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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â