0:00

So we've done this problem. And this problem is a PMT problem. However, what's

Â given to you here? The PMT's given to you, you figured it out. Now, I'm going to do a

Â future value problem with PMT figuring in, but exactly the opposite. So, let's go

Â there. And then I will take a natural break. Okay so, the next problem. Let's

Â just read it, and by the way, if at this point you're feeling little tired, you had

Â too much of future value of an annuity, take a break. That's okay, because I think

Â it's much more important you understand bite size pieces. And you can always join

Â me in a minute, I am not going anywhere, I'm here, okay? Okay so, let's get started

Â with example number two of an annuity. So, I'm going to again draw a time line. And

Â hopefully, we'll get so familiar with doing this, we're going to, I promised

Â myself today that I'm going to go slow. And I'm going to squeeze every ounce of

Â energy from a problem. And that's what computative finance is. So, zero here and

Â how much here? 25. Right? Now, what do I know in this problem? I know that per year

Â the interest rate again is eight percent. Just for simplicity the same number, the

Â numbers will changed, depending on who you are. And now I say, I know the future

Â value. And I'm using dollars again, just for simplicity, right? So just, let's

Â pause. Like last time, I jumped straight into PMT, knowing that it's a PMT problem,

Â but it's not the kind of problem that dictates what you're looking for, it is

Â what information you need to be answered. So here, I know future value. So, the

Â question that's being asked is suppose you want $500,000 when you retire 25 years

Â from now. How much must you invest each year starting at the end of this year if

Â the interest rate is eight%? Now I repeat again. I'm choosing eight%, but actually

Â you are choosing eight%. Not the exact number, but the strategy. And for eight%,

Â you'd better be invested in something risky. You're aren't going to get eight

Â percent from the bank, okay? So, $500,000 you need at retirement, right? And you're

Â using eight%. So, let me ask you this, the, when we go to Excel in a second, you

Â will use the PMT function. Why? Because that's the guy I don't know. And that's

Â the guy I'm trying to solve for. Right? Okay, let's do it. Okay. The good news is

Â I have the same problem set up over there, but now what do I do? And this actually

Â helps. I have the last Problem. What do I do, I change FV to PMT. Why did I do that,

Â because as I said earlier, in this particular example I do not know one of

Â them, and that's PMT. What's the interest rate, eight%. How many years? In the

Â previous problem it was forty, I mean it was forty years, right. In this problem,

Â We have I believe twenty five, and if I make a mistake. That's one of the times

Â you can catch me, and fix it faster than me. Okay? [laugh] So, okay. So, the number

Â of periods, EMT. And then the next information, this is a little bit

Â important because Excel has a system which you got to follow, otherwise you are kind

Â of on your own. If after the number of periods there is, there is a symbol called

Â PV, which we know what it is. Do we know the PV of this problem? The answer's no.

Â So we've got to put zero, because we don't have a number there and then we type FV

Â 500. And hopefully, when I say. If I have all the numbers right, and I am doing it

Â in real time with you, simply to make you recognize that you can do it. You can do

Â it just like I did it. The reason I'm again, I am using the calculator is simply

Â because the number that I need to calculate has got 25 operations involved,

Â right? So, the only operation that's simple is the last one. But, in this case

Â I don't know the last one either. I don't know 25 of them, right? The PMT. So, how

Â do I figure that out? I have to use a calculator or do step wise very slowly the

Â problem, and we'd be here forever, okay. So, 6,840. Hundred and, let me call it

Â 6,840. So I am going to now go back to the problem. The answer to this is in dollars,

Â 6840. Why am I making it 6840, why not 6839.1? Because we are family, now. I

Â mean, I'm not gonna worry about decimals, and you don't nee d to worry about them,

Â at least in the classroom. In real life, probably, yes. Okay, 6840. Let's for

Â convenience assume that it's about 7,000. Approximately, right? So, what's going on

Â here? I need to put away $6,840 and I approximate it, approximately $7000 how

Â many times? 25 times to end up having $500, all right? So, why did I approximate

Â even 6,840 by 7,000? Let me ask you the following question. Suppose the interest

Â rate was zero, right? In other words, there was no value to time. What would you

Â have if you invested $7,000.00 25 times? You just multiply seven by, 7,000 by 25,

Â right. So, what do you do, you take $7,000.00 multiply it by 25, you have 175.

Â 75's the. Why did I do this? Again, as in finance, pause and say compounding, right.

Â So if I didn't have eight percent rate of return, I would make only, have only

Â $175,000. That's not little. And by no means am I saying it's throwaway money.

Â But, compared to 175 to the 500. So, what's going on? The eight percent is

Â helping me and here's my little take before we take a natural break on this, I

Â hope you understand this problem. Secondly, I hope you recognize that the

Â eight percent is coming from where? The market. And I hope you realize now why the

Â market is so awesome. Because you're not doing anything. I'm not doing anything. I

Â mean, I put away my money in my retirement. What am I giving in this

Â example? I'm putting away 68,40, right? I understand that could be my hard-earned

Â money. But the fact is the externality, the positive benefit the market provides

Â to people for their ability to benefit from the economy. At the rate of eight

Â percent is phenomenal. You see what I'm saying. So, so, what's going on here is

Â that I, my money goes to somebody with great ideas, who's able to earn some

Â money, and I still can earn eight%. So, I don't want you to ever forget the beauty

Â of markets. Beauty of markets is an ability for all of us to share, not one

Â person, all of us. That's the beauty of it. The unfortunate thing about life, as I

Â said once in a while I'll go into life, is that not everybody has this opportunity.

Â And yes, it can, we can all say that everybody's not working hard enough. But,

Â sometimes it's difficult to make money, right? It's difficult to have jobs. Lot of

Â people these days don't have the ability to even invest. So, let's do this, let's

Â take a break right now. We have spent a lot of time on two problems. I do not want

Â you to exhaust yourself but I want you to think about these issues. One last

Â thought, while we're off-line, redo these problems and double-check them. Let me

Â explain what I mean. Make 6840 your payment, make number of years 25 and make

Â the interest rate eight percent and solve the problem for what the future value will

Â be. And what should your answer be? 500,000, tell me what's cooler than that.

Â It's internally consistent, it's got to be, if it's not, it's not finance. Okay?

Â So, take a break, and I'll also take a pause, and we'll come back and start off

Â with present value of annuitys. Keep smiling. Thank you.

Â