Final answer:
When the market interest rate increases, the price of an existing bond decreases to offer a competitive yield. For a $10,000 bond with one year remaining and a market interest rate of 9%, the price would be around $9,724.77, which is less than the face value.
Step-by-step explanation:
The question pertains to the valuation of a municipal bond when market interest rates have changed since the bond was issued. Specifically, it asks how to calculate the bond's price given that interest rates have risen since the bond's issuance.
Valuing the Bond
To value the bond when interest rates have increased (from 6% to 9%), we recognize that the bond's fixed payments have become less attractive compared to new bonds issued at the higher current rates. Thus, the price of the original bond would decrease to provide a yield that is equivalent to the new 9% market rate.
Example Calculation
For example, a $10,000 municipal bond originally issued at 6% interest would have one year left of payments amounting to $600 of interest + $10,000 of principal = $10,600. If market rates are now 9%, we can calculate the present value of this payment using the formula PV = Payment / (1+rate). Applying this to the given data:
Present Value (PV) = $10,600 / (1 + 0.09) = $10,600 / 1.09 = $9,724.77 (approximately)
Therefore, you would expect to pay less than $10,000 for this bond, in this case, around $9,724.77.