Final answer:
Given that market interest rates have increased from 6% to 9%, one would expect to pay less than the $10,000 face value for the bond. Calculations show that the approximate fair value of the bond one year before maturity, with a 9% discount rate, is $9,724.77.
Step-by-step explanation:
Understanding Bond Valuation and Interest Rates
When evaluating the purchase of a bond close to its maturity, the prevailing interest rates affect the bond's price. If the bond was initially issued with a 6% coupon rate and market interest rates have risen to 9%, you would expect the bond's price to decrease. This is because new bonds are likely being issued with the higher current interest rate, making the older bond less attractive unless it is sold at a discount.
To determine the fair price of the $10,000 bond paying 6% annually, we'll use the present value formula considering only one more year of interest payments and the principal repayment. The calculations look at the bond's future cash flows discounted back at the higher 9% rate. Let's calculate:
Interest payment: $10,000 × 6% = $600
Principal repayment: $10,000
Total future value: $600 + $10,000 = $10,600
Present Value of a single future payment: PV = FV / (1 + r)^n
Discounting at 9% for one year: PV = $10,600 / (1 + 0.09)^1
Present Value = $10,600 / 1.09 ≈ $9,724.77
You would be willing to pay approximately $9,724.77 for the bond, given the change in the interest rates to 9%.