, droop and indent. Okay, so now let's unhide some cells putting our cursor from B to K so we can see what we've done thus far. Btk, let go, right-click and unhide. So now we had our, we had a running balance getting us to the 101640. We had our 101640 with our Excel formula, which we can add a couple of pennies to if we want. Number group, a couple of pennies, one-on-one, six thirty-nine, seventy one. And then we got 101640 on the tables due to rounding from the tables. And then we've got the 101, six, thirty, nine, seventy one also with the Excel, with the mathematical formula. I'm going to delete this up top. And this number right here from the tables is rounded to four digits. You can see it matching up to this number here, which is actually longer than four digits, which is the result or the cause of the slight difference. Here for rounding. 19. Future Value Annuity Monthly Periods: Personal finance practice problem using Excel, future value of an annuity calculation using monthly periods. Prepare to get financially fit by a Practicing Personal Finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side, I'm going to populate that into the blue area. On the right-hand side, we have a savings type of scenario. We're going to imagine we're going to invest each month One thousand dollars, not per year, but per month. We're gonna do it for 1.5 years on a monthly basis. The rate of return is gonna be the 12%. We're assuming that's the yearly rate. So when we think about the monthly component for it, we'll have to break it down to a monthly rate, which would be the 12% divided by 12 or one per cent. So first let's think about the number of periods that will be covered here. If we're going to talk about 1.5 years, 1.5 years, we're going to take that 1.5 times 12, that would give us 18 months. So the number of periods we have in months will be 18 months. We're going to put in 1 thousand per month over that 18 month or 1.5 years at the yearly rate of 12%, which would be a monthly rate of one per cent. Let's first think about that with a table that's going to be the starting point with this type of investment, which I think is most intuitive to think about. So I'm going to say this is gonna be from period 12 and so on. Notice I'm starting at period one instead of at period 0 because we're looking at an annuity here. And typically the annuity is calculated at the end of the period. So we'll start at the end of the first period. Selecting those two items. I'm going to drag that on down to our 18 periods. Obviously, this running balance calculation table is longer when we're talking about monthly period instead of a yearly kinda calculation. But with Excel, easy to do, we can just drag it on down, not a problem. We're going to center that by going to the Alignment Group and center. There we have it now this might be interests, I'm just going to call it an increase. Because it could be interests are it depends on the investment that we are in as to the format of the gains or whatnot that we will be getting from it. And we're going to say that the payment will be $1 thousand. So that's gonna be the payment that we're putting in to the investment. We're going to say that happens at the end of the year, therefore, no interests accruing on that first payment. So that's gonna be simply our starting point at that $1 thousand than a year later, we're going to have what are increase would be, which will be interest or dividends, or basically gains if we're in stocks and whatnot. And we're going to assume that that's at the 12% gain, which is the yearly rate. But we're talking about months, in this case. 1 thousand times the 12% that would be per year divided by 12 to get the monthly amount, which will be around ten. Now if we thought about that in the trusty calculator, you could do it a couple of different ways. Normally, I would do it like this if I had a calculator and I had to do it by hand, right? 1 thousand times the 0.12, the yearly rate would give us the interest if it were for a year, 120 for a year, but it's per month. So I got to take that and divide it by 12. So we get the ten. Or you can think about it this way, which is kind of the way you need to think about it when you're looking at Excel functions, which would be the yearly rate, 0.12 divided by 12 for the monthly rate of 1%, then times the 1 thousand. And that would give us our ten. Notice that that rate that we used, the yearly rate of the 12% is nice. And even so we can divide it by 12 and get the monthly rate of one. That's not always the case when you're doing that process. But for book problems that could be necessary if you're gonna be using things like tables, having ugly-looking numbers that are below 0 and or nice or not nice even numbers is not a problem. You're doing this in Excel. Okay, So then the next payment is going to be the payment of 1 thousand. And now we're going to say that and let's make the payment. Well, then we're going to say this will equal the 1 thousand plus the SUM shift nine left arrow holding down shift left, again, closing up the brackets. So that would give us the 1 thousand plus the 1 thousand plus the ten or the 2010. Let's do it a few more times and then we'll do the autofill to copy it down, we'll do it then the easy way. In other words, let's go ahead and say this is going to be the 2010 times the 12%. We're gonna take that and divide it by 12. And that'll give us tab Twenty about. And then we're going to say the payment is gonna be the same 1 thousand that we're putting in every month on a monthly basis. This is gonna be the prior amount plus the SUM or some shift nine left arrow holding down shift left again, closing it up, shift 0, Enter. So the 2010 plus 224,013. Then we're going to calculate the 3,030 times the 12% then divided by 12 that I'm going to select tab. And the payment will once again be 1 thousand. So our new balance is going to be the 3,030 plus the SUM some shift nine left arrow holding down shift left again. Plus the 1 thousand and the third, closing up the brackets gives us 4,060. Let's do it one more time and then we'll go back and do it the easy way. This is the 4,060 times the 12% divided by 12. I'm going to select tab. Payment is going to be equal to 1 thousand tab. This is gonna be the prior 4,060 plus the SUM, some shift nine brackets of the 1000s and the 40, closing up the brackets. And there we are at the 500101. Now we're gonna go back and do it again, but thinking about how we can auto fill so we can do it the easy way. So we're going to select these cells, delete them, I'm going to delete them and start all over again, but that's okay because this time, the easy way, this is gonna be the 1 thousand times the 12. And that 12 is outside the table. So I'm going to make it absolute by selecting F4 on the keyboard. Then I'm gonna divide this by 12. That 12 is hard-coded or typed in, and therefore, it will be copied down as we copy the cell down, no need to do anything special to it for that to be the case. Then we're going to say this equals the one thousand. One thousand needs to be the same cell when I copy it down. So we're gonna make it an absolute reference selecting F4 and the keyboard dollar sign before the B and the three. Then we're going to say this is gonna be equal to the one above it plus the SUM some shift nine, the ones to the left and close up the brackets. Although this is a more complex formula, everything's in the table. Everything should move down relative when we copy it down. Nothing special needed, no absolute references. Therefore, now let's go ahead and select those three cells. Use our autofill handle, clicking on it, dragging it on down to 18 periods. And at the end of the day, at the end of the time frame, we get the 19615 about. That's gonna be our ending result. Let's calculate it again this time using the future value of an annuity calculation in Excel, the function, these two components are probably the things that would be most useful in practice. Then we'll move to the mathematical formula and the tables, things you might often see in a school setting more likely. Let's go ahead and hide some cells. Putting our cursor on column C, dragging over to column G, C to G, right-click those cells and hide them. Then we're gonna do our calculation here. I'll do it a little bit more quickly because we've seen it in the past, pointed out the new things that will be here. This is going to be negative to flip the sign future value shifts nine. The rate is gonna be that 12%, but that's a yearly rate. So we've got to divide that by 12. That's the new thing. That's the new thing we're doing here. Then comma number of periods would be years if it were yearly. But no now is to 1.5 years times 12 or 18, which we already have. So I'm gonna be picking up the 1800s instead of the 1.5 years to 18 months comma payment, payment is going to be the 1 thousand, which is pretty straightforward as long as we make sure that we know that that's the payment per period, which in this case is per month. Okay. And then we're going to say Enter, we get that 19614. Let's add a couple of pennies this time Home tab Alignment, couple of pennies on the decimals. 1960s, 14, $0.75. Now let's, let's do it the mathematical formula way and we'll point out the differences that happened here, which will be with the rate in the periods again. So let's put our cursor on column. I think that's h. I can't see it too well because it's kinda, it's hidden. But that's skinny column. We're gonna go to that one on over to j. Let go right-click and hide those cells were looking at the formula down below, which is the future value of an annuity calculation, which is calculated as P times one plus r. R being the rate, not the 12%, but 12 divided by 12, which would be 1% to the number of periods, n, which is not gonna be 1.5 years, but rather 18 months, which is 1.5 times 12. Those are the new things, minus one divided by the rate, once again, being not 12, but 12 divided by 12, which would be 1% the monthly rate. Okay, so let's do it. Let's do it then. Let's do it in our table format. We'll do the table format. So on the outer column we've got the 1 thousand. Then we've got the numerator. The numerator, which is going to be then one plus the rate. So we're right here at the rate now the rate is going to be equal to the 12%, but we're dividing it by 12 for the monthly rate, making that a percent Home tab number group per cent, define it 1%, font group and underline. Then we'll get the subtotals sub TO tau, which will equal the sum of shift up, arrow holding down, shift up again and enter. Let's make that 8% as well. By going to the Home tab numbers, you can add some decimals, 1.01 or make it a percent, which would be 101%. Then we'll take that to the number of periods we're right here in the formula. So we're going to take that to the number. Of periods, which we can say is called N in our formula. And that n is represented by the 1800s, which is in months. So it's not 1.5 years, but 1.5 times 12 or 18. And we're then going to underline that Home tab font group and underline. And that'll give us, let's call it another subtotal, subtotal. And this is gonna be equal to the 101% shift six to the carrot of 18, enter, adding some decimals to that so we can see what's going on in their home tab number group desk and a mobilizing it? Yes, In a mobilized. Then we're going to say less. One, One, One right here. We're right there on the numerator still one. Underlining that by going to the Home tab fonts group and underline. And then finally, we'll bring that out to the outer column and we'll call that the numerate, tore. Numerate, tore numerator. I can't. Okay, here we go. This is going to be equal to this number minus the one. Adding some decimals, Home tab number, group deaths and normalized. So there we have that. Let's do some indentations here. Let's select these. These items. Go to the Home tab Alignment, indent this item. Home tab Alignment in dance. So there we have that. And then we just need the denominator, which is the rate denominator. I typed it better that time. Well, it's faster. I'm not even sure if it's spelled if I spelled it wrong and I apologize, but the rate is gonna be the 12% divided by 12. That's the new thing because we need the monthly rate, not the yearly rate. Home tab number group and percent of phi, that font group underline it, and then we'll add it and make it another subtotal, subtotal. Bringing that to the outer column, that's gonna be this whole thing that we finally got done calculating, which is going to be equal to the numerator divided by the denominator, making that a desk cannibalized number, adding decimals, Home tab numbers, deaths in the Molas, and then font group and underline. And that's gonna give us our future value of an annuity calculation. Finally, just multiplying this outer column out, which is going to be equal to the 1 thousand times that desk normalized number we came to. Let's add a couple of pennies here. Adding pennies Home tab number group, a couple of pennies, 19, 14.75. About let's, let's do it one more time, this time with tables. So I'm going to hide sum from k to o. Now put our cursor on the column K, the skinny column there, and then go on over to o. Let go right-click and hide from the table. We're going to have the payment. This is what she might do in a classroom setting. Payments. And the payment is going to be the 1 thousand. Then we just find the amount from the table, noting that you've got to have the right table. This is an annuity table that we're looking at. So we've got the future value of the annuity. And then we got noticed in the past the periods and the rates represent yearly rates and years. Now they represent months. So that means we have 18 months here. And then the percent isn't 12%, but 12 divided by 12 or 1%. And you can see why we picked 12 as the percent, because 1% is on the table and uneven percent would not be on the table and anything below 1% would not. Therefore, if I chose a yearly percent of anything under 12, wouldn't be on the table and anything that's not evenly divisible by 12 wouldn't be on the table. So that could be useful to know in a school setting if they're going to be using the tables. So we're going to say we got 118 than one in 18 brings us to the 19.61519.615. That's from the table. Let's add some decimals to the Home tab numbers. Animals, make an underlying font group and underline, and that's gonna give us our future value of an annuity, multiplying this out 1 thousand times the 19.61. And we're going to add a couple of decimals Home tab number group coupled decimals worth the 1960s, 15. Let's unhide some cells and just recap what we have done. Putting our cursor on column B, dragging on over to column Q, right-clicking on it and unhide. So now we did this with a running balance, getting us to about 19615. We did this with the annuity formula function within Excel 1961475, got to that same more exact number, more exact in the tables at least of the 1840s and 75 here. And then on the tables we got to the 19615, slightly different due to rounding, noting that this amount here from the tables rounded to three to four digits, whereas the actual number we can see from the mathematical formula is not rounded to four digits, but continues on resulting in that rounding difference. 20. Annuity Due Present Value: Personal finance practice problem using Excel, annuity due present value calculation. Prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Now we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side going to populate that into the blue area on the right-hand side, comparing and contrasting annuity calculations for a standard annuity present value of a normal annuity versus the present value of an annuity due, or in other words, an annuity where the payments happen at the beginning of the period as opposed to the end of the period. In other words, normally when we just think about an annuity by default, the payments we're assuming are happening at the end of the time period. And we can then choose to have the payments happen at the beginning. But of course that will affect the end result. The easiest way to start looking at that is to see the Excel functions, in my opinion, to see what those differences are. Then we'll kinda solidify what is actually happening in our mind by doing a running balance calculation. And we'll try to verify the future value calculation. So we can kind of go back and forth from present and future value, which might give us a better understanding as well. Let's start off with the standard annuity calculation in Excel. So we've seen this in the past. I'll do it fairly quickly. Negative present value so that we can flip the sign shift nine. And we're going to then say that this is going to be equal to the rate. The five per cent were on the rate. And then comma, the number of periods is going to be six. And then comma the payment because this is an annuity, we use the payment of the 1 thousand. Now normally that's where we stop and we just know that the default will then be a normal annuity typically, which will have the payment at the end. And we can say Enter, we get the 5,076 about. But note that if I double-click on this, you see that we still have these two kinds of arguments down here below that we could go to. Now normally these two arguments are the differences between an annuity and a non annuity. So this time we used an annuity, therefore had the payment as opposed to having two commas, not using the payment and having the future value. But I can have another comma. It will then take us to the future value. We're not going to use the future value, but I might want to get over here to this, to the type argument. So comma again will take us to the type argument, which by default they have as a normal annuity. Now, we could choose the number one here, and that would change it to basically an annuity due. So if we want it by default, have that 0 up top, it won't change. The bottom-line number is just gonna be the same thing. If I choose one, then it will change the default settings. So if I keep that there were still at the normal kind of annuity even though we extended the formula to include the type explicitly. Now here let's do that and then we'll change the type to the beginning of the period. So same starting point, negative, present value shifts nine. Rate is gonna be the 5% comma number of periods is now going to be six. Same thing, comma number. And then the payment is once again going to be 1 thousand. And then I'm going to try to get over that type field again. So I'm going to add another comma. And now the future value, we don't have a future value because it's not an annuity calculations. So another comma, and now we have the type which I'm going to choose beginning of the period, which is indicated by a one. You can double-click on it or type in a one. And we get to a different result, which is going to be that 5,329 as opposed to the 5,076. Now, to kind of solidify this in our mind we can do are running balanced type of calculation starting at the end result and working it back to see what is going on here. Sometimes it's a little bit easier with this particular calculation to kinda think about it. Well, because if we have the 1000-dollar payments at the 5%, sometimes it's easier to actually projected out to the future value and then present value it back. Sometimes that clicks more in people's minds. So let's just see what that would look like. For example, if I thought about this as a future value calculation at the 5% and then I brought it back to the current time period. We'll get to the same end result. So for example, I'm gonna make this a future value annuity, the same time series of payments, same rate. But now I'm going forward in time. We're going to end up at a 0.6 years out. And then we're going to have to bring that point back to the present to get to the current present value. So for example, it would look like this negative future value. Shift nine. The rate would be the 5% comma, number of periods would be six periods comma. And then the annuity, we're going to pick the 1 thousand. We have the same kind of thing. I could go to the type here and make it a 0, but it's already there by default, if I leave it as is, so I'm going to say, okay, that would then be the future value. So that would be. Series of payments as if they were earning 5% and that's where we would be six years in the future. Now I can, I can say, okay, well what if I took that future value 60 years out and I use a present value of one, taking that single amount back to time period 0, discounting it at the 5% that should give us to the same result that we got to up here. So let's try that. That's gonna be negative. Present value shifts, nine rate, five per cent, comma, number of periods is going to be six comma and then no payment because now we're going to use present value of one for that one number comma, and then up once to that future value we just calculated and Enter, and that'll give us to that, to that 5,076. Now sometimes the reason that's kinda easier to see sometimes is because when you do the running balance for an annuity, it's kinda easier to build the table of going forward to get to the future value of that 600802 to kind of verify it in your mind and then bring it back using the present value calculation here. Of course, you could do the same thing for like an annuity due. I can do annuity due going forward into the future, which would look like this negative future value shift nine, the rate 5% comma, number of periods would be six comma, the payment would be 1 thousand comma. And then I'm going to try to get over that type field again. So I'm going to say comma, again, bringing us to the type. And this time I'm going to choose the one to make it at the beginning of the period and Enter. So now we're at the 7,142 if we were to visualize it going out six years into the future. And then if I simply present value that back to the current time period, six years back, we should get to this 5 thousand 329, which we could do by saying negative present value shift nine rate is going to be the 5% comma, number of periods is going to be six comma, comma because this is not an annuity. Future value would be that number we just got to. And then that would bring us back to the 5,329. So again, that could give you some idea too. And then you can kinda do you're running balance tables to come up to these numbers, which, which could solidify how this whole thing works. We're going to now try to recalculate, use these numbers to verify what we have done. So let's go over here and think about are running balance for a normal kind of annuity. I'm going to start at 012. Select those three numbers. Autofill on down. We're gonna go to the Home tab, the alignment and center. And I'm going to start at the balance, which is the end result here of our normal annuity, which was a 5,076. And then try to prove this by basically going through a series of payments in ending up at 0 at the end of this process. So in other words, we're going to say that the increase here would be equal to the 5,076 times the 5%. The payment is gonna be that even 1 thousand each time, each time. And I'm just going to copy this down. So I'm going to double-click on this one. That 5% is outside. We're gonna, we're gonna make it an absolute reference selecting F4 on the keyboard dollar sign before the B and to this payment is outside. So I'm going to make it absolute by selecting F4 dollar sign before the B and one. And then I'm going to add this up. This is the prior balance to 5,076 plus the sum of these two numbers. This one being a negative means that when I sum them together, which usually means adding, it means it's going to subtract it because I'm adding a negative number, closing the brackets. There we have it. So the 5,076 plus the 254, about minus 21 thousand, brings us down to 4,329. Obviously the inquiry we're getting, the gain that we're getting is less than the payment that's going out. If we continue this process, we would assume then at the end of the six years, we would be down to 0 at that point. So let's select these three. Use our autofill by putting our cursor on the fill handle and dragging that on down. And we get, We get to 0 at the bottom line number. That should verify because you can say, Okay, if I had a series of payments for $1 thousand, that's going to be equivalent to the 5,765 if the rate was 5% for six years. Because if I was to take out One thousand dollars for each of that time period for 6 thousand over the six years after that 5% rate over that time period, I would end up with a net result of 0, even though I took out basically the 6 thousand over the six-year time period and started with an amount of only the 5,776 about. Now, if we did this one, it's a little bit more of a complex calculation here to do that. So I got a little bit more complex of a table. So we'll start here with 012. We're going to auto-fill that down, dragging on down, auto-fill that down to the bottom. We're going to go to the Home tab Alignment and center that. And we'll say that this balance. Starts at the at the 5329. And then what we're going to say is the payment happens at the beginning of each year. So I'm going to say negative of the 1 thousand. I'm going to select F4 on the keyboard because I'm going to copy that down. So there's our negative 1 thousand. So the beginning balance at the beginning January of year one, we can say January 1st of year one would be that 5329 plus the 1 thousand or in other words, plus a negative number or minus that number, bringing it down to 4,329, which will result in our increase being less because now we're saying it's happening from January, december, given us an ending balance that we're assuming we'll be getting the interests on or whatever our gain is. So that's gonna be the 4,329. Plus. Then we'll, we'll hold on a sec forth. That's 321 times the 5, 5% percent up top. Once again, I'm going to select F4 on the keyboard to make that absolute. So there we have that. So now the interest is going to be less in year one here, because, because we said that the payment happened in the front end. So then if we were to add this up, we would have an ending balance. This would be the ending balance, the sum of the beginning balance plus that increase. So now we're at the 4,546 and this is gonna be, let's call it the ending balance. So then we can copy that down. If I was to copy this down and auto fill that down, we then should get down to 0 at the bottom line once again. So we were at this point at the end of year one, and then at the beginning January 1st of year two, we got the other 1 thousand coming out. That means our beginning balance in January 1st of year two is to 4,546 minus 21 thousand or 3004546. Then there's an increase on that for the year of year to January through December, which is that number times the percent of 5%. And then we can add those two up. That's gonna be then our ending balance at the beginning plus the increase. And then at the beginning of year three, we're going to say that the $1000 went out. So that means that at the beginning of year three, we have this 3,723 minus the 1 thousand or 2723, which we're going to multiply times the 5% and then add those two together to get the ending balance. And then at the beginning of year four, we took out another 1 thousand. And so that means the beginning balances that to nine are the 2859 minus 21 thousand times the 5% was it five per cent is gonna give us 93 ending balances, the adding of those two. And then at the beginning of your five, we took out another 1 thousand. And that means our balanced went down to 952 at the beginning of the year. We earned 45 during the year. And then if we add those two together, we got the 1 thousand left. And at the beginning of your six, we take that out. And that means we're, we're down to 0 and we're not going to get any benefit in the year six because of course the balance is now down and we're not gonna, we're not gonna get any income in on it. 21. Present Value of Annuity using Non Annuity Excel Functions: Personal finance practice problem using Excel, present value of an annuity. Using non annuity, Excel functions prepare to get financially fit by practicing personal finance. We are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab in essence being an answer key information on the left-hand side going to populate that into the blue area on the right hand side will be looking at the present value of an annuity due and the normal kind of annuity type of calculation. Then also breaking it out into its components, into its individual periods, in this case years. And applying the present value of one calculation on a year-by-year basis. Something that you might say, why would I do that? That's somewhat tedious, but it's fairly easy to do in Excel. And it's actually quite common, even if you have a nice annuity kind of set up, because then you get the more detail on a year-by-year basis. And also when you're looking at a more complex cash flows situation that you can't break out into a nice standard annuity, then this is the method that you basically have to use. This is often a common method when we think about the present value of an annuity just to keep us scenario in your mind is if you're budgeting going forward into multiple periods into the future and you're trying to think about, should I do one path or another? For example, should I purchased a new piece of equipment or something like that? And you're trying to project into the future what that would result in terms of cashflow streams or returns into the future, that kind of decision-making process. So here's going to be our information. We've got the amount is going to be $100. We got the rate 7%. The years at five years, we're just going to do this with the Excel functions this time. So we're not going to be using a mathematical calculation and we're not going to be using the tables. We're going to do what we normally do in practice here, which is going to be an Excel function. And then we'll add some more detailed, possibly with a running balance when applicable. So first we'll just do the normal calculation. We'll do it fairly quickly because we've seen this in the past. The normal annuity calculation, I'm going to say negative to flip the sign present value, shift nine, the rate is going to be that 7%. I'm going to say comma, we're going to pick up the number of periods, which is going to be five periods down here, and then comma, and then it is an annuity. So we're gonna be using the payment item. That payment we're going to say is 1 thousand, We present value that we're at the 4,500. Obviously, if we were to add up all the payments, the total cash flow. So cash flow without the present value would simply be equal to the 1 thousand times five versus the 5 thousand. Let's go ahead and make this one black and white. And let's go ahead and make this one. This one will already be there on your Excel worksheet. Okay, so then we might say, well, let's break this out into a one-by-one Present Value of 15 times. And so this hopefully will give you an idea of the interplay between these two things as well. But the present value of one and the present value of an annuity. Also note and be aware of how we're setting up the table here. Because how you set up the table will make these calculations much easier and allow you to do projections and more complex and nuanced to projections a lot more easily as well. So we're going to set this up by putting our years over here. I'm gonna say 12. Selecting those two, going to put our cursor on the fill handle, drag it on down to five periods, or five periods is due five periods. And we'll center that Home tab, Alignment and center. Then the payment is simply gonna be $1000 each period. So I'm gonna say this equals $1 thousand. So there we have it. I'm going to say, we could say F4 on the keyboard expecting that we're going to be copying that down, putting a dollar sign before the B and three, in other words, making it an absolute reference. And then what we'll do is, let's copy that down first. Here's our series of payments. Let's copy that down. So there's our five payments of 1 thousand. If we total this up, we can put up the total here. This is going to be the sum equals the trustee equals SUM, shift up, arrow holding down, Shift Up, up, up, up, and enter. So now what we'll do is we'll just present value of one, not an annuity we have on our annuity setup in our years set up. And we'll just do a present value of one calculation on an individual by individual basis, which is something that we can copy down. So you can see this is fairly easy to set up once you have the table properly put together. We're going to say this is a negative present value, shift nine, the rate is going to be that 7%. Now we will do this a couple times, but if you were to copy it down, you'd say F4 on the keyboard so that you have an absolute reference there. So that you can copy that down and the 7% doesn't move down. Comma, we'd have the number of periods. Now here's where the number of periods is now one, not five, because we're doing this one at a time. So we're trying to take the one payment that's gonna be one year out, bring it back to 0. And I'm going to pick that one up not by typing it in, but having it over here in our formula or in our table. And note how convenient that is. Because by not typing it in and using the table, I can then copy this down and this cell will copy down relatively. So I don't have to deal with reformatting it all the time. And again, that makes your table way easier to be copying down. So we'll say comma and then comma again because this is not an annuity. Now we're doing the present value of one, and we'll simply point to that 1 thousand. And there we have it. So the one payment that's one year out is if I bring it back to time period 0 would be 935 about. Let's do it again. We'll just do it a couple more times and then we'll go back up and copy it on down using the autofill feature, negative present value, shift nine, the rate is going to be that seven per cent. We're going to say comma, number of periods is going to be this two, which we're not hard coding or typing, but rather getting from our table. And notice how nice it is that I can then copy that down comma and then comma because this is not an annuity but present value of one, we're basically taking this $1 thousand, discounting it back two periods to period 0 using the discount rate of 7%. Let's do it again, negative present value, shift nine, we're going to pick up the rate 7% comma. We'll take the number of periods, which is now three, which I'm going to pick up from this cell instead of hard-coding or typing it comma no payment because this is not an annuity comma future value, One thousand again and enter. So we discounted this $1000.3 years out that we're expecting to get it back three years using the discount rate of 7%. Obviously, you're getting a present value, which you get a decrease as we go further out into the future, expecting the cashflows happening further out in the future, which is what you would expect. And also something that gives you a better visual or concept or idea of what's actually happening. Then you get, when you just kinda get the magic number here for five years out. So this can give you a lot more contexts and again, easy to do really in Excel. So now we're going to say Do it again, Present Value, Shift Nine is going to be, then the rate is going to be the 7% comma number of periods four comma and then comma future value, one thousandths. Do we discounted that 1 thousand back for years now at the 7% to get the 763, let's go ahead and delete these and do it one more time this time with the autofill just to see how easy it is to auto-fill it down. So we'll say negative present value. Shift nine rate is that 7%? I'm going to make sure to hit F4 on the keyboard this time, making it absolute dollar sign before the B and four. That means it's not going to move when I copy it down. Comma number of periods is gonna be that one. This one, I do want to copy it down and that's why I structured the table to have the years in a column format like this in if cell reference that I can easily reference just the year. If I put something like year one in this cell, I can't reference it because it's not a number anymore. But if I put a one there, I can reference this and copy it down. Then comma, comma future values that 1 thousand. We want that to move down as we copy it down. So we're gonna say, okay, and then we're just going to do our auto-fill feature, putting our cursor on the autofill, dragging it on down. I'll double-check the last one by double-clicking on it to see if it does indeed do what we want. The rapes pick it up at the 7%. We've got the payment, which is picking up here, and we've got, we've got the future value. This is the number of periods picking up here. Future value, it looks like it's doing what we want now we can just simply sum it up, equals the SUM UP, holding down, Shift Up, up, up, up and enter. That's gonna give us our 4,100 matching out here. Let's put an underlying just to make it look a little nicer font, group and underlined. So there we have it. Like I said before you had Excel, you would try to avoid this kind of calculation whenever possible. And when you're working with book problems, you're going to avoid it because calculating five separate present value calculations is tedious. And you don't wanna do it. But if you're using Excel, you can see how easy it is to do and how much more flexibility you have to do that. And it actually gives you, even with a normal common calculation for an annuity, it gives you more detail that you're going to want to have. So it's often useful to do that even in a standard annuity. And when you have more complex cashflows, if you're doing something and making projections into the future that you're going to have uneven cash flows in some way, then you basically have to do this if you're trying to project or budget into the future and you're imagining what would happen if my revenue goes up by 5% each year or something like that? Well now you've got an uneven cash flow into the future and whatnot if you're going to present value that and try to compare it to some other option where you think revenue is going to grow differently but for a longer time frame and that kind of thing. So we can also set this table up to, I like to see it this way. That's how I tend to set it up. But a lot of times when you do budgets and whatnot, you'll end up with a budget on this kind of horizontal fashion. And then you can use your, use your present value table function in this format as well. So in other words, let's hide this. Sales and look at that, we're going to put our cursor on column C, drag on over to column I. Let go, right-click the selected area and high, don't delete it, just hide it. And then we're gonna, we're gonna do this again. This time we'll just do the same thing, but now the years are on top here. So we've got our years broken out. And the reason this is helpful is if you do like an income statement, you'd have income and expenses that list out here by year possibly. And then you can have a complex series of cash flows for inflows and outflows for an income statement. And then you can get your bottom-line cash flow. And then you can simply apply out your present value to try to discount everything back to the current time period using your discount rate here. So let's try that out. So we're going to, we're going to say the payments. This is gonna be the payments now, just gonna be that 1 thousand. So this is going to be equal to the 1 thousand. I'm gonna say F4 on the keyboard to put a dollar sign before the B and three. And then we can just add that across. We can say, let's bring those payments across with a five payments. That of course, adds up to the 5 thousand that we're expecting to happen in our annuity. Let's do the trustee SUM to say there's our 5 thousand, then we can have our present value calculations. Same kind of concept, except now we just got a little bit different format of a table. So it's useful to see, to be able to see these tapes In your mind, to start to build them. What do I want? Do I want, do I want them the x and y-axis and whatnot? Now, the better you can visualize those that easier it makes things, it's basic stuff. It's nothing, nothing difficult, but it is difficult in that until you start visualizing. It's kinda hard to see how you want to set your table up. So in any case, this is gonna be the present value shift night. Let's make it a negative present value, shift nine. The rate is gonna be that 7%. Once again, we can make an F4 or absolute reference to copy it across. Although we will first do this a couple of times before we do copy it across comma number of periods. Now there up top here, one period out. So we've got one period out. Notice that we do have each of these headings as just one number, because if there's anything other than a number in it, I can't reference to it. I have to hard code the number in my formula and then it doesn't copy across easily. So just be aware of that makes the table a lot easier if you can copy it across and then comma and comma future value is gonna be that 1 thousand right above there and enter. So there we have it. Let's do it a couple more times. Negative present value, shift nine, rate 7% comma, number of periods is now two, which I'm picking up from the table up top comma, comma because it's not an annuity, but present value of one, future value is the 1 thousand. So we discounted back that 1 thousand now two years at the discount rate 7% through it one more time. And then we'll do the autofill negative present value shift nine rate is gonna be that 7% comma number of periods is now three, which I'm picking up from the top column of the table, comma, comma because it's not an annuity but present value of one. Picking up the future value, which is the 1 thousand and Enter. So on. Let's go ahead and then do this for the whole thing here. Let's delete these and do it one more time. Being mindful of what we need to do to copy it across, including things like absolute references. So we'll say negative present value shifts nine, rate 7%, that's outside the table. So I'm going to make an absolute reference by selecting F4 and the keyboard, putting a dollar sign before the B and four, you only need a mixed reference, by the way, but an absolute references easier to think about. Comma, number of periods is now that one. I don't need an absolute reference here because I want that to move to the right as we copy the cells to the right comma it's not a payment because it's not an annuity comma. The future value is the one above it. I don't want an absolute reference here either because I'm going to copy it across. Also note that if this was a basic table, you might just get this number from the reference to the right, which is the 1000s, and make it absolute. But if you've got a more complex series of payments, then of course you'd want the payments will be listed up top. So it's more common to this format. And then we're going to copy it across, put our cursor on the autofill handle and drag it on down, drag it on down to five periods. Then we can sum this up equals the SUM of these items. And there we have that 4,100. Once again, Let's unhide some cells. We're gonna go put our cursor on column B, drag on over to k, Let go right-click on those cells and unhide, unhide those cells. And we can see those in a few different ways here. Now look again, just note that this kind of format to set this up. Like I said, you won't see it in textbook problems as much because they're trying to, they're trying to focus in on what you might be able to do with tables and formulas and on a test set and when they take away excel. But when you have Excel, you can see how much more flexibility this leads you to. I mean, you can come up with much more complex scenarios or what you think is going to be a future cash flow and not be restricted. If you're restricted to something like this, then you start coming up with future cash-flows scenarios that are too even you've got too much perfection. If you're able to easily set up a worksheet like this, which is quite easy to do. You can start to brainstorm in cashflows scenarios that are going to happen in the future that are more complex and possibly more closer to real life and then actually be able to have more predictions and whatnot of what's gonna go on. Obviously, once you set the table up to you can change any of your data here to like 8% and whatnot. And that'll change everything in your scenario as well. And you want to practice setting up your Excel worksheets like that so that you can run different scenarios. 22. Future Value of Annuity using Non Annuity Excel Functions: Personal finance practice problem using Excel, future value of an annuity. Using non annuity, Excel functions prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab, the example tab, in essence D and an answer key, we have the information on the left-hand side. We're going to populate that into the blue area on the right-hand side. First, starting off with the future value of an annuity function, as we have seen it in the past. Then breaking out that function into individual periods, which we will then have future value of one calculations to get an idea of how the two calculations are similar and related. And also because in practice, it can be quite useful to break out the information into a year-by-year basis, both because it gives you more information about the annuity itself on a year by year or period by period basis. And because it allows you to have more complex type of scenarios. So let's see what we have over here. We've got the payment of 1 thousand. We're going to say the rate is 7% and we have five periods this time looking into a future value type of scenario. So we might have a situation where we're estimating how much we're going to be receiving in the future to try to see where we will be at the end of five years. In this case, nice even payments. And we can work that out. But you might imagine a situation where you have less even payments. And in that case you won't be able to do a nice, nice standard annuity calculation, but rather would have to do some combination of an annuity and something else, or just break something out year by year, which is very common in practice. Something booked problems don't often do given the fact that they tried to take away excel. And so you can't really use it to do that. But if you have Excel, it's very practical to set up your spreadsheets in this format. So let's take a look at it. We're gonna say the normal future value of an annuity will do this fairly quickly because we've seen it in the past, will be negative future value shift nine, we're picking up the rate, which is that 7% comma, the number of periods, which is going to be five periods over here, and then comma. And we are using the payment portion because this is an annuity up top, will pick up the 5 thousand that gives us our annuity of the 5,751. Now if we just look at the cash flows, then obviously if we just say we have the 1 thousand times five, that would give us our cashflow of the 5 thousand. But because of the time value of money or the increase, if we're thinking of an investment, we would end up in a future period amount of the 5,751 according to the annuity calculation. We're going to go ahead and format this one. Now let's break that same calculation into a year-by-year calculation. We'll do it this way. I'm going to say years 12. You're going to select those two years and then use our autofill handle to click on the autofill handle and drag it on down to five years. Center that by going to the Home tab, Alignment and center. Then we'll just list out our payments again, which will be equal to the 1 thousand. I'm going to list each of them out one by one. So I'm going to say F4 on the keyboard and just copy that 1 thousand down to the five periods F4, giving us an absolute reference, dollar sign before the B dollar sign before the three. Enter. Putting our cursor back on that, grab the autofill handle, left-click on it, drag it on down for the 1 thousand all the way down five periods. Let's total this up toe down, which is gonna be equal to the SUM of shift up, arrow holding down, Shift Up, up, up, up, summing that column up, giving us the 5 thousand. Let's put an underline here, fonts group and underline. So now once we have this nice setup process, we can easily then do a future value calculation, but this time, do it on a period by period basis. This is a little bit more complex than we saw with the present value calculation because we're gonna be going forward in time. We'll take a look at that shortly. But just note, if you set the table up properly, it's still pretty easy to do the future value calculation and be able to copy that down. Also note that if it wasn't annuity, you might not need this payment column. You can simply do the future value and do an absolute reference of your data, 1 thousand over here. But it was some kind of system where you do not have even cash flows each year, then you'd want to set it up basically in this way. So it's common to kinda set up your payment flows over here and then line up the future value calculation next to it. So now what we're gonna do is we're gonna do future value of one calculations for the five periods. And notice we're going forward, not backwards. I'm not trying to bring this back to a time period 0. I'm trying to go forward to the end of the five periods. So that means this one is gonna be a future value calculation. That's going to be future value of one up four periods, 1234 periods here instead of going back. So that complicates that formula a little bit. When we compare that to the present value, this one starts at year two, so it's got 123 periods. To get to the future after five periods, this one starts at 32 periods to get to period five. So let's do this calculation, see what it looks like. It's gonna be negative future value shift nine will pick up the rate, which would be the 7%. When we copy it down, we would make that absolute reference. But I won't do that yet because we'll practice this a few times comma the number of periods. Now this is where it's a little bit different because what we want here is four periods because we're imagining this starts at the end of year one because it's an annuity. So what we want is for you can type in four. Let's start doing that first, let's put the four there first and then comma. Then the payment would be this one. It's not a payment because it's not a it's not an annuity comma comma. The present value would be this 1 thousand and then Enter. And that would give us the 100311 because we increase in it for that four periods. However, I can't copy this down. If I was to take this and grab it and copy it down, then I've got this messed up thing. One because this, this moved down because I didn't make it an absolute reference. So I could make that an absolute or hit that one. And then, and then also because I have to change this for because what I want it to be as three now, because there's only three periods, the left. So the question then is, well, how can I set this up so that I can copy this thing down? And what you could do is you could say, alright, instead of having four there, what I want is to say this is going to be the five minus the one. And then I can use this same kind of balanced table that'll come up with for the problem with that is when I copy it down, this five is going to move down. I don't want it to move down. This one is going to move down, and I do want that one to move down. This first one right there, which represents the five. I'm going to put an absolute reference on that F for putting a dollar sign before the G and five, so that every time I copy this down, that one stays the same. This one moved down. So I should come up with three next time, which is what we want. Let's test that out. I'm gonna put my cursor back on it, copy it down. And I didn't do an absolute, I'm going to go back and run it again, this one right here. Let's put an absolute reference on this percent, which is our normal standard process. And then let's copy it down. And now it looks like it's doing what we want, right? So this subtraction problem is taking five minus two, which is three, which is how many periods we want, because we're at period t, We want 123 periods left. And then you can copy that down. It's a fairly complex formula, but once you get, once you understand it, it should be, you'll start to pick it up. Let's do it a couple more times and then we'll copy it down the rest of the way. So this one would be negative. Future value shift nine rate would be that 7% comma, number of periods would then be, I'm going to do it this way. That would be the five minus the two, which would be three. Comma payment, no payment because it's not an annuity. Two commas future value the 1 thousand and enter through it two more times here, negative future value, shift nine, rate the 7% comma, number of periods is gonna be five minus three, which gives us two. Which makes sense because if I start at three, we got the two periods 45 left. Comma no payment because it's not a present value of an annuity. So comma, the present value is 1001 more time negative future value shifts nine rate at the seven per cent comma, number of periods is going to be the five minus four or one comma the payment, no payment comma the present value, the 1 thousand and Enter. Now I'm going to delete it and I'm gonna do it one more time being mindful of the absolute references so we can copy them down. So I'm going to delete it, do this one more time so we can do it with the absolute references, negative future value, shift nine, rate 7%, selecting F4 on the keyboard because that one is outside of our cell dollar sign before the B and the four comma, number of periods is going to be five. But I want that not to move down. Here's the tricky one because that one is in our table so that you would think that I don't need to do anything for that one because usually our table and not outside in the data, we don't need to do anything, but this one's a little tricky because that five is always the end date. So I want to make that one absolute. I'm going to select F on the keyboard and then minus the one. That one is not absolute because I do want it to move down so that it's always five minus whatever whatever year we are on, whatever period we are on. So we're going to say comma and then comma again, the present values at 1 thousand. I do want that one to move down, therefore, no absolute reference. And so there we have it. Let's copy it down and see if it does what we would expect. I'll take the fill handle and drag it down five periods. And then I'll just double-click on it, Double-check one of these and say, Yeah. It looks like it's taking the five minus four or one would be there. The 7% is taken. The 1 thousand looks right? So it looks good. And then if we sum this up, we're going to then get in the outer column underlying that font group and underline, we get once again to that 5,751. And we can see how each of those payments, as we now bring it into the future, results in a little bit less in terms of future value dollars because it doesn't have the time to basically accumulate the 7% gain or increase it, you're assuming will happen by the time we get to the end of the five-year time period. Now we can do this again and format our table. This way. We can have where we can have the years up top and we can have the payments on the side. Sometimes this is useful to do just in practice and sometimes people just like to see it that way better. So we want to be able to format our tables both ways so we can work with other people that format their tables differently, possibly format or tables, which whatever way makes most sense with what we are doing and so that we can follow along with anybody else who once again is format in the table in whatever way they want to format the table. So we'll put our cursor on column C, drag on over to column I. We're going to hide those cells. Right-click and hide those cells, hide those cells. And then we'll do it again. So the payment is going to be equal to the 1 thousand. I'm going to select F4 and the keyboard, making that absolute. So I can just copy that 1 thousand through the five periods. Putting my cursor back on that 1 thousand, you could do this with a keyboard, by the way, instead of the autofill, I could say Control C on the keyboards, since we'll start practicing more geeky maneuvers here, right arrow holding down shift, left or right, right, selecting those four cells and then Control V pasting it. And we get the same kind of process as the auto-fill. And you're more, you're impressing the geeks, doing that. You're pressing the geeks, which is good. Then we're going to then do our future value calculation, which is going to be negative future value shift nine. The rate is going to be over here on the seven per cent. And let's do it a couple of times. We would absolute reference that, but those steward a couple of times again, comma number of periods. Here's the tricky part. So we're going to try to do it this way so we can pick it up from our numbers, five minus the one, we would absolute reference times the five. So I can copy it over, but let's just keep it the way it is now. That means that it's going to be for, which makes sense because we have four periods after period one here. Comma, no payment because it's not an annuity. So two commas, present value is the one above it. Then I'm going to select tab on the keyboard which won't take me to the one under as inter would but to the one to the right. Negative future value shift nine, rate 7% comma, number of periods is now the five minus the two comma no payments. So two commas present value is the 1 thousand. Then we're going to select tab on the keyboard and do it again. Negative future value, shift nine, rate 7% comma, number of periods is gonna be that five minus the three to give us two. I think that comes out to two. If I'm doing my math properly, I'm not very good at doing them in my head because I use Excel all the time. But I'm pretty sure that one, okay, in any case, there we have it. Now let's delete these and do it again, keeping in mind the absolute references necessary to copy this thing across. So let's do it again and say, Okay, this is gonna be equal to the Future Value Shift Nine, rate 7% That one's outside the table. So I gotta make that an absolute reference. So I'm going to select F on the keyboard, dollar sign before the B and four, you only need a mixed reference, but an absolute reference is easier to think about comma, number of periods. I'm gonna do it this way. What the five, this is the tricky one because that one, although it's inside the table, I don't want it to move because I want that in number to be the same. So I'm going to select F4 on the keyboard. I think I hit F5 or something, something funny happened there, F4 on the keyboard. So there we have that. And then minus the one, which will give us four periods. But this one, I do want that one to move. Therefore, no absolute reference there. Comma, comma present value is gonna be that 1 thousand, which I do want to move, so I'll keep that one as is. There we have it. I didn't put a negative in front of the f. So let's put a negative in front of the f to make it a positive number. And then let's do our copying and pasting with the keyboard Control C. Instead of a fill handle, you could use the fill handle to right arrow hold down shift, then right, right, right. And then Control V. And there we have that it looks good. I would double-click on a cell over here and say, is it doing what I want? Like there it is. And by the way, if you don't want to double-click and you want to do that in a geeky way. You can hit F2 on the keyboard, F2 to see what's in there. And there we have it. And so, yeah, it looks like it's doing what I would expect. Now let's sum up this way. Let's sum these things up equals the SUM shift nine and left arrow holding down shift left, left, left, left and enter and sum this up equals the SUM shift nine left arrow holding down shift left, left, left, left, and enter. So there we have that 5,751. Once again, let's unhide ourselves by putting our cursor on column B, dragging on over to column K, letting go right-clicking on the selected area and unhide. So there we have our calculations in multiple different formats, which again quite useful to be able to do that. Something you won't get in book problems oftentimes because they take away your spreadsheet. But in practice, you can do a lot more complex projections and possibly get a better conceptual feel of what's happening from a period by period system or period by period process. Which again, I think I can give you some more insights into how you're putting these things together. 23. Home Loan Payment Calculation & Amortization Table: Personal finance practice problem using Excel home loan payment calculation and amortization table prepared to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab. The example tab, in essence being an answer key, we have the information on the left-hand side is going to populate that into the blue area. On the right-hand side. We're going to do the loan payment calculation as well as an amortization schedule. This is very useful when you're talking about a home loan type of situation because it'll give you a little bit more detail than you might have if you're just looking up the calculation on the payment, which is usually what you end up looking up when you're doing your calculations or working with someone else to try to land or budget into the future. Because the amortization table gives you an idea of the interests that would be paid versus the principal. And that can help you out with tax calculations and whatnot if you're taking that into consideration to note, the similar process can be done with any kind of thing when you're doing a financing of a large type of purchase such as a car or something like that. The home loan is often the more complex one, due to the fact that just the length of it is often quite long. So the standard loan, we got, the 30-year type alone going 30 years into the future, which seems very, very daunting to make an amortization table for, given the fact that that's a long time into the future. But with Excel, we can do that and we can do that fairly easily. So that's what we will practice here. Also note, of course there's a bunch of different loan terms that could be out there. We're gonna go with the standard 30-year fixed locking in the rate. So we'll have that set up for us. So we're going to say the loan is the 200 thousand note that when we're talking about the loan for a home purchase, that's not the purchase price of the home, necessarily. Most likely not generally. It's gonna be the loan amount related to it. And then we're going to say the rate is going to be the 5% on the rate. We're going to say the years are going to be 30 years. And we're going to say that we pay monthly note when you're talking about any kind of financing, typically, they will they will quote the rate at the yearly rate, even though most of the times when we're financing things on the personal side, we will be paying on a monthly basis and they will work very hard to give us the monthly amount and make it an even monthly amount so that they can see if we're going to be able to pay that and we can budget easily for a fixed amount. So we're going to have to deal with that rate and kinda into a monthly rate given the fact that we're gonna be doing monthly payments. That's one of the complications we'll talk about. Then we can calculate the payment. When you're planning something like financing and you're working with someone to do so. Or if you're trying to look it up yourself, then oftentimes you'll get the payment calculation down and not the amortization information. The amortization tables give you more insights and I think it's useful to be able to put them together. Once we have this all put together, if we do it properly, we can then change our data and we can easily say, well, what if I have $150 thousand loan? What if I have $100 thousand loan and so on and so forth. And we can make a much more complex and nuanced worksheet than we can basically with one just given us a payment calculation. So let's see how that would start. Now note, when we look at this payment calculation that's similar to the present value calculations. So the payment calculation is related to the present value as we've seen in prior presentations. I won't show that again. But we're extending on with these present value type of calculations, converting it to basically using the payments component of the present value. So in other words, just, just so you know, if I was to say negative present value and see this calculation has a payment component in it right there with the payment component. That's what we're solving for this time would be the payment. First, we need to think about the number of periods. Now if it's a 30-year loan, we're gonna, we're gonna say that there's 12 months of course, each year. So that means that we're going to have equals 30 times 12 or 360 periods that we're going to have to deal with. But again, that's okay because we have Excel to help us. Now let's do our payments calculation. Going to start with a negative instead of an equal and that'll flip the sign to make it a positive result. And then I'm going to say PMT shift nine. That'll start our argument. We have the rate, which is gonna be the five per cent. But this is where the tricky piece is, that's five per cent per year and we need it to be per month. So we're going to divide that by 12 and that'll give us the monthly rate. And then comma, the number of periods is not 30 years, but monthly periods 30 times 12 or 360, which we put in this cell, in cell B5. And then comma, we're not, the present value is gonna be the loan amount that we have up top, the 200 thousand on the present value, and there we have it and enter. So we've got the 1074 about double-clicking on it. There's our data, 1074. Once we have that number, then we can build our amortization table, which once again seems daunting. 360 periods, but not a problem here because we have Excel, we have Excel and Excel makes it easy. So we're going to say 12 are 012, and then I'm going to copy those three sales or autofill them down, selecting them, putting our cursor on the fill handle, I'm going to bring this all the way down to 360. Notice it gives us that nice little number format to help us out, gives us some help there and we'll bring it all the way down. Say Man, that's taken forever. Are we sure we want to get into this giant table that we're making. Sure we do. It's not a problem because Excel can do it. And so then we have There it is. I'm going to then go home tab, Alignment and center. And so there we have that. Then I'm gonna put the loan balance on the right-hand side. Now note, one of the difficult things on setting these, these amortization tables up is just to get your columns Correct. So if you're doing this for a test situation, you might want to practice settings your columns up so you can build your table appropriately. But once you have them set up or if you have a template of your tables, then it's fairly easy to populate. The loan balance is going to be equal to the 200 thousand. That's where we start at period 0, the payments are all going to be the same. That's the point of the payments. Whenever they forced the payment to be the same, even though the interests to be changing from period to period or in other words, the interests changing from period to period is the cost that we pay for basically having the payments be all the same. That's the confusing point of it, so that we can make the payments nice. And even. So we're gonna say the monthly payments we already calculated to be that 104074. I would like to make that an absolute reference so I can copy it down. If I were to copy it down, we will do this a few times. However, I would select F4. The interests then would be calculated by taking this is going to be equal to the prior balance times the 5%. That would be for a year though. So we've got to take that and divide it by 12 to get the monthly amount. In other words, if we pulled out the trusty calculator here and did it within the trustee calculate, we can take the 200 thousand times the 0.05 or 5%. That would be 10 thousand if it were for a year divided by 12 months monthly rate, 833.33. So then we could do it this way, which is kinda how we think about it in Excel. Sometimes 0.05, that's gonna be the rate for a year divided by 12 monthly rate. Is that ugly small number, which is why we don't talk about monthly rates even though we might use them in the calculation, times the 200 thousand. Once again, getting us to that 8.3333. So if this is the amount that we're paying and the interests, which is the rent that we're paying kinda like for the use of the purchasing power and a similar way as when we were renting before we purchased the home, which has paid the rent for the use, and we never get to see that money again, right. It's just goes away. That means that it's going to be, the difference between those two will be the reduction. So the payment minus the interest is how much the loan balance will be going down by. So this is going to be equal to the 200 thousand minus the 240. And this case, notice that the bulk of it during the beginning of the loan is going to interests as opposed to the reduction of the loan. And then towards the end that will switch and change. If we do this again, I'm going to say, Alright, the payment is again 1074. Now the interest is going to be slightly less given the fact that the loan balance has gone down. So it's gonna be this 199760 times the 5%. I'm not going to do the absolute reference right now. I'm just going to calculate it a few times. And so I didn't divide it by 12, then divided by 12. And there we have it. Then if I subtract this out, we got the 1074 minus the 832 gives us the reduction in the loan that the 241 slightly going up here, slightly going down on the interests. That means that the prior balance, the 199760 minus the 241, gives us 199518. Let's do it a couple more times, like three more times here. We've got the payment. Interest is going to be equal to the 199518 times the 5% tab. The reduction in the loan is gonna be the 1074. Hold on a second. I didn't divide it by 12 again. I'll get it right one of these times I'm going to take that that would be the yearly amount divided by 12 tab. Then we're going to take the 1074 minus the 831 tab. Then we're gonna be picking up the 199518 plus or minus to 42. And that brings us to the 199 to 76. Let's see if I could do it cleanly this time. This is gonna be the one O 74 interests is now gonna be the 199276 times the 5% divided by 12 gives us the 830. And then we're going to take this as equal to the payment 1074 minus the 830 and tab. Now we've got the prior balance, the 1997276 minus the 243. Let's do it one more time. This equals the 1074. This is the new balance, 2199033, times the five per cent. And then take that divided by 12 tab. The reduction in the loan balance is the payments minus the amount that's going to interest tab. And then our new balance is the 199033 minus the 244 and entered given us the 298788. Let's do it again. This time. We're going to just figure out what we need to do to copy it down. Then we'll use our autofill to do so. Notice that these changes are fairly small on an incremental month by month basis because the loan is going out so long and we've got the 5% rate. But over the three-year time period, this will have a significant change towards the beginning and end of the loan. So I'm going to delete this and do it one more time. Being mindful of what we need to do to be able to copy it down. So it using our absolute references and so on. So we're gonna do this to the payment that we're going to have is just gonna be equal to the payment we calculated down here. That's outside of our table. I want it to be the same all the way down. So I'm gonna make this an absolute reference, selecting F4 on the keyboard dollar sign before the B and six. Remember you only need a mixed reference, but an absolute reference works and it's easier to think about, then the interests will be equal to that 200 thousand times the 5%. That 5% is outside the table. I don't want it to move down when I copy down. Therefore, I'm going to make it an absolute reference selecting F4 on the keyboard. Instead of tab I hit Tab F4 on the keyboard dollar sign before the B and two. Then I'm gonna divide that by 12 and I'm just going to hard code the 12, meaning it's going to copy down as we copy down as well. Hardcode, meaning typed it in there. Then I'll subtract these two out. This is going to be equal to the payment, the 1074 minus 833 interests. Both of those I want to copy down. Both of those are inside the table, therefore, no absolute reference needed on either of them. Tab, then we got this equals the loan balance prior to this minus the 240 reduction in the loan. Both of those are inside the table. Both of those I want to move down relative as I copy the formulas down. Therefore, no absolute reference needed there either. So then we can just copy these. Now, normally I would select these three or four cells, copy them down one time, grabbing the fill handle, dragging it down one time and double-checking that it does what we think it should. This one looks correct. This one looks correct. So this one looks like it's doing what we want and so does this. So we'll copy it down. Once we get all the way down to the bottom, the loan balance should be 0 after 30 years or 360 periods. That'll give us an indication that we've done this properly. So we'll grab that fill handle again, drag it all the way down to the bottom, which is 360 periods. And you can see how this would be very difficult to do by hand without some kind of computer to do it. But with Excel done magical, and there it is. The end is at 0. I can see that at the bottom line here are payments, now are almost all principle out of that payment. And we made on the last one, we only paid $4 of interest. And it was all principle here. Now notice that's not really a problem for budgeting purposes because you're saying that whatever I can pay the 1074, what do I care? How much is broken out between interest and principal, but one, You gotta, you gotta care to the point that fact that you're paying interest is like the rent that you're paying over and above the value of the loan amount. And to the fact that you could have tax implications on this as well that we need to take into consideration. So that's the next step you can kinda look at if you were financing this. Most of the times you talk to people, they'll only give you this number and they'll say, well, how much can you afford? And they'll just increase in, decrease this number right here. But really you want to know how much interest you're actually paying. You kinda concerned with the interest rate and how much interests you're paying. And you then can start to think about tax impacts. Because in this first year, the interests, if I was to try to figure out the interests for the first year, equals the sum of the interests column for 12 months would be these cells right here. So then I can say, well, that's how much I'm paying in interest for the first year, which will differ from the second year, which would be the sum of 24 up to up to 13, I believe, would be different. I'm paying slightly less interests. And when I start to talk about the tax implications, the interest becomes important. And you gotta be careful with the tax implications because it gets quite confusing as to whether your standard deduction or you have an itemized deduction, then you can take into consideration whether or not you can write off like the the the the taxes related to. 24. Retirement Plan Worksheet: Personal finance practice problem using Excel retirement plan worksheet, prepare to get financially fit by practicing personal finance. Here we are in our Excel worksheet. If you have access to the Excel worksheet, would like to follow along. Note that we're down here in the practice tab as opposed to the example tab, the example tap in essence being an answer key, we have the information on the left-hand side. We're going to populate that into the blue area. On the right-hand side, we're looking at a retirement type of scenario. Our major goal is to take some of the tools that we've gotten with these present and future value time value of money calculations, put them together as we think about a fairly complex decision process, one of the most complex decision processes we have when we're talking about personal finances and that's typically the retirement setting, the retirement planning. Why is it complicated? Well, it's far out into the future. We're thinking about what's going to happen in the future. We don't know what the time value of money is going to be with regards to how much we're going to be earning in the future with regards to our savings accounts, we don't know how much we're gonna be able to earn over our earnings years, meaning how much our cell we will be able to increase, how much will be able to put in to the savings account. We don't know exactly what our life expectancy will be. So we have a lot of unknowns that we kinda have to put into a scenario. Many of those unknowns being specific to us, which is why when you think about a standard cookie cutter type of retirement plan calculator, none of them are gonna be that great really because they're gonna be hard to understand, because they're going to make a lot of assumptions that you may not see transparently. And also, there's so many different variables that it's hard to know what exactly is going on with a standardized type of thing. If you can take some of these tools and put them into a worksheet, then you can, you can customize your retirement plan a little bit more, more easily. And you might also be able to get a better grasp of what is actually happening with it. Also, you can make some more customizations with your Excel worksheet by changing the data for different scenarios to update it and whatnot as you, as you work with it. So we're just going to use some of the tools to basically practice some of the concepts with relation to a retirement plan that you might then take and then put together and put a more customized plan for yourself on. So here's gonna be the basic data. We're going to say first we got the retirement age. Remember there's two kind of things do you got to keep in mind when you do the retirement one is at the point in time that you retire, you're no longer earning money through your earnings, through revenue, although you have earnings from your savings. And then your nest egg is going to be going down at that point in time, although you'll still be generating revenue, you're gonna be pulling more money out then you're generating. So the question is, how much nest egg, how much money do you need in order to last you the rest of your life to live in the comfort that you want to be living in. That's kind of an annuity calculation that you gotta get to that point, then you can think about during your earning years, how much you would have to put away, say on a yearly basis or so on to get to that point in time after retirement point to have enough that you can then eat into it going forward. Okay, So here's our information. We've got the retirement age, we're going to assume it's at 60. We're going to assume we live to a 100. We are going to live to a 100. They got the yearly spending at 75 thousand. Now note this is another unknown kinda component because you might look at your current spending and estimate what you're going to need to spend at retirement. And then you might actually do a time value of money calculation, accounting for inflation, which is like one to 3%. To think about how much you can spend to earn the same amount or live the same way you're currently living now. So that's another thing you can kind of consider. We're just going to assume 75 thousand. We're pulling out 75 thousand a year at retirement. And then we've got the rate, we're going to say is 7%. Another unknown factor, of course, meaning we're going to try to average and say we're going to earn average over this life and whatnot of the 7% on our savings. So when we put it into our retirement plan, we put it into our stocks and whatnot. We're going to assume an average over that time of 7%. Now, people will argue what that percent can be and whatnot. But if you're investing over a long term, then you're more likely to get a reasonable average percent over that time period. So you can talk to your, basically your finance, financial people to see what that percent will be. But just remember if you're thinking long-term investment, hopefully over that long term, you can get a nice, even fairly good return on it would be the idea, even though it's going to fluctuate in-between that time period and it's going to drive you crazy on the downturns at least, right? So then we're going to say that the current savings we currently have 10 thousand already. And the years from years to retirement, the years that we have to retirement, we're going to say is 30 years. So we have 30 years that we're gonna be able to save. So before we get to retirement age 60. So that's how much time we have to build up our income to get there. Now, this second component, we're going to do this when we get a little bit more complex of a scenario. Because when we start to think about our savings plans, we can get more nuanced on that later and so we'll talk about that later. So let's first just think about, okay, well, how much would I need then if I'm gonna be picking up 75 thousand, spending 75 thousand a year after, after 64, until I turned a 100 and then I die right at 100. How much, how much would I need at that point in time in order to have enough in my savings account to be eaten away at it at 75 a year. For that, we do our present value of an annuity calculation. So I'm going to say negative. Present Value Shift Nine, the rate I'm going to say is seven per cent. We're gonna be earning 7% on it. Comma, we got the number of periods, which we're going to say, I'll do it this way, is the 100 minus 60 is how much time we're going to spend from the retirement age to a 100. So we're going to say, alright, and then the payment is going to be, the payment that we have is 75. We're going to have the 75 that we're going to be spending. That means at 60, we're going to need 999878. So that's how much we're gonna we're gonna need at the point of retirement if we're just gonna be eating away at that for the next 40 years, and then we'd be in there. It'll be down to 0 after a 100. So then we've got the target there of the 999878. So now we've got to think, okay, well, what do I gotta do to get there? So I've got 30 years now. I've got 30 years to get to that. 999878. And how am I going to do that? Well, I already have 10 thousand and I'm going to assume that that's 10 thousand. I'm not spending that's 10 thousand in my savings account for retirement. What's that? What if I don't do anything and I just leave that there and it grows at 7% until retirement for 30 years. That's my baseline. Well, if I don't put any more in, I just calculate that one. I'm going to say that's going to be equal to the negative future value. The rate is going to be that 7%. We're going to imagine it grows at the 7% again, comma, we're going to say the number of periods is going to be 30. We've got 30 years for that to grow before we get to 60. And then comma, the payment is going to be then the ten thousand, ten thousand. So there we have that. That means that hold on a sec. It's not a payment. Let me delete that. It's not a payment. That would be an annuity. We're going to say comma comma the present value because I'm not putting this in every year. That's how much we currently have. That would be the present value. There we have it that would give us a future amount at 60 of 76123. That's where we would start at or that's what we have thus far if we assume it just to grow. Now the difference between the two is what we're going to have to start putting in at that point. So that means that we have a difference of 999878 minus the 76123. That means that we're going to have to get an compile another 923756 over our life over the next 30 years to get to that point. Now then the easiest calculation would be, well, how much would I have to put in on an annuity calculation in order to get to that 923756, how much would I have to put in each year? Now, that's gonna be the easiest calculation, but it's not very nuanced because if we're starting off in our, earlier in our career, we probably have less money maybe than we might have in our peak earning years. So that means, that means that later on we'll get a little bit more nuanced and try to think about how much I can put in if I had more money to put it in because obviously I'm limited to how much I can put in. I can't just say I'm going to normally need to put in or be able to put in more when I earn more. But if I was to put it in a nice even amount over 30 years, we can do a nice annuity calculation. And what we're gonna do a payment, we're gonna do a payment formula which is a different or an alteration of the present value and future value formula. So I'm going to say negative to flip the sign PMT. We can then say the rate is going to be the 7% again, comma, number of periods, we're going to say is 30 periods. And we're going to say comma. And the present value that we need is, I'm going to say two commas because we actually need a future value. We need the future value of that 999878. Actually, sorry, we need the future value of the 923756 and then Enter. And that will give us the 9,779 that we'd have to be putting in each year. We would assume in order to get to that to that added amount that the 923756. So that would be a basic kind of scenario. Once you have this kind of setup, then you can change your data over here and you say, well, what if, what if this was 8%? What if this was 10% and so on? What if it was 5%? Now, if you want to make that and that's gonna be a basic scenario, note that we will then do it a little bit more nuanced in a second. But let's first run some tables based on this scenario is just to give it a little bit more concrete in our minds. So if for example, we thought about this 999878 and just kinda verify in our minds that I'm going to have that for 40 years and spent 75 thousand for 40 years. How does that work? Let's run a running balance table for that. And say at the time of retirement, which is when we're 60, we're going to say then from period 01 and so on, we got 40 more years until we die at 100, we are going to die right at 100. Or if we, if we live more than 100, then we're going to be penniless. But that's okay. We're gonna we're gonna go to the Home tab, Alignment and center. Then. We're going to say here that our investment is going to be this. This is how much we have when we'd retire at 60 that we're going to start eating away at. We're going to start eating away at it. So that means if we're earning a 7% return each year, we'd say, okay, in the first year after retirement, we'd have that 999878 times the 7%. I'm gonna say F4. I won't do it yet. I'll just multiply that out. That's how much we would earn, but we're taking out negative 75 thousand each year. So then what's going to happen after year one, we would have the 999878 plus the SUM left holding down shift of those two. And that would give us the 994870. Now I'm going to copy this down after I do it this time. So I'm gonna do it again, but this time thinking about the absolute references needed to copy this down. So this then would be the 994870 times the 7%. The 7% is outside of my cells. I'm going to select F4 and the keyboard dollar sign before the B and for tab. And then the expenses are going to be negative of that 75 thousand. Then I'm going to spend, I want that to be an absolute reference as well, not to, not to move when I copy it down. So F4 and the keyboard dollar sign before the B and three tab. And this is gonna be equal to the one above it plus the SUM shift nine left arrow holding down shift left again, closing up the brackets, shift to 0. So there we have it. Now I'm just going to copy this down and this should decrease. Our investment will slowly decrease for 40 years. If I copy this down until we get down here to 100, at 100 were like I'm going to spend my last penny. And then we keel over and die once we've spent our last penny. And there it is. And you might want more of a cushion, of course, then than that if you're, if you're planning to be a 100, I probably won't make it do a 100, but I feel like that's a cushion already for me, but any case, we have that. And so I can kinda verify our calculation there. So now let's think about this savings amount. If I put this if I put this away, each period, will I really get to that 923. So we can verify that or give us some a little bit more nuance on that. So I'm going to hide some cells to do that. I'm going to put my cursor on column F, drag over to j, let go, right-click and hide. So then let's do this. Do this again. Now, this is going to be for 430 periods. So I'm going to start here at 12, and it's gonna be selecting these two. I'm going to drag it on down, autofill down to 30 periods. T periods is going to be right here. And then I'm going to scroll back up and we're going to say, Alright, so the payment that we're going to have, we're going to say that this payment and notice we're starting because this is an annuity calculation. We're starting basically at the end of the period one. And let's center those two. I'm gonna go to the Home tab Alignment. We'll center these. And then let's say the first payment we're going to say is that 9779. And that's going to be our savings. So that's our savings. And then in period two, that's when we'll start calculating the earnings for it to match our annuity or an annuity calculation. This is going to be equal to then the 9779, we're going to say times then the 7% that's outside the table. So I'm going to say F4 on the keyboard so I can copy it down. Dollar sign between the B and for before the B and for tab. And then we're going to say the payment amount is always gonna be the same, which is going to be equal to that 9779. I want that to copy down or not to move down when I copy it down. Therefore, F4 on the keyboard dollar sign before the E and seven. And then our savings account is going to be equal to the amount we had before plus the sum of both the earnings on it and the payment closing up the brackets and Enter. So this one's going to be going up by earnings and payments. That should be good to copy that down. And once we get to the bottom, we should be able to verify this by checking it to this number just to double-check that that would indeed give us get us to the 923756, which is the added amount we need considering the fact that the 10 thousand we're assuming is going to be earning or get us to the 76123 by the time we get to retirement at 60. So we'll put our cursor on the fill handle. We'll drag this down and say, Okay, That gets us down here to the 923923756. So that verifies this number. It gives us an idea of the earnings that are being populated, that format. So next, you might want to kinda combine these together and try to do a running balance that combines our total investments since we're earning 7% on the entire thing. So that could look something like this just to, just to see how these running balances can be kinda put together in multiple different ways. Putting my cursor on column K, adjusting to call them. Oh, let go. And we're going to hide those cells. So now I'm going to try to get back to this number up top. And I'm going to include the fact that we already have the 10 thousand at time period 0. And see if we can basically do are running balances and get to that number. So let's start with, in this case, we're going to start at time period 0. Which means we have the investment already in place of the 10 thousand and we're going to assume we're earning 7% on that. So I'm going to then have period one and period two. We'll drag this on down, auto-filling that down. We're going to say dragging that on down to the 30 periods. Let's center that Home tab, Alignment and center. So then we're going to the interests can be calculated as that 10 thousand the prior balance times the 7% earnings, which we want to make an absolute reference. So I can copy it down by selecting F4 on the keyboard dollar sign before the B and four. And then we're going to say the payment now starts here. This payment is going to be equal in this 9779 that we're going to be putting in each year selecting F4 on the keyboard so we can copy that down. It stays at the same cell. Then the investment is gonna be the 10 thousand plus the sum of the amounts to the left shift, left again and hold down shift and 0. And then we should be able to copy that down and hopefully get to this 999878 by using their auto-fill auto-fill feature. So there we have the 9998787. Combine them together on our table to look at our at our earnings. Let's hide these cells by going from P, where to put my cursor on P and scroll on over to t. Let go, right-click and hide these cells. Now, the other way you might think about this is you might say, well this is good, but I don't think I'm gonna be able to put the same amount in each year. What if I don't start putting larger amounts until later years, which most people have to do. I can't I can't start putting that big amount in my early years, I don't have the money, but maybe later I can put in more money. And so what if I put it together a scenario like this, I'm gonna say, well, for the next 30 years that I have until I get to 60, I'm going to say that my earnings for years one through five are gonna be 45 thousand. Years six through ten are going to be 55 thousand and then 11 through 2055 thousand for six through 1011 to 20, there's going to be 65. And then from 21 to 30, I'm going to be earning 75 thousand. Now, if that's the case, I would be able to afford possibly putting more money in the later years of my work life than the early years. And I might want to take that kind of nuance into consideration. One way we might take it into consideration is to say, okay, what if I tried to put some percent into into retirement? Let's just pick a percent here. I'm going to choose like 5% that I'm gonna put in of my earnings to start with. And then I'll run my running balanced table. And then I'll try to change that cell using Goal Seek to whatever it needs to be in order to get to my objective, which is going to be in this case that 923756. So let's see how this might work out. So we've got our same 3030 years here, we've got 30 years. I can't use an annuity now because it's complex. I'm going to have to use the future value of one type of calculations. We can do this in a couple of different ways. So let's try this. Let's say if I go 12, I select those two and I copy that down to my 3030 years here. This one will actually be the total downhill sold, total it up, down below. And then let's go ahead and center these. I'm going to select these items and center that Home tab, Alignment and center. So there we have that. And then let's say, let's put our income down on each line out. Now you don't need this. You could take your data from over here. But I'm gonna, I'm gonna try to pick up my income by saying this is going to be equal to, this is what I imagine we're earning each year. I'm going to select F4 on the keyboard and just copy that on down for five periods. So I'll copy that down for five periods. And then I'll try to figure out where I will be on a future value from a year-by-year basis. Now you might say that looks like an annuity for five periods. We could use a combination of annuity and future value of one. We'll take a look at that in a second as well. But having a year-by-year calculation can be just as easy to do with Excel. So let's check that out. We're going to say, alright, and then in your six, we got this 55. I'm going to select F4 that we're gonna be earning and we're going to earn that from your six to ten. So autofill that to your ten. Then in year 11, we're going to earn 65, we believe F4 on the keyboard and we're going to earn that will say from 11 to 20. Then in year 21 we're going to earn 75 F4 on the keyboard. And then we're going to copy that down until we retire at 3030 years. Then what we're gonna do is take 5% of that. There's 5% which I'm going to apply to each one of them and I'm going to keep that cell nice. And even so that I can then change that cell to whatever it needs to be to meet my goal. And that's what that's the plan. So I'm going to say right, that means I'm going to invest 45 thousand whatever my income is, times five per cent. I want to make that 5% an absolute reference so we can copy it down, selecting F4 on the keyboard. Copy that down. That means I'm going to take out of my 47,000 to 50. Probably not gonna do it to get us to that goal, but that's okay. That's our starting point. Copy that down. And then obviously we're taking more out because we're taking the same percent out of a larger income as our income increases. Now we'll do a future value of one for each, each year here. So we'll do our future value of one, negative future value shift nine rate. We're going to assume 7% growth comma, number of periods. This is the tricky part. I gotta, I gotta take, I'm at period one minus the 30, so 29. I'm gonna do that by taking my end number. So I can copy this down easily. The 30 way down here, make that absolute by selecting F4 because I want that to stay the same minus the beginning number. And that one I want to copy down when I copy it down, and that allows me to easily copy this thing down. I also want an absolute reference on the rate, F4 on the rate, and then comma it's not an annuity this time, so no payment two commas present value is going to be that 2 thousand to 50 and enter. So hopefully I did that right. I'm gonna go ahead and copy this down. I believe I did. We'll do a double-check on it. We'll put our cursor on the autofill, drag that down, dragging that down. And so that's gonna be our total. Then, then we have our total down here, which I can sum up. I can sum up and say, all right, what does that get me at 30, where will I be in future value if that's all correct? I would be at the two seventy five sixty seven, which doesn't meet our goal of the of the 923756. So then I can say well, okay, well, how much would I have to put in since I can just change this? I can say, well what if I make, if I take 10% of each? Now, I'd be putting in 4,500 here and then 6 six thousand, five hundred, five thousand, five hundred. And that would add up to 543. So that's getting closer. And then I can use 11% and so on. And try to see what happens. Or I can use goal seek to say, Hey, Excel, would you change this cell to get to this end number to be the same as where I need it to be to meet my objective that 923756. So we could say all right, let's do that. Let's go to goal seek data tab, what-if analysis and the forecast Tools Goal Seek. And I want to say Excel, would you set this cell down here, that cell to be I got a hard-coded in there. I want it to be 923756. Please do that by changing the percent that I'm gonna be taking out of my wages based on this projected income and Enter. And then it's going to even it out for us. So there it is. So it's done that for us. And then they're saying about 17% is about how much we'd have to be pulling out. Which means when we're earning 52,654, when we're earning fifty five thousand nine thousand, three hundred fifty four and sixty five, the 11,055 and so on. These are some ways you can get a lot more nuance with this type of calculation than just a straight annuity over 40 years. Now also note if you see something like this, you might say, well, doesn't that look like for separate annuity calculations? Why don't I do four separate annuity calculations, which you can do, and that could simplify things. But there's a bit of a twist to it. So let me just show you that as well as you can kinda combine the present value of one and the annuity. So let's put our cursor on this cell. I'm going to drag on over to y. Let go, right-click and hide these again. And let's try to do this in like a grouping of annuity groupings. So I'm just going to say this will be equal to this grouping. And then we'll just copy that down. So there we have that. And this is going to be our total tau. And say, let's just calculate our investment now for this time period, which would be the 45 thousand times this percent to 17% or the one we calculated around 17%. I want, I want this to stay the same and these two to copy down. So I'm going to select F4 on the keyboard. So I'm taking 17% of those three numbers by auto-filling this down. So 17% of the fifty-five, seventeen percent of the 65 to seven, 3% of the 75 represented here. Then I'm going to do my annuity for five years here. For, what is it? Five-years here, ten years here, ten years here. Now the problem is that once I do my annuity for five years, I'm left off at the end of year five. And that money is still, is gonna be generating revenue until I retire up to 30 here. And that's why I gotta do two steps when I, when I do this kind of method. So for example, I'd have to say negative future value shift nine, the rate, we're going to say 7% growth comma, number of periods. I'm gonna hard-code as five from years one to 55. We're going to say comma. And then the payment is going to be, we're going to assume that amount is the amount of the payment and enter. So that gives us the 4414, But that's at the end of period five. If I keep that in my investment account until the end of end of retirement, we're going to have to say then I'm going to have more money, right? So then I got to say, Okay, let's do a future value of one, which would be the rate comma, the number of periods, which I'm going to say is 30 total down here, minus the five, which is where I left off on this one. That's how many more periods are gonna be there? 25. And then comma. Comma. It's not a payment this time, but it's because it's not an annuity present value of one for that 44. That means that's going to bring us up to the 238880. So let's do that again here. This is for another five years, negative future value shift nine. The rate is gonna be the 7% comma, number of periods is five again, because it's six through ten. Comma in the payment's going to be that 9354. But that's at the end of year ten and I got till you're 30 for it to keep on earning less money. So we gotta go Future Value Shift Nine rate is gonna be the 7% comma, number of periods is going to be then let's say 30 minus where we left off ten comma. And then comma again to get to the present value is this. And so there we have it. So we are actually 208167. And then this one negative future value shift nine, rate 7% comma number of periods is ten. Now 11 to 20 comma payment is gonna be that 1155. And then I've got another ten years to get to 30 here. So negative future value shift nine, rate 7% comma number of periods, I'm going to say 30 minus the 20, which is where we left off or ten comma not a payment because this is not an annuity. The present value is that 150 to 742 enter one more time, negative future value shift nine, rate 7% comma number of periods is ten. Comma payment 12756. That's going to end at period 30, so nothing else needs to happen. Summing that up. That's another way we can get to that, to that 923756 that we got here. So you might see it grouped in that format. And this is a little bit easier to look at this way as well. Although the running balance for 30 periods was just as easy to construct and you can get more nuanced in your calculations. And then of course you could change these and say, well what if I made 8, 8%? If you've got everything structured properly, you can see what's, what's your earnings would basically be and everything should kind of be able to be adjusted. If I change this back to seven, what if I wanted to spend like 100 thousand because I think there's gonna be inflation or something like that for the whole time. Hopefully that will calculate. So everything, everything will populate for itself, although we use Goal Seek here. So this one, you know, that Goal Seek is going to not, not account for this one will have to adjust that. But in any case, you can see how using your data over here will help you to kinda make adjustments and adjust these things. Let's go ahead and unhide some cells. We're gonna put our cursor on E to the W, a right-click and unhide. So like I said, the basic idea is you can do a general kind of concept for the year projections and this format, but this doesn't give you a lot of nuance. And this in particular limits you to the fact that you're not gonna be able to put in an even amount each year. And then you can try to project what your earnings will be in the future and how much you're going to put in. And you can kinda get a feel of the cost of you waiting later until you put in money. Because if you put money later in towards retirement, you're not getting the earning that you would have if you put it in early. But of course, you can't put it in early because you don't have the money early. You can only put in the money that you have. And you can kinda balance those two things out when you get a more nuanced type of calculation. And that obviously means you've got more complex type of table and you might have to move from an annuity calculation to future value of one to two mole, that kind of thing over.