Rule of 72 calculator: how long to double your money
Years to double at a given return, the return needed to double in a given time, and the exact figure next to the rule-of-thumb.
| Return | Rule of 72 | Exact | Your amount after 30 years |
|---|
Rule of 72: years ≈ 72 ÷ return. Exact: ln 2 ÷ ln(1 + return). Before costs, taxes and inflation.
The rule
Divide 72 by the yearly return and you get roughly the years it takes to double: 72 ÷ 8 = 9 years at 8%. It works because ln(2) ≈ 0.693, and 72 is close to 69.3 while dividing nicely by 2, 3, 4, 6, 8, 9 and 12. The rule is accurate within a few months for returns between about 5% and 12%; outside that range the calculator also shows the exact answer, ln(2) ÷ ln(1 + r).
The rule in reverse
To double in a set number of years, you need 72 ÷ years as a return: doubling in 6 years needs about 12% a year, in 12 years about 6%. Expectations above 15% a year over long periods are outside what broad markets have delivered; see the S&P 500's historical returns.
Inflation uses the same rule
At 3% inflation, prices double in about 24 years, so cash loses half its buying power in that time. At 6% it takes 12 years. The inflation calculator shows the full picture; the compound interest calculator shows the doubling happening year by year.
Frequently asked questions
How does the rule of 72 work?
Years to double ≈ 72 ÷ annual return in percent. At 6% that is 12 years, at 9% it is 8 years, at 12% it is 6 years. The exact formula is ln(2) ÷ ln(1 + r); at 6% that gives 11.9 years, so the rule is very close.
How long does it take to double money at 7%?
About 10.3 years (72 ÷ 7 ≈ 10.3; the exact answer is 10.24 years). At 7% money doubles about seven times in 72 years, so 10,000 becomes about 1.3 million.
Is the rule of 72 accurate?
Between 5% and 12% it is within about 0.2 years of the exact answer. For low rates 69 or 70 is slightly better; for high rates (20%+) the rule underestimates the time by about a year. Use the exact figure shown next to the rule when precision matters.
Does the rule of 72 work for inflation and debt?
Yes: it tells you how long until prices double at a given inflation rate (24 years at 3%), and how long until a debt doubles at a given interest rate if nothing is repaid (4 years at 18% credit-card interest).
From assumptions to real numbers, free
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Illustration only — not investment advice and not a forecast. Real returns vary from year to year and can be negative. Disclaimer.