How long will it take to double your money? Or what interest rate do you need to double your money in a specific timeframe? Use the Rule of 72 for quick estimates and compare with exact calculations.
See how accurate the Rule of 72 approximation is across different interest rates. The rule is most accurate for rates between 5% and 10%.
| Rate (%) | Rule of 72 (Years) | Exact (Years) | Difference |
|---|
At 6%, your money doubles every 12 years (72 ÷ 6 = 12).
Exact calculation: ln(2) / ln(1.06) ≈ 11.9 years.
The Rule of 72 is very accurate at this rate — off by only 0.1 years!
At 8%, your money doubles every 9 years (72 ÷ 8 = 9).
Exact calculation: ln(2) / ln(1.08) ≈ 9.0 years.
Virtually identical to the exact value at 8%.
At 12%, Rule of 72 says 6 years (72 ÷ 12 = 6).
Exact calculation: ln(2) / ln(1.12) ≈ 6.1 years.
Still very close — within 0.1 years of the exact value.
To double your money in 10 years, you need approximately 7.2% (72 ÷ 10 = 7.2).
Exact rate needed: (2^(1/10) - 1) × 100 ≈ 7.18%.
r = Annual interest rate (as a percentage, e.g., 8 for 8%)
Years to Double = Estimated time to double your investment
ln = Natural logarithm
r = Annual interest rate (as a percentage)
r = Required annual interest rate (%)
years = Time period to double your money
The Rule of 72 has been used for centuries as a quick mental shortcut for estimating compound interest growth. While its exact origins are debated, it is believed to date back to the Italian Renaissance, appearing in the works of mathematicians like Luca Pacioli (known as the "Father of Accounting") in his 1494 book Summa de Arithmetica.
The number 72 was chosen because it has many divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), making mental division easy for common interest rates.
The Rule of 72 is derived from the natural logarithm of 2 (≈ 0.693) and the approximation ln(1 + r) ≈ r for small values of r. Since 72 × ln(1 + r) ≈ 72 × r/100 = 0.72r (for small r), and ln(2) ≈ 0.693, the number 72 provides a good balance across commonly used interest rates.
For very high rates, the Rule of 72 becomes less accurate. For rates above 20%, consider using the Rule of 73 or the exact formula.
The Rule of 72 is an approximation that works best for annual interest rates between 5% and 10%. For rates outside this range, the error increases. It also assumes interest is compounded annually and does not account for taxes, fees, or inflation.
Disclaimer: This Rule of 72 calculator is for educational and illustrative purposes only. The Rule of 72 provides a quick approximation, not a guarantee of investment performance. Investment returns are not guaranteed and past performance does not predict future results. Market volatility, taxes, fees, and inflation can significantly impact actual returns. Always consult with qualified financial professionals for personalized investment advice.