Question

Ralph purchases a newly-issued, two-year government bond with a principal amount of $10,000 and a coupon rate of 6% paid annually. One year before the bond matures (and after receiving the coupon payment for the first year), Ralph sells the bond in the bond market. What price (rounded to the nearest dollar) will Ralph receive for his bond if the prevailing interest rate is 4%?

Answer 1

Ralph will receive $1,154 for his bond when the prevailing interest rate is 4%.

Step-by-step explanation:

To calculate the price Ralph will receive for his bond, we need to determine the present value of the bond's future cash flows. Since the bond has a coupon rate of 6% paid annually and the prevailing interest rate is 4%, the bond's cash flows are discounted at the interest rate of 4%. The bond will pay $600 ($10,000 * 6%) as its coupon payment each year. At the end of the first year, Ralph will receive the coupon payment of $600. The present value of this cash flow at a discount rate of 4% is $577 ($600 / 1.04).

On the day Ralph sells the bond, it has 1 year left until maturity, so the bond will only have one more coupon payment remaining. The present value of this final payment at a discount rate of 4% is $577 ($600 / 1.04). Adding up all the present values, the total price Ralph will receive for his bond is $1,154 ($577 + $577).