Julio purchased 700 shares of a certain stock for $22,750 (including commissions). He sold the shares 5 year(s) later and received $32,100 after deducting commissions. Find the effective annual rate of return on his investment over the 5-year period. Round your answer to two decimal places.
A) 7.13%
B) 6.91%
C) 6.95%
D) 7.01%

Question

Julio purchased 700 shares of a certain stock for $22,750 (including commissions). He sold the shares 5 year(s) later and received $32,100 after deducting commissions. Find the effective annual rate of return on his investment over the 5-year period. Round your answer to two decimal places. ​
A) 7.13%
B) 6.91%
C) 6.95%
D) 7.01%

Quizplus · Accepted Answer

The effective annual 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 (initial investment), $r$ is the annual interest rate, and $n$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Substituting the given values: $A = \$32,100$, $P = \$22,750$, and $n = 5$ years, we get $r = \left(\frac{32100}{22750}\right)^{\frac{1}{5}} - 1$. Calculating this gives an effective annual rate of return of approximately 7.13%.

Julio Purchased 700 Shares of a Certain Stock for $22,750