Final answer:
With the rise in interest rates to 9%, you would expect to pay less than $10,000 for the bond. The calculations based on present value discounting show that you would be willing to pay approximately $9,724.77 for the bond.
Step-by-step explanation:
Considering a local water company that issued a $10,000 ten-year bond with 6% interest rate, and now, one year before maturity, the prevailing interest rates have risen to 9%:
- You would expect to pay less than $10,000 for this bond because the market rate of 9% is higher than the bond's coupon rate.
- To calculate the price you would be willing to pay for the bond:
The bond will pay $600 in interest (6% of $10,000) in one year, plus the principal amount of $10,000 at maturity. The present value of these amounts, discounted at the new market rate of 9%, will give you the maximum price you should be willing to pay. - The present value (PV) calculations are as follows:
PV = Interest / (1 + r) + Principal / (1 + r)
PV = $600 / (1 + 0.09) + $10,000 / (1 + 0.09)
PV = $550.46 + $9,174.31
PV = $9,724.77
Therefore, you would be willing to pay approximately $9,724.77 for the bond, considering the increased interest rate.