Final answer:
The price of a risk-free bond with an interest rate below the market rate and one year to maturity should not exceed $964, based on an alternative investment at the market rate that would yield the same return.
Step-by-step explanation:
To calculate the bond's price when its interest rate is less than the market interest rate, consider the scenario where the bond will pay out $1,080 in one year's time, which includes the final interest payment and the repayment of the principal amount of $1,000. Since the market interest rate is currently at 12%, an alternative investment of $964 would also yield $1,080 in one year, given the equation $964(1 + 0.12) = $1080. Therefore, it is reasonable to conclude that the bond's price should not exceed $964.
Considering the risk of the bond, if there is no risk associated with this bond and it is currently in its last year before maturity, the rise in the market interest rate to 12% makes the bond less attractive. An investor would expect a similar return from a risk-free investment. To make the bond more appealing, its price would be lowered below its face value, which, in this case, is supported by the alternative investment's return that sets the upper limit for the bond's price at $964.