Tuesday, October 19, 2010

Rule of 72 - Compounded Interest

Y = Years to double your money
I = Interest rate
Y = 72 / I

Rule of 72 means how long it takes to double your money with any given interest rate with the formula being:

Years to double your money = 72 divided by Interest rate (Y = 72 / I)

Dividing 72 by the Interest rate will tell you how many years it takes to double your money.

e.g. If Interest rate = 10% then  Y = 72 / 10 = 7.2 so it takes 7.2 years to double your money with a 10% interest rate (interest compounded annually - interest rate must be less than 20% or error is too great)

Have you always wanted to be able to do compound interest problems in your head? Probably not, unless you're a sociopath, but it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so good) a potential investment is likely to be.

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years (We're assuming the interest is annually compounded, by the way.)

As you can see, the "rule" is remarkably accurate, as long as the interest rate is less than about twenty percent; at higher rates the error starts to become significant.

You can also run it backwards: if you want to double your money in six years, just divide 6 into 72 to find that it will require an interest rate of about 12 percent.

There's an urban legend that Albert Einstein once said compounding [interest] is the most powerful force in the universe.

Whether or not he really said it, that line has become my financial motto. I strongly suggest you adopt it.

But did the eminent physicist really ever say such a thing? The claim that he did appears dubious for a couple of significant reasons:

The attribution of this sentiment about compound interest to Einstein doesn't seem to have existed during the scientist's lifetime, first appearing in print only several decades after his death, and always repeated as something he supposedly said in some indefinite time and place. (Albert Einstein died in 1955, but the earliest mention we could find of this item was in a 1983 New York Times blurb.)

Just what Einstein reportedly said about compound interest varies quite a bit from source to source: That it was "the greatest invention in human history" (or "the greatest invention of mankind," or "the greatest invention of all," or "the most significant invention of the nineteenth century"), that it is "the most powerful force in the universe," or that it is "more complicated than the theory of relativity." (That last variation echoes another sentiment popularly attributed to Einstein which also began to appear only well after his death, to the effect that "preparing a tax return is more complicated than relativity theory" or "the hardest thing in the world to understand is the income tax.")

We suspect that this perspective on the power of compound interest is a fairly modern invention, one which has been retroactively placed into the mouth of a prominent dead person to give it more punch.

(substitute 115 for 72 to determine how long before amount triples)

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