Rule of 72 calculator
Divide 72 by a yearly return and you have a fast estimate of how long money takes to double; that is the whole rule of 72. Give the calculator a rate to get the doubling time, or a number of years to get the rate required, and it checks the shortcut against the exact result for your chosen compounding. A table shows where the rule is almost perfect and where it starts to slip.
The shortcut and the exact figure, for your inputs
Three popular rules of thumb beside the exact answer for the compounding you selected.
How close is the rule at each rate?
Doubling time by the rule of 72 and by the exact formula, using your compounding. The rule works best between 6 and 10 percent.
| Annual rate | Rule of 72 | Exact | Difference |
|---|
How the shortcut and the exact answer are calculated
The rule of 72 approximates the compound growth formula. The exact answer solves that formula directly for the time, or the rate, that doubles your money.
Rule of 72 for years
Divide 72 by the rate in percent.
years ≈ 72 ÷ rate
Rule of 72 for the rate
Divide 72 by the number of years.
rate ≈ 72 ÷ years
Exact number of years
Using n compounding periods per year.
years = ln 2 ÷ (n × ln(1 + rate ÷ n))
Exact, continuous compounding
The limit as compounding becomes nonstop.
years = ln 2 ÷ rate = 69.3 ÷ rate in %
Exact rate
The rate that doubles money in the number of years you set.
rate = n × (21 ÷ (n × years) − 1)
Rule of 72 FAQ
What does the rule of 72 say?
That 72 divided by the yearly percentage return gives roughly the years it takes money to double. At 6 percent that is 12 years. It also runs in reverse: to double in 9 years you need about 8 percent a year.
How precise is the rule of 72?
Very, for returns of about 6 to 10 percent, where it is usually within a few weeks of the exact figure. It drifts at very low and very high rates, and the table shows the error at each one.
Why use 72 instead of 70 or 69?
The exact constant for continuous compounding is about 69.3, and 70 is a rounded version. 72 fits annual compounding at ordinary rates better and divides cleanly by 2, 3, 4, 6, 8, 9 and 12, so it is easy to do in your head.
Does the rule of 72 work for inflation?
Yes. 72 divided by the inflation rate gives the years for prices to double, or for cash to lose half its buying power. At 3 percent inflation that is roughly 24 years.
What are the rules of 114 and 144?
The same shortcut for tripling and quadrupling: 114 divided by the rate gives years to triple, and 144 gives years to quadruple. The calculator shows both next to the doubling time.
Can it be used for debt?
Yes, and it makes a sobering point. An unpaid credit card balance at 24 percent interest doubles in about 3 years.