Principles of Macroeconomics / Unit 4 MAC 0305 worked example, 60 to 90 seconds
The Rule of 72
The idea
The rule of seventy-two gives doubling time without a calculator: divide seventy-two by the growth rate stated as a whole number, and the answer is roughly the number of years it takes for a quantity to double. It works for anything that grows at a steady percentage rate, including output, income and savings. The rule is an approximation, not an identity, and it is most accurate for rates between about two and ten percent. Used in reverse, it turns a doubling time into a growth rate.
In practice
Worked example: at two percent a year, income doubles in about thirty-six years, so roughly twice in a lifetime. At six percent it doubles in about twelve years, so about six times in the same span. Two economies starting level, one at two percent and one at six, end a lifetime apart by a factor of many times over.
Where people slip
The rule is rough on purpose. At nine percent it predicts eight years, and the exact answer is a little over eight, so treat the result as an estimate rather than a figure to quote.
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