Final answer:
The price of the 3-year coupon bond that pays annual coupons of $50 on a par value of $1,000 is calculated using the present value of future cash flows discounted at the respective forward rates, resulting in a bond price of $897.61.
Step-by-step explanation:
To calculate the price of a coupon bond, we must discount each of the bond's cash flows (annual coupon payments and the final par value repayment) by the market interest rate at each respective time period. For a 3-year bond with annual payments of $50 and a par value of $1,000, we will use the given forward rates to discount each payment. The year 1 payment of $50 will be discounted by 6%, the year 2 payment by 8%, and the final year's payment, which includes both the coupon and the par value, by 9%.
The present value of the first coupon payment is $50 / (1 + 0.06) = $47.17. The present value of the second coupon payment is $50 / (1 + 0.08)^2 = $42.99. The present value of the final year's total payment ($1,050) is $1,050 / (1 + 0.09)^3 = $807.45. To find the price of the coupon bond, we sum these present values: $47.17 + $42.99 + $807.45 = $897.61.