At an investment seminar that I recently attended, I learned about something called “the Rule of 72.” According to the person in charge of the seminar, a good estimate for finding how long it takes for an investment to double is given by the following equation:

Using what you know about the time value of money, calculate the error in using the above equation to estimate how long it takes to double an investment made at the following effective annual interest rates: 5%, 7.5%, and 10%. Express your answers as % error to two significant figures. Comment on the Rule of 72 and its accuracy for typical financial calculations today.

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Number of years to double investment 72 effective annual interestrate (in %)