A $10,000 eight-year investment earns interest at 12% compounded semi-annually. If it is sold 30 months before maturity to yield 16% compounded quarterly, what is its selling price?
A) $17,161.71
B) $6,755.64
C) $10,719.15
D) $4,219.55
E) $20,009.91

Question

Quizplus · Accepted Answer

First, calculate the future value of the investment at the original interest rate for the full term. Since the interest is compounded semi-annually, the number of compounding periods per year is 2, and the annual interest rate is 12%, which gives a period rate of 6%. The total number of periods is 8 years * 2 = 16 periods. Using the formula for compound interest, FV = P(1 + r)^n, where P is the principal, r is the rate per period, and n is the number of periods, we get FV = $10,000(1 + 0.06)^16 = $25,937.42.Next, calculate the present value of this future value 30 months (or 2.5 years) before maturity, with the new yield of 16% compounded quarterly. This gives 4 compounding periods per year, and with 2.5 years until maturity, there are 10 periods. The quarterly rate is 16%/4 = 4%. Using the present value formula, PV = FV / (1 + r)^n, we get PV = $25,937.42 / (1 + 0.04)^10 = $17,161.71.

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