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Male Voice: What I want[br]to do in this video

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is talk a little bit[br]about compounding interest

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and then have a little bit of a discussion

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of a way to quickly, kind[br]of an approximate way,

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to figure out how quickly[br]something compounds.

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Then we'll actually see how good

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of an approximation this really is.

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Just as a review, let's say I'm running

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some type of a bank and I tell you that I

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am offering 10% interest[br]that compounds annually.

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That's usually not the[br]case in a real bank;

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you would probably compound continuously,

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but I'm just going to[br]keep it a simple example,

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compounding annually.[br]There are other videos

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on compounding continuously.[br]This makes the math

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a little simpler. All that[br]means is that let's say

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today you deposit $100[br]in that bank account.

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If we wait one year,[br]and you just keep that

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in the bank account, then[br]you'll have your $100

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plus 10% on your $100 deposit.

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10% of 100 is going to be another $10.

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After a year you're going to have $110.

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You can just say I added 10% to the 100.

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After two years, or a year[br]after that first year,

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after two years, you're going to get 10%

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not just on the $100,[br]you're going to get 10%

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on the $110. 10% on 110 is you're going

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to get another $11, so 10% on 110 is $11,

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so you're going to get 110 ...

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That was, you can imagine,[br]your deposit entering

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your second year, then[br]you get plus 10% on that,

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not 10% on your initial deposit.

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That's why we say it compounds.

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You get interest on the[br]interest from previous years.

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So 110 plus now $11. Every year the amount

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of interest we're getting, if[br]we don't withdraw anything,

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goes up. Now we have $121.

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I could just keep doing[br]that. The general way

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to figure out how much you[br]have after let's say n years

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is you multiply it. I'll use[br]a little bit of algebra here.

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Let's say this is my original[br]deposit, or my principle,

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however you want to[br]view it. After x years,

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so after one year you[br]would just multiply it ...

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To get to this number right[br]here you multiply it by 1.1.

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Actually, let me do it this way.

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I don't want to be too abstract.

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Just to get the math here,[br]to get to this number

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right here, we just multiplied that number

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right there is 100 times 1[br]plus 10%, or you could say 1.1.

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This number right here is going to be,

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this 110 times 1.1 again.[br]It's this, it's the 100

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times 1.1 which was[br]this number right there.

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Now we're going to multiply[br]that times 1.1 again.

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Remember, where does the 1.1 come from?

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1.1 is the same thing as[br]100% plus another 10%.

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That's what we're getting.[br]We have 100% of our

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original deposit plus another 10%,

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so we're multiplying by 1.1.

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Here, we're doing that twice.

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We multiply it by 1.1 twice.

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After three years, how[br]much money do we have?

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It's going to be, after[br]three years, we're going

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to have 100 times 1.1 to the[br]3rd power, after n years.

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We're getting a little abstract here.

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We're going to have 100[br]times 1.1 to the nth power.

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You can imagine this is[br]not easy to calculate.

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This was all the situation[br]where we're dealing with 10%.

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If we were dealing in a[br]world with let's say it's 7%.

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Let's say this is a[br]different reality here.

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We have 7% compounding annual interest.

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Then after one year we[br]would have 100 times,

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instead of 1.1, it would be 100% plus 7%,

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or 1.07. Let's go to 3 years.

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After 3 years, I could do 2 in between,

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it would be 100 times[br]1.07 to the 3rd power,

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or 1.07 times itself[br]3 times. After n years

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it would be 1.07 to the nth power.

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I think you get the[br]sense here that although

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the idea's reasonably[br]simple, to actually calculate

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compounding interest is[br]actually pretty difficult.

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Even more, let's say I were to ask you

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how long does it take[br]to double your money?

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If you were to just use[br]this math right here,

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you'd have to say, gee, to double my money

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I would have to start with[br]$100. I'm going to multiply

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that times, let's say whatever, let's say

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it's a 10% interest, 1.1[br]or 1.10 depending on how

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you want to view it, to[br]the x is equal to ...

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Well, I'm going to double my money so it's

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going to have to equal to $200.

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Now I'm going to have to solve for x

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and I'm going to have to[br]do some logarithms here.

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You can divide both sides by 100.

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You get 1.1 to the x is equal to 2.

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I just divided both sides by 100.

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Then you could take the[br]logarithm of both sides

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base 1.1, and you get x. I'm showing you

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that this is complicated on purpose.

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I know this is confusing. There's multiple

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videos on how to solve these.

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You get x is equal to log base 1.1 of 2.

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Most of us cannot do this in our heads.

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Although the idea's simple, how long will

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it take for me to double[br]my money, to actually

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solve it to get the exact answer, is not

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an easy thing to do. You[br]can just keep, if you have

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a simple calculator, you[br]can keep incrementing

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the number of years until you[br]get a number that's close,

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but no straightforward way to do it.

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This is with 10%. If[br]we're doing it with 9.3%,

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it just becomes even more difficult.

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What I'm going to do in the next video

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is I'm going to explain something called

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the Rule of 72, which[br]is an approximate way

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to figure out how long,[br]to answer this question,

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how long does it take[br]to double your money?

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We'll see how good of[br]an approximation it is

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in that next video.