If $P is invested for n years at rate i (as a decimal), compounded annually, the future value that accrues is given by , and the interest earned is . Find I for the given P, n, and i. Round your answer to two decimal places.
$2,400 for 9 years at 8%

A)$4,797.61
B)$2,042.23
C)$1,133.19
D)$2,397.61
E)$7,197.61

Question

If $P is invested for n years at rate i (as a decimal), compounded annually, the future value that accrues is given by  , and the interest earned is  . Find I for the given P, n, and i. Round your answer to two decimal places. ​
$2,400 for 9 years at 8%
​
A)$4,797.61 
B)$2,042.23 
C)$1,133.19 
D)$2,397.61 
E)$7,197.61

Quizplus · Accepted Answer

Plugging in the given values for P and n, we get:
2400(1+0.08)^9 = $4797.61
The interest earned is:
$4797.61 - $2400 = $2397.61
To find the annual interest rate i, we can use the formula:
A = P(1+i)^n
A/P = (1+i)^n
(1+i) = (A/P)^(1/n)
i = (A/P)^(1/n) - 1
Plugging in the values we calculated, we get:
i = ($4797.61/$2400)^(1/9) - 1 = 0.08
Rounding to two decimal places, we get i = 0.08, which corresponds to 8%. Therefore, the answer is D.

If $P Is Invested for N Years at Rate I