Final answer:
When the interest rates on bonds rise, the present discounted value of future bond payments decreases; therefore, if you are buying a bond with a fixed interest rate lower than the current market rate, you would pay less than the face value. This is because the current investment's opportunity cost is higher with increased interest rates.
Step-by-step explanation:
The question posed requires an understanding of present discounted value (PDV) and how it applies to financial transactions such as bonds and loan payments. When interest rates increase, the present value of future bond payments decreases because you could be earning a higher interest rate on current investments. In the case of the $10,000 bond at a 6% interest rate that you are considering purchasing one year before it matures, given that the current interest rate is now 9%, you would expect to pay less than the face value ($10,000) for the bond. The exact amount you would be willing to pay can be calculated using the present value formula which accounts for the final bond payment plus the interest payment received at maturity, discounted by the current market interest rate of 9%.
Similarly, for the two-year bond that was issued for $3,000 at an 8% interest rate, the present value calculations would be different if the discount rate is at the initial 8% versus an increased rate of 11%. The higher the discount rate, the lower the present value of the bond's future payments.