The rule of 72 is a quick and easy calculation that helps someone estimate how long it takes for an investment, inflation, population, or really anything, to double with compounded growth. The completely accurate calculation involves natural logarithms which are not easy to calculate without a computer or spreadsheet, so this rule helps to estimate that calculation. The formula for the rule of 72 is shown below:
Where:
- T = time to double
- r = growth rate per period
We see here that it would be a somewhat involved calculation to completely accurately calculate the time it would take to double something with compounded growth, yet our approximation is very easy to do in your head or on a basic four-function calculator. All you have to do is divide 72 by the growth rate times 100.
Example
Suppose you have invested $1,000 in an account that pays 8.0% interest compounded annually. How long will it take for you to double your investment?
We can go the long way, and we will find out that your investment will double in 9.006468... years, but we can use our approximation to get quite close to that number. All we have to do is plug our interest rate, 8.0%, into the formula. The work is shown below:
This means that your investment, which in this case is $1,000, will double in approximately 9 years, which is in fact quite close to the completely accurate calculation.
I want to point out that we don’t have to work with only years, as I did in the example. If you were working with an investment that compounds at another frequency, you would simply use the rate per period, and T would be the time to double in however frequently your investment compounds. For example, if your investment compounds quarterly, then you would divide the rate by four, since we are working with quarterly compounding, and the T that you arrive at would be quarters. In this case, your investment would double in approximately 36 quarters.
Additional knowledge: if you perhaps want to use the full formula, the “2” in the denominator denotes the time multiple. If you changed that number to, say, 3, then T would be the number of time periods it would take for your investment to triple.