The Rule of 72

Divide 72 by an annual interest rate and you get a quick estimate of how many years money takes to double. At a hypothetical 8%, the rule says 9 years; the exact answer is 9.01 years. Close — but not exact, and the table below shows how the error behaves at other rates.

Rule of 72 estimate9.00 years
Exact (ln 2 ÷ ln(1 + r))9.01 years
Rule's error-0.01 years (-0.1%)

Rule of 72 vs the exact answer, rate by rate

The exact doubling time for annual compounding is ln(2) ÷ ln(1 + r). The Rule of 72 replaces that with one division. It is most accurate around 7–9% — close to the rates people most often use it with — and drifts further off at very low and very high rates, always in the direction shown below.

Rate	Rule of 72	Exact	Error (years)	Error (%)
1%	72.00 yrs	69.66 yrs	+2.34	+3.4%
2%	36.00 yrs	35.00 yrs	+1.00	+2.8%
3%	24.00 yrs	23.45 yrs	+0.55	+2.3%
4%	18.00 yrs	17.67 yrs	+0.33	+1.9%
5%	14.40 yrs	14.21 yrs	+0.19	+1.4%
6%	12.00 yrs	11.90 yrs	+0.10	+0.9%
7%	10.29 yrs	10.24 yrs	+0.04	+0.4%
8%	9.00 yrs	9.01 yrs	-0.01	-0.1%
9%	8.00 yrs	8.04 yrs	-0.04	-0.5%
10%	7.20 yrs	7.27 yrs	-0.07	-1.0%
12%	6.00 yrs	6.12 yrs	-0.12	-1.9%
15%	4.80 yrs	4.96 yrs	-0.16	-3.2%
18%	4.00 yrs	4.19 yrs	-0.19	-4.5%
20%	3.60 yrs	3.80 yrs	-0.20	-5.3%

Why 72?

The exact constant would be 100 × ln(2) ≈ 69.3 — and for continuous compounding, the "Rule of 69.3" is exact. For annual compounding the true constant creeps upward as the rate rises, passing 72 near 8%. 72 also happens to divide cleanly by 2, 3, 4, 6, 8, 9 and 12, which made it easy to use in the centuries before calculators. It is a deliberate trade: a little accuracy given up in exchange for arithmetic you can do in your head. Variants exist — 70 for lower rates or continuous-ish growth, 114 for tripling, 144 for quadrupling — all built from the same logarithm.

To turn any of these doubling times into actual balances, use the compound interest calculator, or read the full formula it is based on.

Estimates only: doubling times assume a constant hypothetical rate. Real returns vary year to year and can be negative, so real money does not double on this schedule. This page is an educational illustration, not financial advice.

Frequently asked questions

How accurate is the Rule of 72?

Within about a tenth of a year between 6% and 10%. At 2% it overstates by a full year (36 vs the exact 35.00), and at 20% it understates by about 0.2 years — good enough for a mental estimate, not for a contract.

Does the Rule of 72 work for monthly compounding?

Approximately. More frequent compounding doubles money slightly faster than annual compounding at the same nominal rate, so the rule becomes a mild overestimate. The exact comparison depends on the effective annual rate (APY).

Can I use it for inflation or debt?

Yes — the maths is the same. At 3% inflation, prices double in about 24 years. At a 24% credit-card rate, an unpaid balance doubles in roughly 3 years (the exact figure is about 3.22 years).

Where does the rule come from?

It appears in Luca Pacioli's 1494 mathematics text Summa de Arithmetica, presented without derivation as a merchant's rule of thumb — it was already old when he wrote it down.