Final answer:
If interest rates rise from 6% to 9%, you would expect to pay less than $10,000 for a bond nearing its maturity. The present discounted value calculation shows you would be willing to pay approximately $9,174.31 for a $10,000 bond one year before maturity at a 9% discount rate.
Step-by-step explanation:
When the interest rates increase, the market price of existing bonds tends to decrease. Given a bond with an original interest rate of 6% and the market rate increasing to 9%, one would expect to pay less than the face value of $10,000 for this bond if it were purchased one year before its maturity.
To calculate the present discounted value of the bond's payout, we consider what one would need now to equal the payment in the future at the current interest rate. If the bond's final year payment is $10,000 (the face value) and we use the current market rate of 9% for discounting, the present value of that future payment is calculated using the formula PV = FV / (1 + r), resulting in PV = $10,000 / (1 + 0.09), which gives us a present value of approximately $9,174.31.
Therefore, you would be willing to pay around $9,174.31 for the bond issued at 6% if you were to buy it one year before the end date when the market interest rate is 9%, to be indifferent between holding the bond and keeping the cash to invest it elsewhere at the current rates.