Welcome back. Hopefully you have looked at this problem, thought about it. I want to just emphasize one more time the importance of timelines. So what I've done is actually I've drawn one ahead of time. And I'm going to go to that now. So I starting saving at year 30. And for convenience to be consistent with the formula we're going to assume that saving starts at the end of the year. So starting 30 you'll start saving at 31. And I'll quit saving at 50. And whenever I say 31 or 50 it by definition means the end of the year, right? That's the way we talk. I want to retire at 60, so what's going to happen between 50 and 60? If you look at the graph, nothing. So what I'm going to do is I'm going to now annotate and start writing on this. So this is the time period when I'm saving. Here, nothing. In other words, by magic, I'm approximately even. I'm not saving, and I'm not dis-saving. I know you may not have heard that word, but I have. You're basically not spending more than you're earning every year. It's a matter of convenience, right? And now, in this field, what am I doing, I'm consuming. But not earning. Right? Again, that's in a simplification but it will give you a sense I think this word problem is just awesome, you can modify in various ways. Now, the question is, I'm dying at 80. Of course you don't want to die, I haven't met anyone who's said I'm really looking forward to dying. But it's one of the most predictable things, based on statistics, are expected. So let's assume 80, and let's assume for convenience that even in the end of the last year I'm going to spend some money. On my behalf or whatever or given to somebody else or whatever. We can change the problem in many ways. So let's see. What is the question ask me? Is the question asking me how much am I saving 40 year? Is it a PMT question? The answer is yes. But the problem is the question I'm trying to answer, and this is why finance is awesome and you need to try and travel. The answer to it, if you just say PMT to the calculator or Excel and wait, Excel is going to look at you and smack you around and righly so. You expect me to answer a question even I don't know the answer to, right? You Google PMT, the Google is going to laugh back at you. So, the question is, you've got to know something in the future, so yes turns out we do. We know from 61 to 80. What do I want? I want PMT of how much every year? That's why I said we have everything set up, we want a payment of what? We want, if you go back to the problem. Let's go back to the problem for a second so that we are all on the same page. Right? I don't want to confuse numbers. I want to consume $100,000 every year. So once I know that, I know that starting year 61, I need 100,000. And how many of these? 20 over here. So this is a very simple problem to do. It's called a PMT present value problem. So I do the PV at this point, let's do it very quickly. Because if I know the PV at this point, I will know the PV at this point. If I know the PV at this point, I know the future value of my savings. So the thing I'm trying to solve for is 20 PMTs here. Which is money I'm going to invest. And the answer is hidden in 20 PMTs in the future. The only difference between these two is a difference in time. And obviously, in one case I am giving a money to the bank, or a fund, or a retirement account. In the other case I'm withdrawing, right? Okay, everybody, so let's do, if I can somehow figure this out, I'll be much better off. Than I am right now. So [LAUGH] so let's try to get to it. Okay, Excel, so there's another PMT problem. I know the PMT, so what am I going to do? Please recognize your time travel to year 60. Why have I time traveled to year 60? Because I know how to figure out the present value of something starting one year from now. And know 61, I'll need 100,000. Okay, so the interest rate, and we are doing this annual. So we don't want to do the monthly thing, is 0.08 I believe, right? And how many periods? I have 20 periods. And what is PMT? Turns out it's exactly the same number from the previous problem. So $124,999. $124,000 and there must be an error here. Let me just try to make sure we got it. Yep, I could tell there's was a mistake. When I did it quickly, I pressed 0.8 and 0.8 is 80% interest rate. You don't want that. Okay, this makes a lot more sense. So I have 981,814.74. I'm going to go back now I'm going to go back now and say that what I need is 980 and to confirm the number, 981,815. Write it one more time so that it's legible. At what point? This is the PV at .60. Another way, in English, to say this is the following, remember we did the loan problem, and we talked about repaying the loan? It's the same problem, except slightly different. I need to have $981,000, about 982 if you may, in the bank in which year? In year 60 to be able to finance what? $100,000 worth of consumption every year withdraw and at the end of year 80 how much will I be left with? Exactly the same problem. Right? So that's what I want you to understand. In the end, there's only one problem. And if you know how to do it you can apply that thinking to anything. However, I have a problem here. There's a gap of ten years that I don't like. Why? Because I know how to use annuities. But I do not know how to use annuities that end in the year 50 but actually the valuation I know is in year 60. So what do I need to do? Step two, and by the way you can do this many ways. I'm taking the easy way out. So what do I have to do? Remember in finance time value of money is everything and the interest rate is ,what? 0.8%. So now what do I have to do? I have to bring it back, PV, in year 50. What will that do? That will become the future value of the saving annuity I'm trying to solve. So let's do that. And that'll help us as I said, this is a very, very cool problem and I'm going to walk you through it simply because I'm going to make another cell. Notice I have left, sorry. Okay, notice I have left the first cell still open. And I'm going to write zero, I mean sorry, I'm going to write equal and now I'm going to do a PV function, right. And you'll see in the second why I've left that cell in its own place. Because, I can write 0.08, the interest rate is 0.08. Remember I screwed up last time. I put 0.8, don't do that. Number of periods ten. Why? Because I'm bringing a value I know in year 60 back to year 50. Right? And there is no pmt. Remember this is a one shot thing. So we are combining our learnings from the past week. There's no pmt it's a one shot bank account that will finance a future pmt. Right. So zero, don't forget that, and then I know the future value of this. Where is it residing? In Cell A1. So what is the value of 981 year 60 in year 50? Well, the value is about $454,770. So I'm going to, I apologize, there's a little bit of going with this, let me just write out the numbers. So it's about 981,815 I've now brought it back to about 454 and to get the numbers right, 770. I'm just confirming that the numbers are right. So we'll see what has happened. The magnitude, it's almost become half, right? Actually less than half. And the reason is I'm discounting heavily at 8%. Now, I'm almost done. Why? Because this PV is in year 50. This PV is in year 60, but I know if, if I know this PV in year 50, it can become the future value of this problem. So I know the value that I'm saving towards is about $455,000. 454,770 but now I need to ask the following question. How much every year will I put in the bank so that I am sure 454,770 is there? Everybody got that? Right. One more step. Okay. So now. Notice I'll keep that 454 exactly where it is. One, it'll give me a sense of, I've got the right numbers, but now I want to do what? Remember I'm trying to save every year and the amount that becomes 454 after 20 years. So I'm going to do a PMT problem. Five because they don't know their math. Okay, what is the interest rate 0.08. How many times am I saving and M is 20 and what is the present value of it, I don't know the present value because the present value would be in near 30, right? So what do I do now luckily? I know the future value. And where is it sitting? In cell A2, right? Bingo. 46,319, and let me just confirm that this is okay. And turns out this seems to be too much. So what did I do wrong here? I A1, A2, PMT, you see what I did wrong? I wasn't paying attention, I pressed, A2 as PV. It's good to make mistakes, which I know you will, but it's a minor mistake in the sense that I'm making a calculation error. But I could guess my answer was wrong, because it was too high. So, I have 9937. So the answer now is right. Remember, if you look up and you do the PMT function, the first number you press is interest rate, second is number of periods, third is PV. And I said I didn't have any PV but I didn't put zero. And final is FV. So if I knew the PV, I would replace zero by that and make A2 zero. Is that, so okay. So we are cool now and we know, and I'll confirm, that we need 9938. And we are almost done. So here comes the final, there I'm sure you're relieved by now. But how much would I save every year for the next 20 years Is 9938. Look at the awesomeness of this. Look at the awesomeness. In this case the awesomeness of finance is helping you. It's actually really not because it's time value of money but I am saving only $10,000 how many times? 20 times. But I'm going to use that money to consume how much? 20 times. $100,000, 20 times. How the heck is this possible? It's possible because the time value of money is 8%. If the time value of money was zero the world ain't going to make me do this easily right. So I save 9938, I get 9938 back one for one if the interest rate is 0. I hope you like today because I love talking to you today. I'm not kidding you. Which by the way, kidding in the U.S. means making fun of you or joking with you. You know because I have traveled and I have lived in different countries and different words mean different things. But I have tried to tell you the essence and the beauty of finance which has made it a little bit challenging for you. I'm sure. But, I think that's the value of this class, if anything, I have to bring to the table. Just a quick minute. I think I feel I want you to know that I feel very fortunate that I'm able to teach you anything at all. And many times I want to be like to walk. I hope you watched our Star Trek and so on and do the mind meld and do this very quickly. But that's not feasible, right? And that's also probably not the right thing to do. Because if you try to gain knowledge very quickly like that it tends not to stick. So I've tried to make the problems real world. I've tried to go slow with you and therefore the videos will be long. When will the videos be shot? When the content is very crisp. But maybe you need to go to a textbook to reinforce. Or maybe you need to go back later to accounting to reinforce our statistics. See you next time, it was fun talking to you this week. And I hope you stay in touch, and do the problems. In touch with the material, and do the assignment. See you next week, thank you very much, bye.
