Rule of 72 Calculator
Estimate how long it takes for an investment to double (72 / rate).
Overview
The Rule of 72 is a back-of-the-envelope formula for estimating how long it takes an investment to double at a given compounded rate of return. Divide 72 by the rate (as a percent, not a decimal) and the quotient is the approximate number of years. The rule is taught in nearly every introductory finance class because it requires no calculator yet stays remarkably accurate across the range of rates most personal investors face — roughly 4% to 12%.
The constant 72 is not magic; it falls out of the natural-log approximation of compound interest. Exact doubling time is ln(2) / ln(1 + r) ≈ 0.693 / r for small r. Multiplying numerator and denominator by 100 gives 69.3 / rate_pct. The value 72 is preferred because it has many divisors (2, 3, 4, 6, 8, 9, 12) and the error against the exact formula is under 1% in the 6%–10% range. For rates outside that band, 69, 70, or 73 are sometimes substituted as more accurate cousins.
How it works
Years to double ≈ 72 / annual_rate_percent. To find the rate needed to double in a target number of years, rearrange: required_rate ≈ 72 / years. The same rule extends to other multiples: 114 for tripling, 144 for quadrupling. Because the rule assumes constant compounding, it cannot account for variable returns, withdrawals, or contributions; use a full compound-interest calculator when those matter.
Examples
- 6% annual return: doubles in
72 / 6 = 12years (exact answer: 11.9 years). - 8% annual return: doubles in
72 / 8 = 9years (exact: 9.0 years). - 10% annual return: doubles in
72 / 10 = 7.2years (exact: 7.27 years). - 3% inflation: prices double in 24 years — useful for thinking about long-term purchasing power.
- Need to double in 5 years? Required rate is
72 / 5 ≈ 14.4%.
FAQ
Why use 72 and not 69 or 70?
72 is more accurate near 8% and divides evenly more often. The choice is a numerical convenience, not theoretical.
Does it work for daily compounding?
Approximately, yes. Continuous compounding doubles in ln(2) / r ≈ 69.3 / rate_pct — closer to a Rule of 69.
Can I apply it to debt?
Yes — credit card balances at 22% APR double in roughly 72 / 22 ≈ 3.3 years if no payments are made.
Is the rule accurate at high rates?
Less so. At 20% the rule gives 3.6 years but the exact answer is 3.8 years — about 5% off.
Does it work with negative returns?
No. Losses compound asymmetrically: a 50% loss requires a 100% gain to recover, which is not what the rule estimates.