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Divide 72 by the growth rate to get doubling time in years: mental arithmetic accurate to within a few months for rates between 2% and 12%. The same rule run on inflation shows how fast cash under the mattress halves in buying power. Not financial advice.
What The Rule Of 72 Calculator Works Out
- Rule of 72 says: 72 divided by the annual rate gives the years to double. 6% doubles money in 12 years, 8% in 9 and 3% in 24. Run on inflation instead, it gives the years for cash to lose half its buying power.
- Exact answer: ln(2) divided by ln(1 + rate). The rule's error stays within months across the everyday 2% to 12% band, which is why it survived from Pacioli's 1494 textbook into every financial literacy course.
- Quick table: the doubling times worth memorising. 72 sits close to 100 times ln 2 (about 69.3) and divides cleanly by 2, 3, 4, 6, 8, 9 and 12.
- Rule constant (advanced): swap 72 for 70 (preferred by demographers for population and GDP at low rates) or 69.3 (continuous compounding). The error table underneath shows how each constant performs from 1% to 20%.
- Starting amount and years (advanced): grows (or, in halving mode, shrinks) a sum over the chosen period and counts the doublings. 36 years at 8% is four doublings, sixteen-fold, with the late doublings carrying almost all the money.
- Tripling and quadrupling (advanced): the exact times, which the rules of 114 and 144 approximate.
- Fees and inflation (advanced): deducts an annual charge and an inflation rate from the growth rate before working out the doubling time. A 1.5% fund fee compounds into a swallowed doubling over a working life, and a 2% gap between two pensions is the difference between doubling four times and three times over forty years.
- Rule error (advanced): the gap between the rule and the exact figure at your rate, in years and as a percentage. The rule assumes a steady rate markets never deliver; its best use is a sniff test: anyone promising to double money in three years is quoting 24% a year.