Final answer:
Given that the market interest rates have risen to 9%, one would expect to pay less than the face value of a bond with a 6% coupon rate. To calculate the actual payment, the present value of the bond's future cash flows is determined using the new interest rate. The calculation indicates one would be willing to pay approximately $9,724.77 for a $10,000 face value bond.
Step-by-step explanation:
The question involves understanding how changes in interest rates affect the market value of bonds. When interest rates rise, the market value of existing bonds with lower interest rates (coupon rates) falls. Conversely, if interest rates fall, the market value of these bonds increases as they become more attractive compared to new bonds with lower rates.
In the given scenario, a $10,000 bond with a coupon rate of 6% is considered for purchase when the market interest rate is 9%. Since the market rate is higher than the coupon rate, you would expect to pay less than the face value of the bond. To calculate the actual amount you would be willing to pay for the bond, we need to find the present value of the bond's forthcoming cash flows (one year of coupon payments and the bond's face value at maturity) discounted at the new market interest rate of 9%.
Let's calculate the present value of the bond's cash flows:
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Under these circumstances, you would be willing to pay approximately $9,724.77 for the bond, which is less than its face value.