Question

A $6,000 bond had a coupon rate of 5.50% with interest paid semi-annually. Corey purchased this bond when there were 9 years left to maturity and when the market interest rate was 5.75% compounded semi-annually. He held the bond for 3 years, then sold it when the market interest rate was 5.25% compounded semi-annually.

a. What was the purchase price of the bond? Round to the nearest cent.
b. What was the selling price of the bond? Round to the nearest cent.
c. What was Corey's gain or loss on this investment?

Answer 1

The purchase price of the bond is approximately $8,740.29.

Step-by-step explanation:

To find the purchase price of the bond, we need to calculate the present value of the bond's future cash flows. The bond pays semi-annual interest, so it will make 18 payments over the next 9 years. We can use the present value of an annuity formula to calculate the present value of these payments.

The bond's coupon rate is 5.50%, so each interest payment is $165 ($6,000 * 0.055). The market interest rate is 5.75% compounded semi-annually, so the discount rate is 2.875%. Using the present value of an annuity formula, the present value of the bond's interest payments is approximately $2,740.29. Adding this to the present value of the face value of the bond ($6,000), we find that the purchase price of the bond is approximately $8,740.29.