Stephen's grandmother deposited $100 in an investment account for him when he was born, 25 years ago. The account is now worth $1,500. What was the average rate of return on the account?
A) 6.00%
B) 16.67%
C) 15.00%
D) 11.44%

Question

Quizplus · Accepted Answer

The average rate of return can be calculated using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $n$ is the time the money is invested for in years. Rearranging the formula to solve for $r$ gives us $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Substituting the given values ($A = 1500$, $P = 100$, $n = 25$) into the formula gives $r = \left(\frac{1500}{100}\right)^{\frac{1}{25}} - 1 = 15^{0.04} - 1 \approx 0.1144$ or 11.44%.

Stephen's Grandmother Deposited $100 in an Investment Account for Him