The Rule of 72 is a quick, useful formula that is popularly used to estimate the number of years required to double the invested money at a given annual rate of return. Alternatively, it can compute the annual rate of compounded return from an investment given how many years it will take to double the investment.

While calculators and spreadsheet programs like Microsoft Excel have functions to accurately calculate the precise time required to double the invested money, the Rule of 72 comes in handy for mental calculations to quickly gauge an approximate value. For this reason, the Rule of 72 is often taught to beginning investors as it is easy to comprehend and calculate. The Security and Exchange Commission also cites the Rule of 72 in grade-level financial literacy resources.

The Rule of 72 can be leveraged in two different ways to determine an expected doubling period or required rate of return.

Expected Rate of Return: 72 / Years To Double

To calculate the expected rate of interest, divide the integer 72 by the number of years required to double your investment. The number of years does not need to be a whole number; the formula can handle fractions or portions of a year. In addition, the resulting expected rate of return assumes compounding interest at that rate over the entire holding period of an investment.

Years To Double: 72 / Expected Rate of Return

To calculate the time period an investment will double, divide the integer 72 by the expected rate of return. The formula relies on a single average rate over the life of the investment. The findings hold true for fractional results, as all decimals represent an additional portion of a year.

Who Came Up With the Rule of 72?

The Rule of 72 dates back to 1494 when Luca Pacioli referenced the rule in his comprehensive mathematics book called Summa de Arithmetica. Pacioli makes no derivation or explanation of why the rule may work, so some suspect the rule pre-dates Pacioli’s novel.

How Do You Calculate the Rule of 72?

Here’s how the Rule of 72 works. You take the number 72 and divide it by the investment’s projected annual return. The result is the number of years, approximately, it’ll take for your money to double.

For example, if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money. Note that a compound annual return of 8% is plugged into this equation as 8, and not 0.08, giving a result of nine years (and not 900).

If it takes nine years to double a $1,000 investment, then the investment will grow to $2,000 in year 9, $4,000 in year 18, $8,000 in year 27, and so on.

How Accurate Is the Rule of 72?

The Rule of 72 formula provides a reasonably accurate, but approximate, timeline—reflecting the fact that it’s a simplification of a more complex logarithmic equation