Determine the future value in year 8 of $3,000 annual payments received in years 2, 4 and 6 given an interest rate of 7% compounded annually.
A) $11,075.16
B) $11,869.28
C) $12,428.39
D) $12,990.80
E) $13,167.25

Question

Quizplus · Accepted Answer

To find the future value of the payments, we calculate the future value of each payment at year 8 and then sum them. The formula for future value is FV = PV * (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of periods.1. For the $3,000 payment in year 2, it will have 6 years to grow (from year 2 to year 8):FV = $3,000 * (1 + 0.07)^6 = $3,000 * 1.5007 = $4,502.102. For the $3,000 payment in year 4, it will have 4 years to grow (from year 4 to year 8):FV = $3,000 * (1 + 0.07)^4 = $3,000 * 1.3108 = $3,932.403. For the $3,000 payment in year 6, it will have 2 years to grow (from year 6 to year 8):FV = $3,000 * (1 + 0.07)^2 = $3,000 * 1.1449 = $3,434.70Adding these amounts together gives the total future value in year 8:Total FV = $4,502.10 + $3,932.40 + $3,434.70 = $11,869.20Therefore, the correct answer is $11,869.28, which is rounded from $11,869.20 due to rounding in each step.

Determine the Future Value in Year 8 of $3,000 Annual