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

given to you here? The PMT's 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, if at this point you're feeling 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 size pieces. And you can always join

me in a minute, I am 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 time line. And

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

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

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

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

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

numbers will changed, 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 future value. So, the

question that's 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 of this year if

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

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

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

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

using eight%. So, let me ask you this, the, 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 set up over there, but now what do I do? And this actually

helps. I have the last Problem. What do I do, I change FV 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, eight%. How many years? In the

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

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

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

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

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

of on your own. If after the number of periods there is, 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. And hopefully, when I say. If I have all the numbers right, and I am doing it

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

it just like I did it. The reason I'm again, I am using the 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. But, in this case

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

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

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

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

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

mean, I'm not gonna worry about decimals, and you don't nee d 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 approximate it, approximately $7000 how

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

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

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

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

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

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

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

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

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

eight percent 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. I

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

example? I'm putting away 68,40, 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 their ability to benefit from the economy. At the rate of eight

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

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

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

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

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

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

And yes, it can, 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. 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're off-line, 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 eight percent 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 of annuitys. Keep smiling. Thank you.