 Personal finance practice problem using OneNote. Investment estimated gains using time value of money calculations. Prepare to get financially fit by practicing personal finance. It's not required, but if you have access to OneNote, would like to follow along. We're in the icon on the left-hand side, practice problems tab in the 11020 investment estimated gains time value of money tab. Also take a look at the immersive reader tool, our practice problems typically in the text area too with the same name, same number, but with transcripts. Transcripts that can be translated into multiple languages either listened to or read in them. Information on the left calculations on the right, we're looking at investments whenever we do, we're asking questions like, how much will this investment grow? How much money will we have at some future timeframe? Or if I have a goal that I'm trying to reach, how long will it take until we reach that goal to answer those questions? We use time value of money calculations. Now note that different investments will grow at different rates, have different risks related to them. We can build more complex models to take those into consideration, but the baseline of the model will typically have this time value of money considerations. Remember that for individual investors, we usually have like two main categories of investments, bonds and stocks, stocks and bonds. The stocks are typically gonna be more volatile. We don't know exactly what the growth is gonna be. We're gonna have to use some estimates and averages of the growths typically when we're trying to consider our time value of money, taking risk into consideration as we do so. Also note that the return on stocks could come in different formats. We could one, get dividends, a return of the earnings paid out from the corporation or we can have them the growth of the company. The company goes up in value, making our holdings go up in value as owners and allowing us to sell it if we so choose at a gain at a future point in time. On the bonds side of thing, there still could be risk related to it. That's basically us kind of loaning money to an organization, either the government or a corporation, but the terms are gonna be more fixed. So it could be the case that the corporation goes out of business and then they don't pay off the bond, possibly they default on it. However, if they don't do that and they pay off the bond, the rate that we're gonna get is fixed in the bond. We could also sell the bond on the secondary market, which kind of confuses things, but if you're just gonna hold on to the bond, then the rate of growth is basically determined on the bond. We'll get into that more in future presentations, but the bottom line here that we're the baseline thought process will be these time value of money calculations. So here's the information on the left, annual deposits, rate of return, and years to maturity. These are great practice problems to be working in Excel because you can think about your tables that you're putting together and you can put your time value of money together. You can set it up in such a way that you can adjust the data on the left-hand side and have that automatically adjust on the right practicing your kind of estimates and your model calculations. So we've got our table that we put together, first annual deposit. I'm gonna put the 4,000 for A, the rate of return, we're gonna say is 4%, if not stated otherwise. When we see a percent, we usually think rate of return per year, which is our assumption here. The number of years is gonna be 20 years, so 20 years that we have. And then we're gonna say the investment at maturity, how much would we have at maturity? How much would that 4,000 grow to if we were to put annual deposits? Not just one $4,000, but 4,000 down each year for 20 years. How much would we have at maturity? There's different ways you can do this future value calculation. We're just using Excel here. We do this in Excel, so you can practice that. If you so choose, I'll go over it quickly here. We've got the rate. The rate's gonna be the 4%. The number of periods is the second item here, which is 20, and then the payment, because it's an annuity, because we're putting 4,000 in place. In this case, each year would be the 4,000. That means we're gonna have the 119, 112, if everything rolls out the way it should. And again, we're kind of doing a generic kind of investment here. Bonds would typically pay out in the form of interest payments, either annually and semi-annually, and have an end amount that they would pay back. Stocks, we might just assume that they're gonna basically grow at 4% based on whatever model or assumptions that we have on what they're gonna be growing at. So if we compare that to the total amount invested, how much did we actually put in? Well, if we put in 4,000 each year for 20 years, we'd put in 80,000. 80,000 minus 119, 112 would mean that we earned then the 39, 112. Again, how did we earn that? Well, if it was bonds, we might call it, it might be interest that we had. If we were on stocks, it might be the growth in the value of the stock and or dividends that we're receiving that are accumulating in that format. So that is that. Let's try it again. Well, let's pretend that we had 4,000 for B here, but the rate of return is now 7% for the same 20 years. So 20 years here. So I'm just populating this data in a table format. We could do our future value of money. That would mean that the rate now is gonna be 7%. Number of periods is gonna be 20 and the payment is gonna be 4,000 each month for 20 years. That's gonna get us up to 163,982. If I compare that then to how much we invested 4,000 times 20, then I can look at the difference, which would mean that what would we earn over that timeframe? Well, we put 163,982 minus 80,000, which is what we put in. We earned 83,982. Now you gotta be a little bit careful with these earnings because notice that we're talking about future value dollars here. So that means that there's gonna be inflation related to them. So that's another thing that we will talk a little bit about as we think about this, because if you're planning for something like retirement or how much money you need to pay for college or something like that, you can't really say, well, the amount that it's gonna cost is gonna be the same that it costs today because the dollar will be worth less because inflation is usually shot for. The Federal Reserve looks to inflate by anywhere from one to like, you know, 3% to 5%, three, and you'd like to keep it under that typically. So you gotta take that into consideration. But in any case, let's say we got another 4,000, same 4,000, 6% this time. I'm just pulling the data in, but this time it's for 30 years. Okay, so now we're gonna say after 30 years, if I do this calculation, the rate wouldn't then be 6%. The number of periods is now 30 and the payment is gonna be 4,000. Now we'd be at 316,233. How much money would we have put in over that timeframe? We put in $4,000 times 30 because we entered the annually. And so that would mean that we had earned after 30 years, 316,233, the money's been working for us. Hold on, I've missed a couple of zeros. 316,233 minus 120,000 is 96,233. Okay, last one, we're gonna say the 4,000 here at the 9% for 30 years. And that's gonna give us, if we did this again, the rate would be the 9%, number of periods 30, the payment would be the 4,000. That's gonna give us the 545, 230. How much did we put in? Same 120, so the 545, 230, minus 120,000 is gonna give us the 425, 230. Okay, note that you can also think about this. Well, what if I just did this, this is an annuity kind of payment because we put multiple with the same payment in each timeframe, each period. So what if I did, what if I did it? And I said, I just put the 4,000 in as a one-time payment and just let it lie, I didn't put any more in there. How much would we have after the 20 years at 4%? So the investment then would be growing to just the 8,764. This is a similar future value calculation in Excel. The rate would be 4%, the number of periods would be 20. And notice we have two comments here because it's not using a payment format because that would be for an annuity, but rather the present value, the one-time payment, the one-time $4,000 at 4,000 would bring us up to the 8,764. So the total earnings would just simply be the 8,764 minus the 4,000 we would have earned 4,764. If we did the 4,000 at the 7% for 20 years, we would get up to 15,479. That would be the rate of 4,000 number of periods, I'm sorry, the rate 7% number of periods, 20, no payment because it's not an annuity. The present value would be the 4,000. And then the difference we would have earned 11,479 there. And then we've got the 4,000 after 6% for 30 years, that would get us to the 22,974. That would be the rate 6% number of periods, now 30, no payment, the present value would be 4,000 getting us there. That minus 4,000 means we would have earned 18,974. And finally, 4,000 at 9% for 30 gets us to the 53. So that would be the rate 9% number of periods would be 30 and then no payment, the present value 4,000. And we would have earned over that 49,71. Okay, so let's kind of prove a couple of these just so we can see how it works, how the earnings are working. So let's think about A here, where we put the 4,004% 20 years. So if we looked at period one, we put in the 4,000 and then it earns 160, which is 4,000 times 0.04, 160 plus we put in another 4,000. Brings us to the 4168 plus the prior 4,000 is gonna give us the 8160. If we take that 8160, which is now growing and multiply it times the same rate of return 0.04, we're gonna get the 3s 26 plus the 4,000. We're gonna put in N plus the prior balance of the 8160. That's gonna get us to the 12486. If we take that multiply it times 0.04, that's gonna give us the 499 plus the 4,000 plus the prior balance, 12486. You can see how the growth is taking place here and it's growing larger, given the fact that we have this total here, which is increasing, making the earnings go up even though the rate is the same. So that's why if we start earlier, we're typically better off because we have so much more time for it to grow. B is the same thing, so we can kind of prove this. If I get down to the bottom, we're at the 119, 112. I really think it's useful putting this together in Excel. It's pretty easy to do. We do it in Excel because it gives you a better understanding of not just where you end off at after 20 years, but how the growth is happening and you can visualize the growth happening and you can look at where you are at at any point within the calculation. You can also kind of double check and verify to yourself how and why this is working. It's not just a magical thing so much as if you kind of work out the calculations as opposed to an Excel function, which seems kind of like a magical thing. You don't really understand how you got there. So here's another four. If we did it for this one, for B, we're earning 7% so we could do the same thing and you can see how the total is increasing, making our earnings increase and so on and so forth until we get down to the 163, 982, which matches the 163, 982 up here in our table. Noting here we did this getting to one point in time. And again, I highly recommend when you're doing these kind of projections, mapping it out so you can kind of double check it, verify it, make it more concrete in your mind and then also you can see where you stand at any given point in which can give you some more relevant information. Oftentimes you did the same for C, now we got the 4,000 that is growing at 6% for 30 years and so you can see it's growing here and as we get to this point down at the bottom, you can see it's growing at much higher rates and when you're thinking about retirement, you're starting to think, wow, if I had 294, 559, I wouldn't even have to dip into it and I can be earning 17, I mean, so your goal when you're thinking retirement, well, can I have enough money in here so I can just live off the earnings and not have to dip into the principle, that would be ideal, that would be nice, wouldn't it, that would be good. So you'd like to have all your money and like bonds and fixed income and like dividend stocks and then you just live off of the earnings or something like that. You say, how much money do I need there? So you can see this, like this next one here, if we were to see this one for 30 years, if I do this for 30 years and then I'm down here, I've got the 4, 96, 5, 41, I can earn 44,000 on that. Well, yeah, if you get a 9% earnings on it, which you might not get all the time, but you can start to say, well, that would be nice so then I can have that much in there and I can just live off the earnings of that, right? That's kind of, so those, but what if I started retiring up here, then I'd have 204 and then I'd have 184, right? These are the kind of questions that you start to look into that's a lot easier to visualize in your mind if you don't just stop here at the table but kind of verify and map it out a little bit more in terms of building the tables, which we do in Excel, it's also just great times. It's like doing a puzzle, so check it out.