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# Compound interest introduction

## Video transcript

what I want to do in this video is talk a little bit about compounding compounding interest and then have a little bit of a discussion of a way to quickly kind of an approximate way to figure out how quickly something compounds and we'll actually see how good of an approximation this really is so just as a review let's say I'm running some type of a bank and I tell you that I am offering 10 percent interest that compounds annually compounds compounds annually that's usually not the case in a real bank you would probably compound continuously but I'm just going to keep it a simple example compounding annually there are other videos on compounding continuously this makes the math a little simpler and all that means is that let's say today today you deposit $100 in that bank account if we wait one year and you just keep that in the bank account then you'll have your hundred dollars you'll have your hundred dollars plus 10% on your hundred dollar deposit 10% of 100 is going to be another ten dollars so after a year you're going to have one hundred and ten dollars one hundred and ten dollars you can just say I added ten percent to the hundred and then after two years or a year after that first year after two years you're going to get ten percent not just on the hundred dollars you're going to get ten percent on the one hundred and ten dollar so your ten percent on 110 is you're going to get another eleven dollars so 10 percent 110 is$11 so you're going to get 110 that was you can imagine your deposit entering your second year and then you get plus ten percent on that not ten percent on your initial deposit that's why we say it compounds you get interest on the interest from previous years so 110 plus now eleven dollars so every year the amount of interest we're getting if we don't redraw anything goes up so now we have a hundred and one hundred and twenty one dollars and I could just keep doing that and the general way to figure out how much you have after let's say n years is you multiply it so let's say so let's say my original I'll use a little bit of algebra here so let's say this is my original deposit or my principal however you want to view it after X years so after one year you would just multiply it to get to get to this number right here you multiply it by one point one one actually let me do it this way I don't want to be too abstract so just to get the math here so to get to this number right here we just multiplied that number right there is one hundred times one plus ten percent or you could say one point one now this number right here is going to be this one hundred ten times one point one again so it's this it's the hundred times one point one which was this number right there and now we're going to multiply that times one point one again and remember where does the one point one come from 1.1 1.1 is the same thing as one hundred percent plus another 10 percent right that's what we're getting we have a hundred percent of our original deposit plus another 10 percent so we're multiplying by one point one here we're doing that twice we multiply by one point one twice so after three years how much money do we have it's going to be so after three years we're going to have 100 times one point one to the one point one to the third power after n years now we're getting a little abstract here we're going to have a 100 times one point one to the nth power and now you can imagine this is not easy to calculate and if we this was a this was all the situation where we're dealing with 10% if we were dealing a world with say let's say it's seven percent so let's say this is a different reality here where we have seven percent compounding annual interest then after one year one year we would have 100 times instead of one point one it'd be 100 percent plus 7% or 1.07 after let's skip let's go to three years after three years I could do two in between would be 100 times 1.0 seven to the third power one point Oh 7 times itself 3 times after n years would be 1.07 to the nth power so I think you get the sense here that although the idea is reasonably simple to actually calculate compounding interest is actually pretty difficult and even more let's say I want to ask you how long does it take how long does it take to double your money so if you were to just use this math right here you'd have to say gee I would have to double my money I would have to start with $100 and I'm going to multiply that times let's say whatever let's say it's a 10% interest 1 point 1 or 1 point 10 and depending on how you're going to view it to the X is equal to well I'm going to double my money so it's going to have to equal to$200 and I'm now I'm going to have to solve for X and I'm going to have to do some logarithms here and you can divide both sides by 100 you get 1 point 1 to the X is equal to 2 I just divided both sides by 100 and then you could take the logarithm of both sides base 1 point 1 and you get X and I'm showing you that this is complicated on purpose and any of this is confusing there's multiple videos on how to solve these you get X is equal to log base 1.1 of 2 and most of us cannot do this in our head so although the idea is simple how long will it take for me to double my money to actually solve it to get the exact answer is not an easy thing to do you can just keep if you have a simple calculator you can kind of keep incrementing the number of years until you get a number that's close but no straightforward way to do it and this is with 10% if we're doing it with 9.3% it just becomes even even more difficult so what I'm going to do in the next video is I'm going to explain something called the rule of 72 which is an approximate way to figure out how long to answer this question how long does it take to double your forgot the word right the most important word how long does it take to double your money and we'll see how good of an approximation it is in that next video