Final answer:
The present value of a two-year bond with a face value of $3,000 and an 8% interest rate is $3,000 when discounted at 8%. However, if the discount rate increases to 11%, the present value of the bond will be lower as both interest payments and the principal repayment have lesser present values at a higher discount rate.
Step-by-step explanation:
To calculate the present value of a two-year bond with a face value of $3,000 and an interest rate of 8%, we must consider the annual interest payments and the principal amount to be received at the end of the term. The first year's interest is calculated as 240 (which is 3,000 × 8%). The present value of this interest payment, discounted at 8%, is $240 / (1+0.08) = $222.20. For the second year, the interest payment is also $240, and the principal amount of $3,000 is returned, totaling $3,240. The present value of the second year's payment, using the same discount rate, is $3,240 / (1+0.08)² = $2,777.80. Summing up the present values of both years, the total present value at an 8% discount rate is $3,000.
If the discount rate rises to 11%, the calculation should be redone to reflect this higher rate. The present value of the first year's interest payment becomes $240 / (1+0.11) = $216.22, and the present value of the second year's payment becomes $3,240 / (1+0.11)² = $2,634.57. These recalculated present values yield a lower total value due to the higher discount rate.