Why the Rule of 72 Works
Doubling time for compound growth follows ln(2) ÷ ln(1 + r), and for interest rates in the everyday range (2%–12%) that formula happens to be closely approximated by simply dividing 72 by the rate. At 6%, the rule says 12 years; the exact answer is 11.9. Close enough for any mental estimate — and 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, which is why it beat the slightly more accurate 69.3 in popularity.
Practical Uses
- Savings reality check: at a 4.5% CD rate, money doubles in ~16 years — safe but slow.
- Inflation warning: the rule works in reverse. At 3% inflation, your cash loses half its purchasing power in ~24 years.
- Fee awareness: a 2% annual fee means your advisor's cut doubles relative to your money every 36 years of compounding drag.
Its Limits
The approximation drifts at extreme rates — at 50% growth the rule is off by more than a year. This calculator shows both the shortcut and the exact answer so you always have the honest number.