Final answer:
The price of a bond inversely correlates with the market interest rate. If the market interest rate is higher than the bond's fixed interest rate, you would pay less for the bond. For a bond issued at 6% when the market rate is 9%, the present value calculation shows a willing payment amount of $9,724.77, less than the bond's face value.
Step-by-step explanation:
When the interest rates in the market rise, existing bonds with lower interest rates become less attractive, and their price on the market typically decreases. This is because new bonds are likely to be issued with higher interest rates, making them more profitable than the older bonds with lower rates. In the scenario where a local water company issued a $10,000 bond at 6% but the market rate is now 9%, you would expect to pay less than $10,000 for the bond because it is less competitive with the current higher interest rates available.
Calculating the Bond's Value :
To calculate the bond's current value, we need to discount the bond's future cash flows, which include the final year's interest payment ($600) and the principal repayment ($10,000), at the new market rate of 9%. The formula for the present value of a future payment is PV = FV / (1 + r)n, where FV is the future value, r is the rate, and n is the number of periods. We have two future payments, one year away, so we compute:
- Present value of the final interest payment: PV = $600 / (1 + 0.09)1 = $550.46
- Present value of the principal repayment: PV = $10,000 / (1 + 0.09)1 = $9,174.31
The total amount you might be willing to pay for this bond would therefore be the sum of these two present values, which totals to $9,724.77. Thus, given the 9% market interest rate, you would pay less than the face value of the bond because the bond's fixed-interest rate is lower than the current market rate.