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So I hope all of you get a sense of this very simple problem because I think what,

what, what the future problems will be, will be complicated versions of this. And

I get very excited with simple stuff too because it's, it's kinda cool. So, how

much will $100 become after two years, right? So, so now what have I done? I have

taken the one year problem and broken it into a, and made it into a two year

problem. So let's see how to do that. And I really would appreciate it if you did

what I am doing, either now or later. And by the way, I'll do this for relatively

simple problems, and let you work with the more difficult ones. So how many periods

do I have? I have zero, one and two. And as I said, the length of the period, the

length of the period, is a year, but that's artificially chosen. I'm just

choosing it for simplicity. It can be anything. We'll see that in a second. So,

okay. So, one year, two years, and what is the question asking me? So you put 100

bucks in the bank. And you're asking yourself, how much will you become. At

this point, so what is the future value of this? Right? So, so the, so the question

is pretty straightforward, Abut it is a little bit complicated. So, here's what

the answer will be. And I'll tell you the answer first. The answer will be $121.

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It's clearly more than 110, but it's 121. And this, in all of this, that $one, this

guy, if you understand where that's coming from, you'll see how it'll blow your mind

when you increase the number of periods, okay? So here's, here's a simple way of

understanding what's going on. So, I'm going to do the example without a formula,

right? Or, whatever, the formula that we already know. So, can you tell me, how

much will this be, at this point? Do we know how to solve a period problem? Of

course we do. We know this is 110. Why? Because this was 100 x 1.1, right? So, you

don't need the formula to do this, hopefully. But you could do it in the

heads. But now, noticed what has happened. I can use the same one period concept

conceptually to move one period forward. So, what will this amount, which is 110,

be after one year? And what will you do again? You'll take 110, multiply again by

1.1, and that should give you an answer of 121. So what's going on here? Answer is

very simple. You're doing a one period problem, twice. And, so, so, think of a

bank. It's, dumb, right? Not people, the bank. So the bank is looking in the first

period and saying, "What's going on a times zero? You have 100 bucks." At the

end of one period, what does it do? Give an interest rate of ten%. It says, "Now

you have 110." But the bank doesn't know the difference between the ten bucks that

you didn't have in the first year. But now have, so 110 bucks, bucks are the same. So

it thinks you now have, right this so, 110 bucks and takes it forward another period,

it has become $121. So, what's going on? Where is that one buck coming from? So, if

you think about it, you're getting ten bucks here, and ten bucks here. That's one

way to think about it. Why? Because this ten is ten percent of this, for the first

period, and this ten is again, a ten of this in the first period. So, if you add

up those, you have 100 + ten + ten, you have 120 at the end, right? So, you have

100 + ten + ten, so you have 120. So, you'd be saying, "How did I go from 120 to

121? " The answer is very simple. What we have ignored in all this is this ten

bucks, which was not here, is added here, will also earn interest over the second

period. And what is ten percent of ten bucks? One buck. So, plus one. Is it 121.

So, it's, it's pretty straight-forward. I'm writing all over the graph, but I want

you to understand that, this is not complicated. The complication is simply

coming because you, if you, if you're thinking, you're not thinking about the

ten bucks that comes as interest, will also start earning interest in the next

period. So, so I've, I've given you a sense of, what is the future value of 100

bucks, two years from now. And the concept and formula, let me just repeat one more

time, so that you, you can, understand. So the formula says this. If I have P at

times zero, after one year it will be P(1 + r), after two years, what will it be?

P(1 + r) (one + r). Why? Because this P in our case was 100. But after one year, this

whole thing has become 110, and then when you carry it forward, again, it will

become 121, and turns out P(1 + r)^2 is exactly, equal to 121. Now, isn't this

cool? The formula is, is telling you exactly what's going on, instead of me

throwing the formula at you. Formula makes sense, but here's where Einstein got blown

away too. You see Einstein said this, Einstein's most famous equation was E =

MC^2. Now it's square of square out here, right? They're common to the two. But

turns out, if I have 100 years passing by, if two were to increase to 100, what would

this formula would become? It would become P(1 + r)^100. And, even Einstein saw

compounding work that is interest on, interest on, interest. In this case, it

was only one buck initially over one, two periods. Interest on, interest on,

interest works. So, its so powerful, that in fact I would give this advice to you.

Anytime you're asked a finance question, say, the answer is compounding. And you

are likely to be right, 90 percent of the time. The only thing you want to do, is

you want to look intelligence. In life, looking intelligence is far more important

than being intelligent. So, what you want to do is you want to say, you know, pause

and say, "Is it compounding?". Because what that will do, is make people think

like you're really cool, you know, something they don't. But seriously,

compounding is, is really, really, tough thing to internalize. So, what I'm going

to do now, is I'm going to take advantage of, Excel. And I promised you that I

wouldn't teach Excel. But I'm going to do a problem where I'll be forced to use

Excel. So, let's, let's stare at this problem. And if you want to take a break

right now, this may be a great time to take a break. Because we have done future

value, where we actually could, by hand and do the calculation. So, repeat again

in words, I will. $100 after one year, 110. Why? I got ten percent ,ten bucks,

over one year, I have 110. After two years, what's happened? Well, one way to

think about it, which is very intuitive, is, how much do I have after one year? If

the bank is still there, of course. It's 110, right? I told you, I won't talk about

risks. So, I'm assuming the bank is still there. So, 110 you still have, and after

two years, it would have become 121. And the real ton in your side, is that one

buck. And if you understand that one buck comes simply from the fact, that you're

going, you now have ten more dollars after one year, which is also earning ten

percent because it didn't do any harm to anybody, you know, it's just like the 100.

What did it do? So ten percent of that, that's the one buck. Now, that is what is

compounding's power interest on interest. But it's only one buck. Otherwise, if you

didn't have interest on interest, you would still have 120, right? Ten bucks

each year on the original 100. Now, you have 121. So, it says, what's the big deal

here? Well, let me try another example, and then I'll give you some examples which

are really awesome. Just the simple idea, and I think if you understand compounding

as how difficult it is for a human being to internalize, you'll understand why

finance is so viewed as so difficult, but if you understand the intuition, it's

pretty straightforward, right? So, let's do this problem.