Rule of 72 Calculator
Enter an annual interest rate to instantly estimate how many years it takes an investment to double in value, using the quick mental-math Rule of 72 — plus the precise calculation for comparison.
How the Rule of 72 formula works
The Rule of 72 approximation, and the exact formula:
Rule of 72: Years to double ≈ 72 / rate Precise: Years to double = ln(2) / ln(1 + rate/100)
Step-by-step calculation
- Divide 72 by the annual interest rate (as a whole number, not a decimal) for a quick estimate.
- For the precise version, divide the natural log of 2 by the natural log of (1 + rate as a decimal).
Worked example
At 8% annual growth: Rule of 72 estimate = 72/8 = 9 years. The precise calculation gives ln(2)/ln(1.08) ≈ 9.01 years — remarkably close, which is why the shortcut works so well in the typical 6–10% range.
Frequently asked questions
How accurate is the Rule of 72?
It's most accurate for interest rates roughly between 6% and 10%, where the approximation and the precise calculation differ by only a small fraction of a year. At much higher or lower rates, the gap widens somewhat, though it stays a useful quick estimate.
Does the Rule of 72 work for anything besides money?
Yes — it applies to any quantity growing at a steady percentage rate, including population growth, inflation's effect on purchasing power (halving time), or any compound growth process.