Final answer:
To figure out the price of a 10-year bond with a 6% coupon and a 7.5% yield to maturity, calculate the present value of the coupon payments and the face value at maturity. Typically, when the yield to maturity is higher than the coupon rate, the bond will sell for less than the face value. The correct option will reflect the bond's present value below $1,000.
Step-by-step explanation:
To determine how much you should be prepared to pay for a 10-year bond with a 6 percent coupon and a yield to maturity of 7.5 percent, you need to calculate the present value of all future coupon payments plus the present value of the bond's face value at maturity.
Calculating Present Value of Coupon Payments
The annual coupon payment is 6% of the bond's face value. For a $1,000 bond, this would be $60 per year. To find the present value of these payments, you would discount them at the bond's yield to maturity of 7.5%. The formula for the present value of an annuity is used here.
Calculating Present Value of the Face Value
The face value is $1,000 and will be paid in ten years. This amount must also be discounted back to the present using the yield to maturity.
By calculating the present value of both the coupon payments and the face value and summing them up, you would find out which option (a. $411.84, b. $985.00, c. $897.04, d. $1,000.00) most accurately reflects the current value of the bond. Given that the yield to maturity (7.5%) is higher than the coupon rate (6%), you would typically expect the price of the bond to be less than the face value of $1,000.
The coupon rate being lower than the market interest rate indicates that the bond's price should be discounted, as newer bonds would probably offer higher interest payments.