The rule of 72 for compound interest발음듣기
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The rule of 72 for compound interest
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and our example was interest that compounds annually, not continuously, like we would see in a lot of banks,발음듣기
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but I really just wanted to let you understand that although the idea is simple, every year,발음듣기
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you get 10% of the money that you started off with that year, and it's called compounding because the next year,발음듣기
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you get money not just on your initial deposit, but you also get money or interest on the interest from previous years.발음듣기
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If you have a reasonable calculator, you can solve for some of these things, if you know how to do it,발음듣기
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For example, at the end of the last video, we said, "Hey, if I have $100 and if I'm compounding "at 10% a year,"발음듣기
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that's where this 1 comes from, "how long does it take for me to double my money?" and end up with this equation.발음듣기
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To solve that equation, most calculators don't have a log (base 1.1), and I have shown this in other videos.발음듣기
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I say this because most calculators have a log (base 10) function, and this and this are equivalent, and I have proven it in other videos.발음듣기
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In order to say, "How long does it take "to double my money at 10% a year?" you'd have to put that in your calculator, and let's try it out.발음듣기
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It's 0.3 divided by ... divided by... I'll open parenthesis here just to be careful …divided by 1.1 and the logarithm of that, and we close the parentheses, is equal to 7.27 years, so roughly 7.3 years.발음듣기
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As we saw in the last video, this not necessarily trivial to set up, but even if you understand the math here, it's not easy to do this in your head.발음듣기
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Sometimes it's the Rule of 70 or the Rule of 69, but Rule of 72 tends to be the most typical one,발음듣기
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especially when you're talking about compounding over set periods of time, maybe not continuous compounding.발음듣기
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Continuous compounding, you'll get closer to 69 or 70, but I'll show you what I mean in a second.발음듣기
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To answer that same question, let's say I have 10% compounding annually, compounding, compounding annually,발음듣기
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10% interest compounding annually, using the Rule of 72, I say how long does it take for me to double my money?발음듣기
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So it will take 12 years for me to double my money if I am getting 6% on my money compounding annually.발음듣기
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The 2 means 2x our money, divided by log base whatever this is, 10 of, in this case, instead of 1.1, it's going to be 1.06.발음듣기
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Once again, you see, this is a pretty good approximation, and this math, this math is much, much, much simpler than this math.발음듣기
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Just to get a better sense of how good this number 72 is, what I did is I plotted on a spreadsheet.발음듣기
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I'm actually using this formula right here to figure out the actual, the precise amount of time it will take to double.발음듣기
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Let's say this is in years, if we're compounding annually, so if you get 1%, it will take you 70 years to double your money.발음듣기
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This is the actual, this is the correct, this is the correct, and I'll do this in blue, this is the correct number right here.발음듣기
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This is also giving you an appreciation that every percentage really does matter when you're talking about compounding interest.발음듣기
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It really is really important, especially if you're thinking about doubling your money, or even tripling your money, for that matter.발음듣기
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Rule of 72 says it will take you 18 years to double your money at a 4% interest rate, when the actual answer is 17.7 years, so it's pretty close.발음듣기
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For low interest rates, for low interest rates, so that's these interest rates over here, the Rule of 72, the Rule of 72 slightly, slightly overestimates how long it will take to double your money.발음듣기
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As you get to higher interest rates, it slightly underestimates how long it will take you to double your money.발음듣기
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If you just take the interest rate and you multiply it by the actual doubling time, and here, you get a bunch of numbers.발음듣기
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You can see it took us pretty well all the way from when I graphed here, 4% all the way to 25%, which is most of the interest rates most of us are going to deal with for most of our lives.발음듣기
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