The Rule of 72 and doubling time

How the Rule of 72 works

Take the annual growth rate as a whole number and divide 72 by it. At 8% a year, 72 ÷ 8 = 9 years to double. It works for any compound growth: investment returns, revenue, population — and in reverse for inflation, which halves the purchasing power of money in about 72 ÷ 6 = 12 years at 6% inflation (exactly 11.9).

Accuracy: Rule of 72 vs the exact answer

The rule is almost perfect from 6% to 10%, the range most long-run investment returns fall into. At low rates it slightly overestimates; at high rates it underestimates — at 25% it is off by about three months.

Why 72?

The exact doubling time is ln(2) ÷ ln(1 + r). For small r, ln(1 + r) ≈ r, so doubling time ≈ 0.693 ÷ r — which gives the Rule of 69.3. 72 is used instead because it is close and divides neatly by 2, 3, 4, 6, 8, 9 and 12, and because it happens to be more accurate around 8%, where the approximation’s error is smallest. The Rule of 70 is a common compromise for low rates such as GDP growth or inflation.

Using it backwards: the CAGR you need

Divide 72 by the number of years you have to double:

• Double in 6 years → 72 ÷ 6 ≈ 12% a year (exact: 12.25%)
• Double in 10 years → 72 ÷ 10 ≈ 7.2% a year (exact: 7.18%)

For an exact answer, or for targets other than doubling, use the reverse CAGR calculator. The main CAGR calculator also shows the doubling time for every result.

Doubling in real terms

A doubling of nominal money is not a doubling of what it buys. At a 9% CAGR with 3% inflation, the real rate is (1.09 ÷ 1.03) − 1 ≈ 5.83%, so purchasing power doubles in about 12.2 years rather than 8. To see how typical asset classes compare, readwhat is a good CAGR.

Sources and further reading

• Wikipedia: Rule of 72 — derivation and variants (69.3, 70)
• Investor.gov (U.S. SEC): Compound interest calculator
• Wikipedia: Doubling time

Educational information only — not investment advice. Past performance does not guarantee future results.