A $10,000 eight-year investment earns interest at 12% compounded semiannually. If it is sold 30 months before maturity to yield 16% compounded quarterly, what is its selling price?
A) $17,161.71
B) $6755.64
C) $10,719.15
D) $4219.55
E) $20,009.91

Question

Quizplus · Accepted Answer

First, calculate the future value of the investment at the end of 8 years with a 12% annual interest rate compounded semiannually. Use the formula A = P(1 + r/n)^(nt), where P = $10,000, r = 0.12, n = 2 (since it's compounded semiannually), and t = 8. This gives A = $10,000(1 + 0.12/2)^(2*8) = $22,080.40. Since the investment is sold 30 months (or 2.5 years) before maturity, we need to find its present value 2.5 years before the end of the 8 years, which means at 5.5 years. Use the formula for present value, PV = FV / (1 + r/n)^(nt), where FV = $22,080.40, r = 0.16 (since the yield is 16% compounded quarterly), n = 4, and t = 2.5. This gives PV = $22,080.40 / (1 + 0.16/4)^(4*2.5) = $17,161.71.

A $10,000 Eight-Year Investment Earns Interest at 12% Compounded Semiannually