You just purchased a 15-year bond with an 11 percent annual coupon. The bond has a face value of $1,000 and a current yield of 10 percent. Assuming that the yield to maturity of 9.7072 percent remains constant, what will be the price of the bond 1 year from now?

Question

Quizplus · Accepted Answer

Since the current yield is 10 percent and the coupon rate is 11 percent, the bond must be selling at a discount. Therefore, the bond price today must be lower than its face value. To determine the current price, we can use the formula for present value of a bond:

PV = (C / r) [1 - 1 / (1 + r)^n] + FV / (1 + r)^n

Where PV is the present value or price of the bond, C is the annual coupon payment, r is the yield to maturity, n is the number of years until maturity, and FV is the face value of the bond.

Plugging in the values for the bond described, we get:

PV = (110 / 0.097072) [1 - 1 / (1 + 0.097072)^15] + 1,000 / (1 + 0.097072)^15 = $1,060.18

Therefore, the current price of the bond is $1,060.18.

To calculate the price of the bond 1 year from now, we just need to discount the future cash flows by the yield to maturity at that time. Since the yield to maturity is assumed to remain constant at 9.7072 percent, the price can be found using the same formula as above, but with n = 14 (since there will be 14 years remaining until maturity 1 year from now):

PV = (110 / 0.097072) [1 - 1 / (1 + 0.097072)^14] + 1,000 / (1 + 0.097072)^14 = $1,096.64

Therefore, the price of the bond 1 year from now will be $1,096.64, which is closest to choice C.

You Just Purchased a 15-Year Bond with an 11 Percent