Rule of 72 Calculator
Print
The Rule of 72 Calculator provides a quick mental math approximation to determine how many years it takes for an investment to double in value at a fixed annual compound interest rate, or how long it takes for inflation to halve your purchasing power.
The Rule of 72 Formula
The classic Rule of 72 formula divides the number 72 by the annual interest rate (R) expressed as a whole percentage number:
Years to Double Money = 72 / Annual Interest Rate (%)
Required Interest Rate to Double = 72 / Desired Years to Double
Years to Cut Purchasing Power in Half = 72 / Annual Inflation Rate (%)
Where:
- Annual Interest Rate (%): Fixed annual rate of return (e.g., enter 8 for 8.00% APR).
- Desired Years: Target number of years to double your initial capital.
- Exact Compound Formula:
Exact Years = ln(2) / ln(1 + r) ≈ 0.693 / r.
Rule of 72 Doubling Time Benchmarks
Compare Rule of 72 estimates against exact logarithmic compounding math across common interest rates:
| Annual Return Rate (%) | Rule of 72 Estimate | Exact Doubling Time | Growth on $10,000 in 10 Years |
|---|---|---|---|
| 4.00% APR (Savings / CD) | 18.0 Years | 17.67 Years | $14,802.44 |
| 6.00% APR (Conservative Portfolio) | 12.0 Years | 11.90 Years | $17,908.48 |
| 8.00% APR (Balanced Portfolio) | 9.0 Years | 9.01 Years | $21,589.25 |
| 10.00% APR (S&P 500 Historic Avg) | 7.2 Years | 7.27 Years | $25,937.42 |
| 12.00% APR (Growth Equity) | 6.0 Years | 6.12 Years | $31,058.48 |
Step-by-Step Rule of 72 Calculation Example
Here is an example calculating how fast a $25,000 investment will grow to $50,000 at a 9.00% annual return:
- Identify Interest Rate: Annual Rate R = 9 (representing 9.00%).
- Apply Rule of 72 Formula:
72 / 9 = 8.0 years. - Check Exact Compound Math:
ln(2) / ln(1.09) = 0.69315 / 0.08618 = 8.04 years. - Result: Your $25,000 investment will double to $50,000 in approximately 8 years.
Frequently Asked Questions
Why does the Rule of 72 work?
The Rule of 72 is derived from the natural logarithm of 2 (ln 2 = 0.693). Because 72 has many whole-number divisors (2, 3, 4, 6, 8, 9, 12), financial mathematicians selected 72 as a convenient numerator that matches realistic interest rates (6% to 10%) remarkably well.
How accurate is the Rule of 72?
The Rule of 72 is extremely accurate for interest rates between 6% and 10%. For lower interest rates (below 5%), the Rule of 69 or 70 is slightly more accurate.
Can the Rule of 72 be used for inflation?
Yes! If inflation averages 3% per year, dividing 72 by 3 shows that the purchasing power of your money will be halved in 24 years.
How can I use the Rule of 72 to calculate required interest rate?
If you want to double your money in 6 years, divide 72 by 6: you need a 12% annual rate of return.