Final answer:
The rule of 72 is an approximation used to estimate the time required to double an investment at a fixed annual interest rate by dividing 72 by the interest rate. The accuracy of this estimate can be evaluated using the percentage error formula, comparing the estimated time to the actual time calculated with compound interest.
Step-by-step explanation:
The rule of 72 is a simple way to estimate the number of years required to double the investment at a given annual fixed interest rate.
By dividing 72 by the annual interest rate, you get a rough estimate of the number of years it will take to double your money.
For example, at a 6% interest rate, you would divide 72 by 6 to get 12 years.
To determine how closely the rule of 72 estimates the actual number of years for an investment to double, one would need the exact doubling time calculated using the formula for compound interest.
The percentage error can then be calculated using the formula: % error = (actual - estimated) / actual.
Assuming the actual doubling time is given or calculated, the percentage error shows the accuracy of the rule of 72 as an estimation tool.