Final answer:
Given that market interest rates rose to 9%, one should expect to pay less than $10,000 for a bond initially issued with a 6% interest rate. The actual price can be calculated as the present value of the bond's future cash flows, using the current market interest rate. In this case, the bond would be worth $9724.77.
Step-by-step explanation:
Understanding Bond Pricing
When interest rates increase, existing bonds with lower interest rates become less attractive because new bonds are available that pay higher interest. Hence, these existing bonds sell at a discount to attract buyers. In this case, if you're considering buying a $10,000 ten-year bond that was initially issued with an interest rate of 6%, but the market interest rates have risen to 9%, you would expect to pay less than the face value of $10,000.
Calculating the Price of the Bond
To calculate what you would actually be willing to pay for this bond, you need to discount the future cash flows, which are the interest payments you would receive plus the principal amount at maturity, using the new market interest rate of 9%. Assuming an annual interest payment, you would receive $600 each year from the bond's coupon payments, and $10,000 at the end of the last year. The bond's price can be calculated using the present value of these cash flows.
The present value of these cash flows can be calculated using the formula:
PV = C * [1 - (1 + r)^(-n)] / r + F / (1 + r)^n
where PV = present value, C = annual coupon payment, r = market interest rate, n = number of years until maturity, and F = face value of the bond.
In our scenario, there is one coupon payment of $600 and a face value of $10,000 due in one year. So, the calculation would be:
PV = $600 / (1 + 0.09) + $10,000 / (1 + 0.09)
PV = $550.46 + $9174.31
PV = $9724.77
Therefore, you would be willing to pay $9724.77 for the bond in today's dollars.