Final answer:
If the market interest rate is 9% and the bond's rate is 6%, you would expect to pay less than the bond's face value. At a 9% discount rate, the present value of the bond's $600 interest payment and $10,000 principal is approximately $9,724.77.
Step-by-step explanation:
When interest rates increase in the market, the value of existing bonds with lower interest rates tend to decrease. This inverse relationship is due to the fact that new bonds would be issued at the higher current rate, making the existing bonds less attractive unless they are sold at a discount. Hence, if you are considering buying a $10,000 bond with a 6% interest rate while the market rate is 9%, you would expect to pay less than $10,000 for the bond to make it a worthwhile investment.
Let's say the bond will pay you $600 (which is 6% of $10,000) one year from now, and then it will also repay the principal amount of $10,000. You want these future payments to be equivalent to what they would be worth in today's dollars considering the current 9% interest rate which would be used as the discount rate. Using the present value formula, you can calculate the present value of the interest payment and the principal separately and then sum them up:
- Present Value of Interest Payment = $600 / (1 + 0.09) = $550.46 approximately
- Present Value of Principal = $10,000 / (1 + 0.09) = $9,174.31 approximately
Adding both amounts, the total present value (price you'd be willing to pay for the bond) is $550.46 + $9,174.31 = $9,724.77.
This demonstrates that the bond's value decreases as the market interest rate rises above the bond's coupon rate.