Question 21.41

11. The rule of 72 is a handy rule of thumb for estimating how long it takes money to double with annual compounding: If is the annual interest rate, expressed as a decimal, then the doubling time is approximately years. If you express the interest rate as , then the doubling time is approximately years.

  1. Calculate the balance at the end of the predicted doubling time for each $1000, with annual compounding, for the small growth rates of 3%, 4%, and 6%.
  2. Repeat part (a) for the intermediate interest rates of 8% and 9%.
  3. Repeat part (a) for the larger interest rates of 12%, 24%, and 36%.
  4. What do you conclude about the rule of 72?

11.

(a) $2,032.79; $2,025.82; $2,012.20

(b) $1,999.00; $1,992.56

(c) $1,973.82; $1,906.62; $1,849.60

(d) For small and intermediate interest rates, the rule of 72 gives good approximations to the doubling time.