If $11,000 had been invested in the Fictious Fund on June 30, 1991, then on June 30, 2000 the investment would have been worth $34,575.25. What interest rate compounded annually would this investment have earned? Round your answer to two decimal places.
A)27.14%
B)13.57%
C)11.27%
D)15.33%
E)6.79%

Question

If $11,000 had been invested in the Fictious Fund on June 30, 1991, then on June 30, 2000 the investment would have been worth $34,575.25. What interest rate compounded annually would this investment have earned? Round your answer to two decimal places. ​
A)27.14%
B)13.57%
C)11.27%
D)15.33%
E)6.79%

Quizplus · Accepted Answer

We can use the compound interest formula: 
$P(1+r)^n = A$ 
where $P$ is the principal (initial investment), $r$ is the annual interest rate (in decimal form), $n$ is the number of years, and $A$ is the amount of money after $n$ years. 
Plugging in the given values, we get: 
$11,000(1+r)^9 = 34,575.25$ 
Dividing both sides by $11,000$, we get: 
$(1+r)^9 = 3.14320$ 
Taking the ninth root of both sides, we get: 
$1+r = 1.135731$
Subtracting $1$ from both sides, we get: 
$r = 0.135731$ 
Converting to a percentage, we get $13.57\%$, which rounds to 13.57%. Therefore, the answer is B.

If $11,000 Had Been Invested in the Fictious Fund on June