So I hope all of you get a sense of this very simple problem, because I think what the future problems will be, will be complicated versions of this. And I get very excited with simple stuff too, because it's kind of cool. So how much will $100 become after two years? Try it. So now what I have done. I have taken the one year problem 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'm 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 0, 1, and 2. And as I've said, the length of the period, length of the period, Is a year, but that's artificially chosen. I'm just choosing it for simplicity. It can be anything. You'll see that in a second. So okay, so one year, two years. And what does the question asking me? So you put 100 bucks in the bank. And you are asking yourself, how much will you become at this point? So, what is the future value of this, right? So, the question is pretty straight forward but it is little bit complicated, so here's what the answer will be and I'll tell you the answer first. The answer will be $121. It's clearly more than 110, but it's 121. And this, in all of this, that $1, 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 a simple way of understanding what's going on. So, I'm going to do the example without a formula. Right? Or with 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 one period problem? Of course we do. We know this is 110. Why? Because this was $100 times 1.10. Right? So, you don't need the formula to do this, hopefully. But we could do it in our heads. But, now notice 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? The answer is very simple, you're doing a one period problem, twice. And so think of a bank, it's dumb, right? Not the people, the bank. So the bank is looking in the first period and saying, what's going on at time zero, you have 100 bucks. And then the one period, what does it do? Given an interest rate of 10% it says now you have 110. But the bank doesn't know the difference between the 10 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, rightly so, $110, and takes it forward another period, and 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 10 bucks here. And 10 bucks here. That's one way to think about. Why? Because this 10 is 10% of this for the first period, and this 10 is again a 10% of this in the first period. So if you add up those, you have 100, plus 10. Plus 10. You have 120 at the end, right? So you have 100 + 10 + 10, 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 10 bucks. Which was not here, is added here will also earn interest over the second period. And what is 10% of ten bucks? One buck. So plus one is 121. So it's pretty straightforward, I'm writing all over the graph, but I want you to understand that this is not complicated. The complication is simply coming because if you're thinking, you're not thinking about the ten bucks that comes as interest will also start earning interest in the next field. So 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 can understand. So the formula says this, if I have B at time zero. After one year it will be P(1+r). After two years what will it be? P(1+r)(1+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'll become 121. And it turns out P times 1+r squared is exactly equal to 121. Now, isn't this cool? The formula is telling you exactly what's going on instead of me throwing the formula at you. The formula makes sense. But here's where Einstein got blown away too. You see, Einstein said this. Einstein most famous equation was E = M C squared. Now its squared and squared right here, right? They're common to the two. But turns out if I have 100 years passing by. If 2 were to increase to 100, what would this formula become? It will become E Times 1 + r raise to power 100. And even Einstein saw compounding work that is interest on interest on interest, in this case it is only 1 buck initially over two periods interest on interest on interest works is so powerful that in fact I will give this advice to you. Any time you are asked a finance question, say the answer is compounding. And you are likely to be right 90% of the time. The only thing you want to do is you want to look intelligent. In life, looking intelligent 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 it will make people think you are really cool. You know something they don't. But seriously, compounding is. Is a 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 stare at this problem and if you want to take a break right now this might be a great time to take a break. Because we have done future value where we have trickled by hand to the calculation. So repeat again in words, I will $100 after one year 110. Why? I got 10%, 10 bucks over one year, now 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 thorn in your side is that one buck. And if you understand that one buck comes simply from the fact that you now have $10 more after one year, which is also earning 10% because it didn't do any harm to anybody, you know, it's just like the 100, what did it do? So at 10% of that, that's the one buck, and 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'd still have 120. 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 this 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.