Final answer:
To calculate the bond price, we need to determine the present value of the future cash flows. For this $1,000 bond paying interest semiannually with a required rate of return of 11% annually, the price would be approximately $333.07 in 2001. None of the given options (a) $700, (b) $800, (c) $900, or (d) $1,000 are correct.
Step-by-step explanation:
In this scenario, the bond pays interest semiannually, and the required rate of return is 11% annually. To calculate the price of the bond, we need to determine the present value of the future cash flows.
For a $1,000 bond, we need to calculate the present value of the semiannual interest payments and the principal repayment. Each interest payment is half the annual interest rate, so it would be 11% / 2 = 5.5%. Given that the bond pays interest semiannually, there will be a total of 20 interest payments over the 10-year period. Using the present value formula, we can calculate the present value of the interest payments as follows:
- Calculate the present value factor using the discount rate (11%) and the number of periods (20): 1 / (1 + 0.055) ^ 20 = 0.324174.
- Multiply the present value factor by the semiannual interest payment amount of $27.50 ($1,000 * 0.055), so 0.324174 * $27.50 = $8.90.
Next, we need to calculate the present value of the principal repayment at the end of the 10-year period, which is the face value of $1,000. Using the same present value formula, we can calculate:
- Calculate the present value factor using the discount rate (11%) and the number of periods (20): 1 / (1 + 0.055) ^ 20 = 0.324174.
- Multiply the present value factor by the face value of $1,000, so 0.324174 * $1,000 = $324.17.
Finally, we sum the present values of the interest payments and the principal repayment to find the bond price: $8.90 + $324.17 = $333.07.
Therefore, you should pay approximately $333.07 for a $1,000 bond in 2001. None of the given options (a) $700, (b) $800, (c) $900, or (d) $1,000 are correct.