Rule of 72
Estimate doubling via interest rate.
What does Rule of 72 mean?
The Rule of 72 is a simple mental-math shortcut that estimates how many years it takes for an investment to double at a given fixed annual interest rate. You divide 72 by the interest rate to get the approximate doubling time. While it is an approximation, it is remarkably accurate for rates between 2% and 15%, making it a favorite tool among investors and financial planners for quick back-of-the-envelope calculations.
How to calculate Rule of 72
The Rule of 72 formula is: Years to Double = 72 / Interest Rate. For example, at a 6% annual return, your money doubles in approximately 72 / 6 = 12 years. The exact formula uses logarithms: Exact Years = ln(2) / ln(1 + r/100). At 6%, this gives ln(2) / ln(1.06) = 11.90 years. The difference between the two results shows how close the Rule of 72 approximation is to the mathematically precise answer.
FAQ
The Rule of 72 is derived from the compound interest formula. When you solve 2 = (1 + r)^n for n, you get n = ln(2) / ln(1 + r). For small values of r, ln(1 + r) is approximately equal to r, so n is approximately 0.693 / r. Multiplying numerator and denominator by 100 gives roughly 69.3 / rate. The number 72 is used instead of 69.3 because it has more divisors (making mental math easier) and provides a slight correction that improves accuracy for typical interest rates.
The Rule of 72 is most accurate for interest rates between 6% and 10%, where the error is less than 1%. It remains reasonably accurate (within a few percent) for rates between 2% and 15%. At very low rates (below 2%) or very high rates (above 20%), the approximation becomes less reliable and the exact logarithmic formula should be used instead.
Yes. The Rule of 72 works for anything that grows at a compounded rate. You can use it to estimate how quickly prices double due to inflation, how fast a population grows, how long it takes GDP to double, or even how quickly a debt balance doubles if no payments are made. Any constant percentage growth rate can be plugged into the formula.
Both are mental-math shortcuts for estimating doubling time. The Rule of 70 (dividing 70 by the rate) is slightly more accurate at lower interest rates, while the Rule of 72 is more accurate at moderate rates around 8%. The Rule of 72 is more popular because 72 is evenly divisible by 2, 3, 4, 6, 8, 9, and 12, making mental division much easier.
No. The Rule of 72 assumes a fixed, uninterrupted compound growth rate. In practice, taxes on investment gains, management fees, and inflation will reduce the effective rate of return. To get a more realistic estimate, subtract expected taxes and fees from your gross return before applying the rule. For example, if your gross return is 8% but fees and taxes reduce it to 6%, use 6% in the calculation.
Related calculators
- Compound Interest— Growth of money with reinvested interest.
- CAGR— Average annual growth rate.
- Doubling Time— Time required to double.
- Exponential Growth— Growth proportional to size.