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Rule of 72 — Definition, Formula & Examples

The Rule of 72 is a quick mental-math shortcut that estimates how many years it takes for an investment to double in value. You simply divide 72 by the annual interest rate (as a whole number) to get the approximate doubling time.

The Rule of 72 states that the number of periods required for a quantity growing at a fixed compound rate r%r\% per period to double is approximately 72/r72 / r, where rr is expressed as a percentage rather than a decimal. This approximation is most accurate for rates between 2% and 15%.

Key Formula

t≈72rt \approx \frac{72}{r}
Where:
  • tt = Approximate number of years for the investment to double
  • rr = Annual interest rate expressed as a percentage (e.g., 6 for 6%)

How It Works

Take the number 72 and divide it by the annual interest rate written as a whole number. The result is roughly how many years your money needs to double, assuming interest compounds annually. For instance, at 8% per year, your money doubles in about 9 years. The rule works because it closely approximates the exact formula t=ln⁡(2)/ln⁡(1+r)t = \ln(2)/\ln(1 + r) for typical interest rates. It also works in reverse: if you know you want to double your money in 6 years, divide 72 by 6 to find you need roughly a 12% annual return.

Worked Example

Problem: You invest $5,000 in an account that earns 6% annual compound interest. Approximately how many years will it take for your investment to grow to $10,000?
Apply the Rule of 72: Divide 72 by the annual interest rate.
t≈726=12 yearst \approx \frac{72}{6} = 12 \text{ years}
Check against the exact answer: Using the exact formula gives t=ln⁡(2)/ln⁡(1.06)≈11.90t = \ln(2)/\ln(1.06) \approx 11.90 years, so the Rule of 72 estimate is very close.
Answer: At 6% annual compound interest, your $5,000 will double to $10,000 in approximately 12 years.

Why It Matters

The Rule of 72 lets you evaluate savings accounts, loans, and investment options without a calculator. Financial advisors, bankers, and anyone comparing retirement plans use it to make fast, informed decisions. It also appears regularly on standardized tests and in personal finance courses.

Common Mistakes

Mistake: Using the rate as a decimal instead of a whole number (e.g., dividing 72 by 0.06 instead of 6).
Correction: Always express the rate as a percentage number. For 6%, use 6, not 0.06. Dividing 72 by 0.06 gives 1,200 — far too large.