The Rule of 72

The Rule of 72 is a very easy way to calculate how long it will take to double your money or debt based on a given fixed interest rate, assuming the interest is annually compounded.

Use of the Rule of 72 is very simple. All you have to do is divide 72 by the interest rate. The resulting number is the number of years it will take for the amount to double, given that fixed interest rate. For example: if you invest $10,000 in a CD paying 4% compounded annually, it would take about 72/4 = 18 years to turn that into $20,000. On the flip side, if you have some amount of debt, say $30,000 in student loans, at a 5% interest rate which you don’t make payments on, it will take 72/5 = 14.4 years for the amount owed to double to $60,000.

You can also run the calculation the other way, if you want to determine what interest rate you’d need to double your money in a given amount of time. For instance: if you have $20,000 in savings and would like to double it in the next 10 years without adding anything to it, you’d need an interest rate of around 72/10 = 7.2%.

You can, of course, also use the Rule of 72 to calculate the effect of inflation on your money that you don’t invest. So, if the annual inflation rate is at 2%, for instance, then in 72/2 = 36 years, your money that you didn’t invest will be worth half what it is today.

There is also a “Rule of 69″ that is derived and used in a similar fashion to Rule of 72, except that it is used to calculate doubling when the interest is compounded continually, rather than annually. In this case, 69 is chosen because, when you work the math, compounding daily for typical interest rates comes out to around 69-70 and compounding daily is a reasonable approximation for compounding continually.

The earliest reference to the Rule of 72 is from Summa de Arithmetica which was written around 1494 in Venice by Luca Pacioli. In this work, he uses the rule without deriving it, so it is assumed that the rule was already well known at that time: “In wanting to know for any percentage, in how many years the capital will be doubled, you bring to mind the Rule of 72, which you always divide by the interest, and the result is in how many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; obtaining 12, and in 12 years the capital will be doubled.”

The Rule of 72 also gives rise to the rule of 144, which is used in exactly the same way as the Rule of 72, except 144 instead of 72. This will tell you when the value will quadruple.

The Rule of 72 doesn’t just apply to money; it actually applies to anything that grows. For instance, if the average population growth rate for the planet Earth is 2%, then it will take just 72/2 = 36 years for the population of the Earth to double from the current 6.8 billion to 13.6 billion, then in another 36 years it will have doubled again to 27.2 billion.

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