Video transcription

So how does one calculate compound interest? Hi, I'm Jimmy Chang, I've been teaching college math for almost a decade now, and we're here to address exactly that. Compound interest is a very complicated thing in that it uses a couple of formulas, but we're going to use the most commonplace formula today. Even though it is a little bit on the long side, it is a very practical thing in that it lets you figure out how much money you'll have at the end of a certain period in time. Now, here's the common formula that we'll be exploring today. You have a rather involved formula over there, A equals P times in parentheses one plus R over N to the NT power. Now A is the amount, it's how much you want to have at the very end. P stands for principle, how much you'll have in the beginning, how much you're depositing. R is the interest rate, N is the number of times interest is compounded per year. Now different accounts will have different terms, so N is going to be very important. And T is the time, T is generally mentioned in years. Now, let's go over a really quick scenario here for you. Suppose you have three thousand dollars invested, that's three thousand is your P, invested at five percent, that's going to be your rate of interest. Over seven years time, so T would be seven and compounded monthly. Now because there's twelve months out of the year, N is going to be twelve. Now, when you plug all those things in, this is what the first line should look like. P is three thousand, N is twelve, notice the two places that N is going to be, now when you express the percentage though be sure to shift the decimal two places so five percent should really be zero point zero five. Now you're going to need a calculator for this because it's really hard to do all of this in your head, but when you do the math, you'll find that point zero five divided by twelve is going to give you point zero zero four two twelve times seven over here, is going to be eighty-four. Now, you have to add it with the one, so one point zero zero four two and the key calculation is being able to raise this number to the eighty-fourth power, now this is weird calculators going to do the work for you. But when you see that, you're going to have one point four two two as the result and here's the moment of truth because you have to multiply that with three thousand to figure out how much money you'll have at the end of seven years, and you'll find out if you plug in your numbers right, that it's going to be four thousand two hundred and sixty-five dollars and ninety-nine cents, which is quite a lot more than three thousand dollars that you had to begin with. So, I hope this gives you a glimpse as to how to - how this works and I'm Jimmy Chang and that is how you calculate compound interest.