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One rate of return

Annual rate of return

Expected yearly growth rate, from 0.01% through 100%.

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Years to double your money9 years

At 8% per year, your money doubles in about 9 years.

Precise doubling time: 9.0065 years
Rule of 72 estimate: 9.0000 years

Formula & methodology

How the Rule of 72 works

The Rule of 72 is a mental-math shortcut for estimating how long an investment takes to double at a fixed annual rate: divide 72 by the rate expressed as a whole number. The precise doubling time comes from the compounding formula using natural logarithms. The two are close for typical rates — the Rule of 72 is most accurate near 8% and drifts slightly at very low or very high rates.

Years to double ≈ 72 ÷ Rate
Precise years = ln(2) ÷ ln(1 + Rate)

Rate: Annual rate of return, as a whole number for 72 ÷ Rate
ln: Natural logarithm

Worked example

Doubling at an 8% annual return

At an 8% annual rate of return, the Rule of 72 estimates the doubling time as 72 ÷ 8 = 9 years. The precise calculation, ln(2) ÷ ln(1.08), works out to about 9.0065 years — so the shortcut is within a fraction of a year of the exact answer at this rate.

This is an educational calculation based only on the rate you provide. It does not look up live prices, and it is not investment advice.

Assumptions

What this calculator assumes

The rate of return is constant every year and compounds once per year.
No contributions, withdrawals, taxes, or fees are modeled — only the growth rate matters.
The Rule of 72 is an approximation; the precise doubling time is the exact figure for annual compounding.
Results are rounded for display.

Common questions

Rule of 72 FAQ

Why 72 and not another number?

72 is chosen because it divides evenly by many common rates (2, 3, 4, 6, 8, 9, 12) and gives estimates close to the exact doubling time for typical returns. The mathematically ideal constant is closer to 69.3, but 72 is easier to divide in your head.

When is the Rule of 72 least accurate?

It is most accurate around 8%. At very low rates it slightly underestimates the time to double, and at very high rates it slightly overestimates it. For an exact figure, use the precise doubling time shown alongside the estimate.

Primary sources

Sources and review notes

Methodology last checked Jul 14, 2026. Formula implementation is covered by deterministic unit tests. No financial professional review is claimed yet.