Rule of 72 calculator
The rule of 72 is a quick way to estimate how long money takes to double: divide 72 by the yearly return. Enter a rate to get the doubling time, or a number of years to get the rate you need, and this calculator compares the shortcut with the exact answer for the compounding you choose. The table shows where the rule is spot on and where it starts to drift.
Shortcut vs exact, for your numbers
Three common rules of thumb next to the exact figure for the compounding you picked.
How accurate is the rule at each rate?
Doubling time by the rule of 72 and exactly, with your compounding. The rule is closest in the 6 to 10 percent range.
| Annual rate | Rule of 72 | Exact | Difference |
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How the rule and the exact answer are worked out
The rule of 72 is an approximation of the compound growth formula. The exact answer solves that formula directly for the time, or the rate, at which money doubles.
Rule of 72, years
Divide 72 by the rate in percent.
years ≈ 72 ÷ rate
Rule of 72, rate
Divide 72 by the years.
rate ≈ 72 ÷ years
Exact years
With n compounding periods a year.
years = ln 2 ÷ (n × ln(1 + rate ÷ n))
Exact with continuous compounding
The limit as compounding becomes constant.
years = ln 2 ÷ rate = 69.3 ÷ rate in %
Exact rate
The rate that doubles money in the years you set.
rate = n × (21 ÷ (n × years) − 1)
Rule of 72 questions
What is the rule of 72?
It is a mental shortcut for compound growth: divide 72 by the annual percentage return and you get the approximate number of years it takes to double your money. At 6 percent, 72 divided by 6 is 12 years. It also works the other way round: to double in 9 years you need about 8 percent a year.
How accurate is the rule of 72?
Very accurate for returns between about 6 and 10 percent a year, usually within a few weeks of the exact answer. It drifts at very low and very high rates. The table below the calculator shows the error at each rate.
Why 72 and not 70 or 69?
The exact figure for continuous compounding is about 69.3, and 70 is a common round version of it. 72 works better for annual compounding at everyday interest rates, and it divides neatly by 2, 3, 4, 6, 8, 9 and 12, which makes it easy to use in your head.
Can I use the rule of 72 for inflation?
Yes. Divide 72 by the inflation rate to see how long it takes prices to double, or for your money to lose half its buying power. At 3 percent inflation that is about 24 years.
What are the rules of 114 and 144?
They are the same idea for tripling and quadrupling. Divide 114 by the rate for the years to triple, and 144 for the years to quadruple. The calculator shows both alongside the doubling time.
Does it work for debt?
Yes, and it is a useful warning. A credit card balance at 24 percent interest that is left unpaid doubles in about 3 years.