Final answer:
You would pay less than $10,000 for a bond when the market interest rate rises from 6% to 9%. The payment one year from now should be discounted at the current market rate to find the present value. At 9%, the present value of a $10,000 bond with one year remaining and a 6% coupon rate is approximately $9,724.77.
Step-by-step explanation:
Regarding question 37, when a local water company issued a $10,000 ten-year bond at an interest rate of 6% and you are considering buying the bond one year before maturation with interest rates at 9%, you would expect to pay less than $10,000 for the bond due to the increase in market interest rates.
When interest rates rise, existing bonds with lower interest rates become less attractive, hence their market value decreases. To calculate what you would actually be willing to pay for the bond, you would use the present value formula to discount the bond's final year payment, which includes both the final interest payment and the principal repayment, by the current market interest rate of 9%. Given that the bond pays 6% annually, the payment in one year would be $10,000 (principal) + $600 (interest). Using the formula:
PV = FV / (1 + r)n
Where PV is the present value, FV is the future value, r is the market interest rate and n is the number of periods to maturity, which in this case is 1.
Therefore, the present value of the $10,600 due in one year, discounted at the new interest rate of 9%, would be approximately:
PV = $10,600 / (1 + 0.09)1 = $10,600 / 1.09 ≈ $9,724.77
So, under these market conditions, you would be willing to pay roughly $9,724.77 for this bond. This calculation illustrates the inverse relationship between bond prices and interest rates.