A condominium complex was purchased by a group of private investors for $1.3 million and sold 7 year(s) later for $3.9 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places.
A) 15.67% per year
B) 15.63% per year
C) 15.69% per year
D) 15.61% per year
E) 15.65% per year

Question

A condominium complex was purchased by a group of private investors for $1.3 million and sold 7 year(s) later for $3.9 million. Find the annual rate of return (compounded continuously) on their investment. Round your answer to two decimal places. ​
A) 15.67% per year
B) 15.63% per year
C) 15.69% per year
D) 15.61% per year
E) 15.65% per year

Quizplus · Accepted Answer

The formula for continuous compounding is:
A = Pe^rt
where A is the ending value, P is the beginning value, e is Euler's number (approximately 2.71828), r is the annual interest rate, and t is the time in years.
We can use this formula to find the annual rate of return:
3.9 million = 1.3 million e^(r*7)
e^(r*7) = 3
r*7 = ln(3)
r = ln(3)/7 ≈ 0.223
The annual rate of return is approximately 22.3%, so the closest answer choice is C: 15.69% per year. However, this is only an approximation, since the problem specifies continuous compounding, while the answer choices are rounded to the nearest hundredth of a percent.

A Condominium Complex Was Purchased by a Group of Private