What Is the Rule of 72?

Quick Answer

The Rule of 72, sometimes written the rule of seventy two, is a quick way to estimate how long money takes to double. It answers "how long to double money" without a calculator: divide 72 by the annual growth rate written as a percent. For example, at 8% a year, money doubles in about 72 / 8 = 9 years. It is an approximation, but a remarkably good one at the compound growth rates people see in practice.

How It Works

Doubling is a compounding question, and the exact answer involves logarithms. The Rule of 72 replaces that with simple division because 72 happens to approximate the exact math closely for common rates, and it divides cleanly by many numbers. You can run it in reverse too: to double in a set number of years, divide 72 by the years to get the rate you need.

How to Find the Rate Needed to Double in N Years

Run the rule in reverse: divide 72 by the number of years you have. For example, to double your money in 10 years you need about 72 / 10 = 7.2% a year, and to double in 6 years you need about 12%. This is a fast way to judge whether a target return is realistic.

Examples

For example, how long to double at 8%? 72 / 8 = 9 years.

What rate doubles money in 6 years? 72 / 6 = 12% a year.

Inflation in reverse. At 3% inflation, prices double, and purchasing power halves, in about 72 / 3 = 24 years.

Rule of 72 Versus the Exact Formula

Compared to the exact doubling time, the Rule of 72 trades a little accuracy for speed. The difference between the two is tiny between roughly 6% and 10%, and grows at extreme rates. Some people use 70 or 69.3 instead of 72 for slightly better accuracy at low rates, but 72 wins on mental math because it divides cleanly by so many numbers.

The Formula

Years to double ≈ 72 / rate%

The exact doubling time is ln(2) / ln(1 + r), where r is the rate as a decimal. The Rule of 72 is the friendly approximation of that expression. This tool shows both so you can see how close the shortcut is at your rate.

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