Find out how long an investment takes to double. The Rule of 72 is a quick mental shortcut — this calculator also shows the exact answer, so you can see how close the shortcut gets.
Dividing 72 by the annual percentage return gives an approximate doubling time.
The exact answer uses logarithms, which is what the comparison figure shows.
The shortcut is closest to correct for rates of roughly 6% to 10%, and drifts further out at very high or very low rates.
Rule of 72: Years ≈ 72 ÷ annual return %
Exact: Years = ln(2) ÷ ln(1 + r)
An investment returning 12% a year.
Annual return: 12%
Apply the rule: 72 ÷ 12 = 6
The exact answer is ln(2) ÷ ln(1.12) = 6.12 years
The shortcut is within about six weeks
Answer: Roughly 6 years to double
Why 72 and not some other number?
The exact number, mathematically, is about 69.3. But 72 is used because it divides neatly by 2, 3, 4, 6, 8, 9, and 12, which makes it easy to work out in your head. It is also a little more accurate for the common return range where people use it most.
How accurate is it?
It is accurate to within a few months, for rates between about 6% and 10%. At very low rates like 2%, or very high rates like 25%, the error grows bigger, so use the exact number when precision matters.
Does it account for inflation?
Only if you use a real return, not a normal (nominal) one. To find out when your buying power doubles, subtract inflation from your return first.