How to Use
- Enter interest rate
Input the annual interest rate or growth rate (%).
- Calculate
Click the calculate button to see the result.
- View results
See the estimated doubling time and comparison with actual compound interest calculation.
What is the Rule of 72?
The Rule of 72 is a back-of-the-envelope technique for estimating, in your head, how many years it takes for an asset growing at compound interest to double in value. Instead of working through complicated logarithms, you simply divide the number 72 by the annual rate of return, which is why it is so widely used in investment conversations and quick mental comparisons.
Why 72 of all numbers?
The exact doubling time is governed by the natural logarithm ln(2)≈0.693. Multiplying 0.693 by 100 gives 69.3, but 72 divides cleanly by 6, 8, 9 and 12, which makes mental math easy, and it produces the smallest error across the range of typical investment returns (6–10% per year).
Where is it used?
- Investing: a fund earning 8% a year roughly doubles in about 9 years.
- Inflation: at a 3% inflation rate, the value of money halves in about 24 years.
- Debt: at an 18% revolving credit-card rate, the balance doubles in about 4 years.
The Formula
This calculator shows both the quick approximation and the exact value side by side.
Rule of 72 (approximation): Years to double = 72 ÷ annual return (%)
Exact compound-interest formula: Period = ln(2) ÷ ln(1 + annual return ÷ 100)
For example, entering an annual return of 8% gives an approximation of 72÷8 = 9.0 years, while the exact value is 0.693 ÷ ln(1.08) = 0.693 ÷ 0.0770 ≈ 9.0 years—an almost perfect match. After this period, $10,000 becomes $20,000.