Final answer:
When interest rates rise, the value of existing bonds decreases. In this scenario, the bond was issued at a lower interest rate, but the current interest rate is higher. You would expect to pay less than $10,000 for the bond. To calculate the actual price, you can use the present value formula.
Step-by-step explanation:
When interest rates rise, the value of existing bonds decreases. This is because new bonds issued at the higher interest rate would generate more income for investors compared to existing bonds with lower interest rates. In the given scenario, the bond was issued at a lower interest rate of 6%, but the current interest rate is 9%. Therefore, you would expect to pay less than $10,000 for the bond.
To calculate the actual price you would be willing to pay for the bond, you need to use the present value formula. The present value formula calculates the present worth of future cash flows by discounting them at the applicable interest rate. Here's how you can calculate the present value:
- Calculate the future cash flows: The bond will pay $10,000 at the end of 10 years, which means you will receive $10,000 in the future.
- Calculate the present value: Using the present value formula, which is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. In this case, PV = $10,000 / (1 + 0.09)^10 = $4,452.89. Therefore, you would be willing to pay approximately $4,452.89 for the bond.