What is the Rule of 72?

Sometimes I explain math concepts that you might think you won’t really use in the real world. But not today—because today’s topic has to do with money! There are many ways to make money, but the easiest way is to invest the money that you already have and allow it to make you more money by earning interest. But what does that really mean? And how fast does it work? Well, the answers to those questions depend upon a couple of factors. Once you know what those factors are, finding the answer is surprisingly easy. As we’ll talk about today, the trick that you need to know is called “the rule of 72.”

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What Does It Mean to Earn Interest?

I’ll leave it to Money Girl to explain most of the ins-and-outs of the various ways in which you can earn interest on your money, but there are a couple of basics that we should go over before going any further. First, what is interest? Well, when you make an investment—such as putting money into a bank savings account—the bank pays you in exchange for you letting them temporarily use your money. That money the bank pays you is interest, and the amount of interest you earn is usually paid out every year as some percentage of the total amount of money you’ve invested.

For example, right now the interest on a typical savings account is somewhere around 1% per year. That means that if you have $1000 invested in this savings account, you will earn 1% of $1000 or 0.01 x $1000 = $10 in interest the first year. After that year, your account will have a total of $1000 + $10 = $1010 in it. The next year, you’ll again earn 1% interest (unless the rate has changed), but instead of earning that 1% interest on $1000, this time you’ll earn it on $1010. So, in the second year you’ll earn 1% of $1010 or 0.01 x $1010 = $10.10, for a grand total of $1010 + $10.10 = $1020.10. That type of interest where you make money on the interest you’ve already earned year after year is called compound interest—we’ll talk more about it next week.

What is the Rule of 72?

But, you might be wondering, what does this really mean in terms of how much money you’ll make over the long haul? Is there some way to quickly estimate something like, say, how long it will take for this type of compound interest to eventually double your money? Well, I’ve got good news for you: there is—it’s called the rule of 72．

The quick and dirty tip for estimating how long it will take to double an investment is to divide the number 72 by the percentage of the interest rate earned. The number you get will be the approximate number of years that it will take to double your money.

How Long Does It Take to Double Your Money?

So what does the rule of 72 look like in practice? Well, let’s go back and look at that example of a savings account earning 1% interest annually. At 1%, the rule of 72 says that it will take 72 divided by the percentage rate of return, or 72 / 1 = 72 years to double your money! So, if you invest $1000 right now in that savings account, your money won’t double to $2000 until the year 2083! Ouch! That’s not such a great deal…and it shows you why even though in better economic times you can earn a little bit more than 1% interest in a savings account, this type of investment is usually not the way you want to invest for the long haul since it takes too long for your money to grow.

On the other hand, the US stock market has returned something like 10% per year when averaged over the past century. So, if you instead put that $1000 into mutual funds that invest in stocks, the time it takes to double your money drops to 72 / 10 = 7.2 years. And that’s certainly a lot faster! But beware: It’s also a lot riskier since over any 7 year period the stock market isn’t guaranteed to return 10%. In fact, it could do much worse than return 10%—it could lose 10%…or even more! But, over a long enough time period, these drops will eventually combine with gains that will ultimately double your money faster. And you can figure that out using the rule of 72．

Wrap Up

But why does the rule of 72 work? Where does it come from? Well, unfortunately we’re out of time for today. But don’t fret because we’re going to learn the answers to these questions next time.

Remember, you can email your math questions and comments to mathdude@quickanddirtytips.com. Also, get updates about the Math Dude podcast, the “Video Extra!” episodes on YouTube, and all my other musings about math, science, and life in general by following me on Twitter. And don’t forget to join our great community of social networking math fans by becoming a fan of the Math Dude on Facebook.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading math fans!
 

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