Rule of 72
Years to double an investment at a given rate
What is Rule of 72?
The Rule of 72 is a quick mental arithmetic shortcut to estimate how many years it takes an investment to double at a given compound annual growth rate. Divide 72 by the annual return percentage, and the result approximates the doubling time. At 6%, it takes 72/6 = 12 years to double. The rule is remarkably accurate between 6% and 10%, the most common range for long-term investments. It also works in reverse: if a quantity doubles in N years, the implied CAGR ≈ 72/N. The constant 72 (sometimes 69.3 for continuous compounding or 70 as a round alternative) comes from the natural log of 2 (ln 2 ≈ 0.693).
Formula
Years to Double ≈ 72 / Annual Return (%)
Exact: Years = ln(2) / ln(1 + r) = 0.693 / r (for continuous compounding)
Calculator
How to Use
- 1Enter the annual return: The compound annual growth rate as a percentage (e.g. 8 for 8%).
- 2Divide 72 by that rate: 72 ÷ 8% = 9 years to double.
- 3Use in reverse: If you want to double in 6 years, you need 72/6 = 12% annual return.
- 4Apply to inflation: At 3% inflation, the purchasing power of $1 halves in 72/3 = 24 years.
Worked Example
Example: S&P 500 at 10% historical return
Annual Return
10%
Years to double = 72/10 = 7.2 years. $10,000 becomes $20,000 in ~7 years, $40,000 in ~14 years, $80,000 in ~21 years. The exponential power of compounding means the fourth doubling adds $40,000 whereas the first added only $10,000: the same rule but an exponentially larger absolute gain.