The Rule of 72 is a mental math shortcut that tells you how long it takes to double your money at a given interest rate. Divide 72 by the annual rate of return, and the result is approximately how many years it takes for your investment to double. It works well across a broad range of rates and requires no calculator.
The Formula
Years to double = 72 / annual interest rate (%)
At 6% return: 72 / 6 = 12 years At 8% return: 72 / 8 = 9 years At 10% return: 72 / 10 = 7.2 years At 12% return: 72 / 12 = 6 years
Why 72?
The exact formula for doubling time uses natural logarithms:
Exact years to double = ln(2) / ln(1 + r)
= 0.6931 / ln(1 + r)
At most practical interest rates (between 2% and 20%), the denominator ln(1 + r) is very close to r itself, so the formula simplifies to approximately 0.6931 / r. Multiplying numerator and denominator by 100 gives roughly 69.3 / rate(%). The number 72 is used instead of 69.3 for two reasons: it is divisible by more integers (1, 2, 3, 4, 6, 8, 9, 12), and it gives a slightly more accurate result for the rates most commonly encountered in investing (6% to 10%).
Accuracy Comparison
Rate Rule of 72 Exact formula Difference
2% 36.0 years 35.0 years +1.0 years
4% 18.0 years 17.7 years +0.3 years
6% 12.0 years 11.9 years +0.1 years
8% 9.0 years 9.0 years 0.0 years
10% 7.2 years 7.3 years -0.1 years
12% 6.0 years 6.1 years -0.1 years
15% 4.8 years 5.0 years -0.2 years
The rule is most accurate around 8% and remains usefully close across the full range of typical investment returns.
Applying It to Debt
The rule works equally well in the other direction. If you carry a credit card balance at 24% APR and make no payments, your debt doubles in:
72 / 24 = 3 years
A $5,000 balance becomes $10,000 in three years from interest alone. At 18% APR: 72 / 18 = 4 years. The rule makes the cost of high-interest debt immediately visceral in a way that an APR percentage often does not.
Using It in Reverse
You can also flip the formula: if you want to double your money in a specific number of years, divide 72 by the years to get the return you need.
Required return = 72 / years to double
Want to double in 5 years? You need roughly 14.4% annual returns (72 / 5 = 14.4). Want to double in 10 years? You need roughly 7.2% annual returns. Want to double in 20 years? You need roughly 3.6% annual returns.
This reverse application is useful for evaluating whether a claimed investment return is realistic. An investment promising to double your money in 2 years requires 36% annual returns, a threshold that should invite serious scrutiny.
Rule of 70 and Rule of 69
Two close relatives exist. The Rule of 70 divides 70 by the rate, and is commonly used for continuous compounding scenarios (such as population growth or inflation estimates). The Rule of 69 (or 69.3) is mathematically the most accurate for continuous compounding. In practice, 72 is preferred for its divisibility and accuracy at common investment rates.
Calculate Doubling Time
To get the exact doubling time or required rate for any scenario, use the Rule of 72 Calculator.