What is the Rule of 72? Definition, Formula, and Example
The Rule of 72 is a mental-math shortcut that estimates how many years it takes for money to double at a given compound annual return: 72 divided by the annual rate.
What is the Rule of 72?
The Rule of 72 estimates the doubling time of a compounding investment: divide 72 by the annual rate of return, and the result is the number of years required for the principal to double. At 8% per year, money doubles in roughly 9 years. At 12%, in 6. It requires no calculator, no spreadsheet, and no finance background — which is why it survives as the most-used heuristic in portfolio math.
How It Is Calculated
Years to double ≈ 72 ÷ annual rate of return (in percent)
The rule is an approximation of the exact logarithmic solution. The precise formula for doubling time is:
t = ln(2) ÷ ln(1 + r)
At r = 8%, the exact answer is ln(2) ÷ ln(1.08) = 0.693 ÷ 0.0770 = 9.01 years. The Rule of 72 gives 9.0. The number 72 works because it approximates 69.3 (100 × ln 2) while being cleanly divisible by 2, 3, 4, 6, 8, 9, and 12 — the rates people actually quote. Accuracy is best between 6% and 10%; at 2% it overestimates slightly (72 gives 36 years vs. exact 35), and at 20%+ it underestimates meaningfully.
The rule inverts: to find the rate needed to double in N years, compute 72 ÷ N.
Worked Example
An investor holds an S&P 500 index fund tracking SPY and assumes the index's long-run nominal return of about 10% annually.
Years to double = 72 ÷ 10 = 7.2 years
A $50,000 position becomes $100,000 around year 7, $200,000 around year 14, and $400,000 around year 22 — three doublings inside a single career. Now apply the rule to inflation: at 3% inflation, purchasing power halves in 72 ÷ 3 = 24 years. At 8% inflation (2022-style), it halves in 9 years. The same two-line calculation prices both the asset side and the liability side of a retirement plan.
When Traders Use It
- Sanity-checking return claims: a promoter promising to "double your money in 2 years" is claiming a 36% annual compound return (72 ÷ 2). The rule converts marketing language into an auditable number instantly.
- Comparing fee drag: a 1% advisory fee on an 8% gross return cuts net return to 7%, stretching doubling time from 9.0 to 10.3 years — over 40 years, that is nearly one full lost doubling.
- Debt math: a credit card at 24% APR doubles the balance in 3 years if unpaid. The rule makes compounding's cost visceral.
- Quick DCF cross-checks: verifying whether a growth assumption implies an absurd doubling cadence.
Limitations and Common Misconceptions
The Rule of 72 assumes a constant compound rate, and markets do not deliver constant rates. Sequence-of-returns risk — a 30% drawdown early in the holding period — breaks the smooth-doubling picture entirely, even if the long-run average return is unchanged. It also ignores taxes, fees, contributions, and withdrawals, all of which move realized doubling time far from the headline figure. Above roughly 20% or below 2%, the approximation drifts enough that the exact logarithmic formula is worth the ten extra seconds. And it says nothing about volatility: two assets with identical 8% averages and identical doubling times can have wildly different maximum drawdown profiles.