How accurate is the rule of 72?

Very good between about 6% and 10%, and it drifts outside that. At 8% it predicts 9.0 years against an exact 9.01; at 20% it predicts 3.6 against an exact 3.80. Use 69.3 for continuous compounding and 72 for annual, which is why 72 was chosen: it divides cleanly and it is close.

Does it work for inflation as well?

Yes, and it is more sobering that way round. At 6% inflation, prices double in twelve years, which means money left in a 3% account halves in purchasing power over roughly twenty-four.

Finance & Loansinterest

Rule of 72 Calculator

Exact doubling time next to the Rule of 72 and the Rule of 70, so you can see where each approximation is good and where it drifts.

Also called: how long to double money, 72 rule investment.

Years to double (exact)

9.01

At 8% money doubles in 9.01 years. The Rule of 72 estimates 9, the Rule of 70 estimates 8.75.

Rule of 72 estimate

Rule of 70 estimate

8.75

Rule of 72 error (years)

-0.01

How this is calculated

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for India change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

Doubling needs (1+r)^t = 2, so t is ln2 over ln(1+r). The shortcut works because ln(1+r) is approximately r for small rates, giving 69.3/r. It is stated as 72 for two reasons: 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, and the linear approximation understates the true time, so inflating the numerator corrects for it. The correction happens to land near 8%.

t = ln(2)/ln(1+r), approximated by 72/rate

r: Annual rate as a decimal (decimal)

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

at 8% the rule is near-exact

Annual rate of return: 8%

Years to double (exact)9.01

DRV-006 verified table

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at 2% the Rule of 70 is better

Annual rate of return: 2%

Years to double (exact)35

DRV-006 verified table

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at 12% both drift

Annual rate of return: 12%

Years to double (exact)6.12

DRV-006 verified table

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Frequently asked questions

How accurate is the rule of 72?: Very good between about 6% and 10%, and it drifts outside that. At 8% it predicts 9.0 years against an exact 9.01; at 20% it predicts 3.6 against an exact 3.80. Use 69.3 for continuous compounding and 72 for annual, which is why 72 was chosen: it divides cleanly and it is close.
Does it work for inflation as well?: Yes, and it is more sobering that way round. At 6% inflation, prices double in twelve years, which means money left in a 3% account halves in purchasing power over roughly twenty-four.