So, we have done this problem and this problem is a PMT problem. However, what's given to you here? The PMT is given to you, you figured it out. Now, I'm going to do a future value problem, with PMT figuring in, but exactly the opposite. So, let's go there and then I will take a natural break. Okay. So the next problem. Let's just read it. And by the way, at this point, you're feeling a little tired. You had too much of future value of an annuity. Take a break. That's okay because I think it's much more important you understand bite sized pieces, and you can always join me in a minute. I'm not going anywhere, I'm here. Okay? Okay. So let's get started with example number two of an annuity. So I'm going to again, draw a timeline. And hopefully, we'll get so familiar with doing this, we are going to. I promised myself today that I'm going to go slow and I'm going to squeeze every ounce of energy from the problem. And that's what the beauty of finance is. So, 0 here, and how much here? 25 right? Now what do I know in this problem? I know that. The interest rate again is 8%. Just for simplicity the same numbers. The numbers will change depending on who you are. And now, I say I know the future value, and I'm using dollars again just for simplicity, right. So just let's pause like last time. I jumped straight into PMT knowing that it's a PMT problem, but it's not the kind of problem that dictates what you're looking for, it is what information you need to be answered. So here, I know FV. So the question is being asked is, suppose you want $500,000 when you retire 25 years from now. How much must you invest each year, starting at the end starting at the end of this year, if the interest-rate is 8%. Now I repeat again I'm choosing 8%, but actually you are choosing 8%. Not the exact number, but the strategy. And for 8%, you better be invested in something risky. You aren't going to get 8% from the bank, okay. So $500,000 you need at retirement, right, and you're using 8%. So let me ask you this, when we go to Excel in a second, you will use the PMT function Why? Because that's the guy I don't know and that's the guy I'm trying to solve for, right? Okay, let's do it. Okay, the good news is I have the same problem setup over there, but now what do i do? And this actually helps, I have the last problem, what do i do? I change FP to PMT why did i do that? Because as i said earlier in this particular example i do not know one of them and that's PMT. What's the interest rate? 8%. How many years? In the previous problem, it was 40 years. Right? In this problem, we have, I believe 25. And if I make a mistake, that's one of the times you can catch me and fix it faster than me. So the number of repeated be empty. And then the next information, this is a little bit important, because Excel has a system which you've got to follow. Otherwise, your kind of on your own. If after the number of periods there is a symbol called PV which we know what it is. Do we know the PV of this problem? The answer's no so we've got to put zero because we don't have a number there and then we type FV. 500 Hopefully, if I have all the numbers right, and I'm doing it in real time with you simply to make you recognise that you can do it, you can do it just like I did it. The reason that I'm using a calculator is simply because the number that I need to calculate has got... 25 operations involved, right? So the only operation that's simple is the last one. [LAUGH] But in this case, I don't know the last one either. I don't know 25 of them, right? The PMTs. So how do I figure that out? I have to use a calculator. I'll do step wise very slowly the problem and we'd be here forever. Okay, so it’s 6,800, and let me call it 6,840. So I’m going to now go back to the problem. The answer to this is, in dollars, 6,840. Why am I making it 6,840? Why not 6839.1? Because we are family now. I'm not going to worry about decimals and you don't need to worry about them, at least in the classroom. In real life, probably yes. Okay, 6840. Let's, for convenience, assume that it's about 7,000. Approximately, right? So what's going on here? I need to put away $6,840, and I'll approximate it approximately $7,000. How many times? 25 times to end up having 500 bucks, all right. So why did I approximate even 6840 by 7,000? Because let me ask you the following question. Suppose the interest rate was zero, right. In other words, there was no value to. What will you have? If you invested $7,000 25 times. You just multiply 7,000 by 25. So what do you do? You take $7,000 multiplied by 25 You have 175,000. Why did I do this? Again as in finance pause and say Compounding, right. So if I didn't have 8% rate of return, I would have only $175,000. That's not little, and by no means am I saying it's throwaway money, but compare the 175 To the 500. So what's going on? The 8% is helping me, and here's my little take before we take a natural break on this. I hope you understand this problem. Secondly, I hope you recognize that the 8% Is coming from where? The market, and I hope you realize now why the market is so awesome. Because you're not doing anything. I'm not doing anything when I put away my money in my retirement. What am I giving in this example? I'm putting away 6840, right? I understand that could be my hard-earned money. But the fact is the externality, the positive benefit the market provides to people for the ability to benefit from the economy at the rate of 8% is phenomenal. You see what I'm saying? So what's going on here is that my money goes to somebody with great ideas. Who's able to own some money, and I still can own eight percent. So I don't want you to ever forget the beauty of markets. The beauty markets is an ability for all of us to share. And not one person, all of us. And that's the beauty of it. The unfortunate thing about life, as I said once in awhile I'll go into life, is that Not everybody has this opportunity. And yes, we can all say that everybody's not working hard enough but sometimes it's difficult to make money, right? It's difficult to have jobs. A lot of people these days don't have the ability to even invest. So let's do this. Let's take a break right now. We have spent a lot of time on two problems. I do not want you to exhaust yourself, but I want you to think about these issues. One last thought. While we are offline, redo these problems and double check them. Let me explain what I mean. Make 6840 your payment. Make number of years 25 and make the interest rate 8%. And solve the problem for what the future value will be, and what should your answer be? 500,000. Tell me what's cooler than that. It's internally consistent. It's got to be. If it's not, it's not finance, okay. So take a break and I'll also take a pause and we'll come back and start off with present value annuities. Keep smiling, thank you.