Rule of 72 Calculator
How many years it takes money to double at a given rate, by the rule of 72 and exactly.
Good to know. The rule of 72 works for debt too: at 24% on a credit card, what you owe doubles in about three years.
How it works
In plain words
Divide 72 by the yearly rate in percent for the years it takes to double. The exact answer is ln 2 ÷ ln(1 + rate). 72 works well because it is close to the exact figure for common rates and divides evenly by 2, 3, 4, 6, 8, 9 and 12.
The formula
years to double ≈ 72 ÷ rate % exactly: ln 2 ÷ ln(1 + rate) triple: ln 3 ÷ ln(1 + rate)
Worked example
At 8% a year, 72 ÷ 8 = 9 years to double. Exactly, ln 2 ÷ ln 1.08 = 9.01 years, so the rule is off by less than a month.
Sources
No outside data or rates: this is plain arithmetic.
2 automated tests check its answers on every change.
About the rule of 72 calculator
The rule of 72 is a quick way to see compound growth in your head: divide 72 by the yearly rate, and that is roughly how many years it takes for money to double. At 6%, 12 years; at 9%, 8 years; at 12%, 6 years.
It works for anything that grows by a steady percentage: savings, investments, prices under inflation, and debt. At 3% inflation, prices double in about 24 years, so money in a drawer loses half its value in that time. At 24% on a credit card, an unpaid balance doubles in about 3 years.
The rule is most accurate between about 6% and 10%. For lower rates, 70 or 69.3 is closer (69.3 is exact for continuous compounding); for higher rates, 72 underestimates slightly, and 76 or 78 does better above 20%. The calculator shows the exact figure beside the rule, and the table compares them at other rates.
Doubling times add up quickly: at 8%, money doubles in 9 years, quadruples in 18 and grows eightfold in 27. That is why starting to save early matters more than the amount you start with.
Questions people ask
What is the rule of 72?
A shortcut for compound growth: divide 72 by the yearly rate to get the years it takes to double. At 8%, about 9 years.
How long does it take to double money at 7%?
About 10.3 years by the rule of 72, and 10.24 years exactly.
Is the rule of 72 accurate?
Within a few months for rates between about 4% and 12%. For low rates, 70 is closer; for high rates, the rule underestimates.