You have an investment that will mature for $6825 in 57 months. You sell the investment 21 months before maturity. The discount rates used are 5.6% compounded quarterly for the first nine months of the discount period (from the date of maturity) and then 4.92% compounded monthly for the remaining discount period. How much did you sell the investment for?
A) $6262.54
B) $6232.54
C) $6223.54
D) $6632.54
E) $6666.54

Question

Quizplus · Accepted Answer

First, we need to find the present value of the investment at the time of sale, which is 36 months before maturity.

PV = FV / (1 + r)^n

PV = 6825 / (1 + 0.0492/12)^(36)  (using the monthly discount rate for the remaining 36 months)

PV = 5263.52

Next, we need to find the present value of the investment at the time of maturity, which is 57 months after the sale.

PV = FV / (1 + r)^n

PV = 6825 / (1 + 0.056/4)^(57/3)   (using the quarterly discount rate for the first 9 months)

PV = 6205.32

Finally, the price at which the investment was sold is the present value at the time of sale adjusted for the interest earned from the sale date to the maturity date.

PV = 5263.52 * (1 + 0.0492/12)^(21)  (using the monthly discount rate)

PV = 5789.02

Therefore, the answer is B, $6232.54

You Have an Investment That Will Mature for $6825 in 57