# Rule of 72

## What it is:

The "rule of 72" is a method of estimating how long it will take compounding interest to double an investment.

## How it works (Example):

The rule of 72 is a method used in finance to quickly estimate the doubling or halving time through compound interest or inflation, respectively.

For example, using the rule of 72, an investor who invests \$1,000 at an interest rate of 4% per year, will double their money in approximately 18 years.

72 / [periodic interest rate] = [number of years to double principal]

or

72 / 4 = 18

Using the same rule of 72, an investor who invests \$1000 with an annual inflation rate of 2% will lose half of their principal in 36 years.

72 / 2 = 36

The rule of 72 can also be used to demonstrate the long term effects of period fees on an investment, such as a mutual funds, life insurance, and private equity funds.  For example, not counting any appreciation of the underlying investments in the fund, a mutual fund with a 3% annual loading and expense fee on principal invested will cut the principal in half over 24 years.

72/ 3 = 24

The rule of 72 is an approximation.  It is not exact.  Indeed, the rule of 72 is accompanied by the rule of 70, and the rule of 69 which are used the same way, but are more accurate for smaller periodic interest rates.  The rule of 72 is popular because it is divisible for more numbers (i.e. possible interest rates).

## Why it Matters:

While this calculation is relatively simple with a calculator or spreadsheet, the rule of 72, which was derived before the 14th century, is still a quick, mental calculation for the effects of compound interest.

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