A condominium complex was purchased by a group of private investors for $1.2 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places.
A) 22.73%
B) 23.17%
C) 22.52%
D) 23.84%

Question

A condominium complex was purchased by a group of private investors for $1.2 million and sold 5 year(s) later for $3.7 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places. ​
A) 22.73%
B) 23.17%
C) 22.52%
D) 23.84%

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal amount, $r$ is the rate, and $e$ is the base of the natural logarithm. Rearranging the formula to solve for $r$, we get $r = \frac{1}{t} \ln(\frac{A}{P})$. Substituting $A = 3.7$ million, $P = 1.2$ million, and $t = 5$ years, we get $r = \frac{1}{5} \ln(\frac{3.7}{1.2})$, which calculates to approximately 0.2252 or 22.52% when converted to a percentage.

A Condominium Complex Was Purchased by a Group of Private