Final answer:
Given the increase in market interest rates to 9% from the bond's coupon rate of 6%, you would expect to pay less than the face value of $10,000 for the bond. By calculating the present value of the bond's payments at the new market rate, you would be willing to pay approximately $9,724.77 for the bond one year before its maturity.
Step-by-step explanation:
Understanding Bond Valuation
When the market interest rate is higher than the bond's coupon rate, the bond will sell for less than its face value, which is known as a discount. In the question, a $10,000 ten-year bond with a 6% interest rate is considered for purchase when the market rate is at 9%, one year before maturity. Given the change in interest rates, we would expect the bond to be worth less than $10,000, also known as its par value.
To calculate the price of the bond, we examine the expected payments. The bond will pay $600 in interest (6% of $10,000) at the end of the year, along with the principal amount of $10,000. Since current market rates are at 9%, we would use a discount rate of 9% to find the present value of these cash flows. Therefore, the calculation involves discounting the sum of the final interest payment and the repayment of principal ($10,600) at the market interest rate of 9% to determine the current price of the bond.
Present Value Calculation:
$$
PV = \frac{FV}{(1 + r)^n}
$$
$$
PV = \frac{\$10,600}{(1 + 0.09)^1}
$$
$$
PV ≈ \$9,724.77
$$
Based on this, we would be willing to pay approximately $9,724.77 for the bond one year before maturity when the market interest rate is 9%.