The annual rate of return on an initial investment of P dollars is given by $r = \left( \frac { A } { P } \right) ^ { 1 / t } - 1$ where A is the current value and t is the number of years since the money was invested. Find the annual rate of return on a $22,000 investment that grew to $32,000 after 10 years. Round to the
Nearest hundredth of a percent.
A) 13.82%
B) 23.82%
C) 0.04%
D) 3.82%

Question

Quizplus · Accepted Answer

The formula for the annual rate of return is $r = \left( \frac { A } { P } \right) ^ { 1 / t } - 1$. Plugging in the given values, $A = 32000$, $P = 22000$, and $t = 10$, we get $r = \left( \frac { 32000 } { 22000 } \right) ^ { 1 / 10 } - 1$. Calculating this gives an annual rate of return of approximately 0.0382, or 3.82% when converted to a percentage and rounded to the nearest hundredth of a percent.

The Annual Rate of Return on an Initial Investment of P