Final answer:
The present value of a bond with coupon payments of $80 and a face value of $1,000, over 2 years with a constant spot interest rate of 10%, is closest to $950.
Step-by-step explanation:
The present value of a bond is calculated by discounting the future coupon payments and face value back to their current worth using a discount rate. In this case, we have two coupon payments of $80 and a face value of $1,000, with the payments being made at the end of each year for two years. The present value is calculated using the spot interest rate for each year. Assuming the interest rate is constant at 10%, the present value for each year would be calculated as follows:
Year 1: The present value of the first $80 coupon payment discounted back one year at 10% is $80 / (1 + 0.10) = $72.73.
Year 2: The present value of the second $80 coupon payment and the $1,000 face value discounted back two years at 10% [(80 + 1000) / (1 + 0.10)^2] = $890.91.
The total present value of the bond is the sum of these present values, which is $72.73 (Year 1) + $890.91 (Year 2) = $963.64.
Given the choices, the amount closest to the present value of the bond is $950.