Use the Rule of 72 to quickly estimate how long an investment takes to double at a given interest rate, or what rate you'd need to double it in a given number of years, alongside the exact answer for comparison.
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The Rule of 72 is a quick mental-math shortcut for estimating compound growth: divide 72 by an annual interest rate to estimate how many years it takes to double an investment, or divide 72 by a number of years to estimate the annual rate needed to double it in that time.
For example, at 8% annual interest, 72 ÷ 8 = 9 years to roughly double your money, very close to the exact answer of about 9.01 years.
72 is used because it has many small divisors (1, 2, 3, 4, 6, 8, 9, 12...), making the mental math easy, and it happens to closely approximate the exact formula ln(2) ÷ ln(1 + r) across the typical range of investment returns (roughly 6% to 10%). Outside that range, the approximation drifts further from the exact answer, which is why this calculator shows both side by side.
It's most accurate for annual rates between roughly 6% and 10%, where the estimate is typically within a few hundredths of a year or a few tenths of a percentage point of the exact answer. Accuracy decreases at very low or very high rates.
Yes, it works for any quantity that grows at a steady compounding rate, including inflation (how long until prices double), population growth, or debt growing at a fixed interest rate.
For years to double: ln(2) ÷ ln(1 + r), where r is the annual rate as a decimal. For required rate: (2^(1/years) − 1) × 100. These come directly from the compound growth formula rather than the Rule of 72 approximation.
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