Final answer:
If interest rates rise from 6% to 9%, one would expect to pay less than $10,000 for a $10,000 bond. The actual price one would be willing to pay can be determined by discounting the expected future cash flows at the new 9% interest rate, which amounts to approximately $9,724.77 for the bond described.
Step-by-step explanation:
When considering purchasing a bond on the secondary market, the interest rates at the time of purchase are a critical factor in determining the price you would expect to pay for the bond. In the scenario where a local water company issued a $10,000 ten-year bond at an interest rate of 6%, if the current market interest rates have risen to 9%, one would expect to pay less than $10,000 for the bond. This is because the bond's fixed-rate payments are less attractive compared to new bonds issued at the higher current rates.
To calculate the actual price you would be willing to pay for this bond, you need to discount the future cash flows (the final year's interest payment and the principal repayment) at the new market rate of 9%. Assuming the bond pays annual interest, the calculation involves finding the present value of the $600 interest payment and the $10,000 principal repayment one year from now. The formula to discount these amounts is: Present Value = Future Cash Flow / (1 + interest rate)^number of periods. Thus, the present value of the interest payment is $600 / (1 + 0.09) = $550.46, and the present value of the principal is $10,000 / (1 + 0.09) = $9,174.31. Summing these up, the price you'd be willing to pay for this bond is approximately $550.46 + $9,174.31 = $9,724.77.