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How It Works
The Rule of 72 is a mental-math shortcut: divide 72 by the annual interest rate to estimate how many years it takes for an investment to double. It works best for rates between 2% and 18%.
You can also reverse it: divide 72 by the number of years to find the rate needed to double your money. Want to double in 6 years? You need 72 / 6 = 12% annually.
Example Problem
You invest in an index fund earning 8% per year. How long until your money doubles?
- Years = 72 / 8 = 9 years
At 6%, it takes 12 years. At 10%, it takes 7.2 years. At 4%, it takes 18 years. The exact compound formula gives 9.006 years at 8%, so the Rule of 72 is remarkably accurate.
Frequently Asked Questions
Why does the Rule of 72 work?
It is a simplification of the natural logarithm formula for doubling time: t = ln(2) / ln(1+r). Since ln(2) is approximately 0.693, and for small rates the math simplifies nicely, 72 provides a convenient divisor that gives accurate results for typical interest rates.
Is the Rule of 72 accurate for all interest rates?
It is most accurate between 6% and 10%. At 2%, the Rule of 69.3 is more precise. At 20%, the actual doubling time is 3.8 years vs. the Rule of 72's estimate of 3.6 years. The error is typically less than 5%.
Can the Rule of 72 be applied to inflation?
Yes. At 3% inflation, prices double in about 72 / 3 = 24 years. This means $100 of purchasing power today will buy only $50 worth of goods in 24 years. It highlights why investments must outpace inflation.
Related Calculators
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Reference: Investopedia. Rule of 72 Definition. Retrieved from investopedia.com.