Rule of 72 calculator
Divide 72 by the growth rate to get the doubling time. It is a good approximation between about 6% and 10%, and this shows exactly how good.
%
Rule of 72 estimate
10.29years
- Exact doubling time
- 10.2448 years
- Error of the shortcut
- 0.0409 years
- Relative error
- 0.400 %
- Time to triple
- 16.238 years
- Time to grow tenfold
- 34.032 years
Show the working
- Annual growth rate = 7
- Rule of 72 estimate = 72 / 7 = 10.2857
- Exact doubling time = log(2, 1 + 7/100) = 10.2448
- Error of the shortcut = 10.2857 - 10.2448 = 0.040 945 9
- Relative error = 0.040 945 9 / 10.2448 * 100 = 0.399 677
- Time to triple = log(3, 1 + 7/100) = 16.2376
- Time to grow tenfold = log(10, 1 + 7/100) = 34.0324
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- approximate doubling time = 72 / rate
- exact doubling time = ln 2 / ln(1 + rate)
69.3 would be the theoretically better numerator for continuous compounding, but 72 divides nicely by more integers.