The Rule of 72: How to Calculate Money Doubling Time

Doubling time at key rates

What the Rule of 72 is

The Rule of 72 is a mental calculation shortcut derived from the mathematics of compound interest. It allows you to estimate doubling time without a calculator by performing a single division: 72 divided by the annual interest rate expressed as a whole number.

At 6 percent: 72 / 6 = 12 years to double. At 9 percent: 72 / 9 = 8 years. At 3 percent: 72 / 3 = 24 years.

The rule is not an approximation invented for convenience. It is a mathematically derived estimate of the exact compound interest doubling formula, accurate to within less than 1 year for rates between 3 and 12 percent. Outside this range the error increases, but the rule remains useful for rough estimation up to about 20 percent.

The mathematical derivation

Where the number 72 comes from

To derive the rule mathematically: for money to double, the future value must equal twice the present value, so (1 + r)^n = 2. Taking the natural logarithm of both sides gives n x ln(1 + r) = ln(2). For small values of r, ln(1 + r) is approximately equal to r. And ln(2) equals approximately 0,693. So n is approximately 0,693 / r, or multiplied by 100 to use percentage rates: n is approximately 69,3 / r.

The number 69,3 is mathematically exact but inconvenient for mental arithmetic. It is not evenly divisible by 2, 3, 4, 6, 8, 9, or 12, which are the most common interest rates encountered in practice. The number 72 is divisible by all of these, making the mental division much easier while adding very little error. The maximum error from using 72 instead of 69,3 is less than 0,3 years at common rates.

Rule of 72 vs exact doubling time

Worked examples

The rule in reverse — finding the required rate

The Rule of 72 also works in reverse. If you know how many years you want to double your money, divide 72 by that number to find the required annual return.

Want to double in 10 years? You need 72 / 10 = 7,2 percent annual return. Want to double in 6 years? You need 72 / 6 = 12 percent annual return. Want to double in 20 years? You need 72 / 20 = 3,6 percent annual return.

This reverse application is useful for setting realistic investment targets and evaluating whether a claimed investment return is credible. If someone promises to double your money in 3 years, the implied annual return is 72 / 3 = 24 percent. That is far above any conventional investment benchmark and should prompt serious scrutiny.

Applying the rule to inflation and debt

The Rule of 72 applies to any quantity growing at a compound rate, not just money.

Inflation and purchasing power: at 3 percent annual inflation, purchasing power halves in 72 / 3 = 24 years. The same 100 euros buys only 50 euros worth of goods 24 years later. At 6 percent inflation (as seen in several EU countries during 2022), purchasing power halves in 72 / 6 = 12 years.

Debt growth: a 15.000 car loan at 7 percent interest on which only minimum payments are made doubles its interest cost in 72 / 7 = 10,3 years. This is why high-interest debt must be paid aggressively rather than managed with minimum payments.

GDP and economic growth: a country growing at 3 percent annually doubles its economic output in 24 years. A country growing at 7 percent annually doubles in just over 10 years. This helps explain why small differences in long-term growth rates produce large differences in prosperity over decades.

Common mistakes

Methodology

Frequently asked questions

Formula based on standard mathematical and financial methods. Results are for informational purposes. Last reviewed May 2026. Version 3.