Rule of 72

The rule of 72 is a mental shortcut that estimates how many years an investment takes to double: divide 72 by the annual percentage growth rate. It is most accurate for rates roughly between 6% and 10%.

ByHoang TruongUpdated July 11, 2026

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The rule of 72 estimates doubling time: divide 72 by the annual growth rate as a whole number. At 8% growth, 72 ÷ 8 = 9 years, versus the exact ln(2) ÷ ln(1.08) ≈ 9.01 years — essentially exact. The shortcut is most accurate for rates of roughly 6% to 10%.

Where it fits

TopicTime Value of MoneyCoreSubjectCorporate FinanceCore

The formula

LaTeX

T \approx \frac{72}{r}

Variables

$T$: Estimated years to double (years)
$r$: Annual growth rate (%)

Quick estimate of doubling time, where r is the annual growth rate as a whole number percentage (use 8, not 0.08).

LaTeX

T_{exact} = \frac{\ln 2}{\ln(1+r)}

Variables

$T_{e x a c t}$: Exact years to double (years)
$r$: Annual growth rate (decimal)

The precise compound-growth doubling time, used to check the rule of 72 approximation; here r is a decimal (0.08, not 8).

Check yourself

PracticeCORE

An investment grows at a constant 6% a year. Using the rule of 72, approximately how many years will it take to double in value?

Select an answer to check your understanding.