Final answer:
If the bond sold at 98 1/2, the correct answer is that the market rate was greater than the stated rate.
Step-by-step explanation:
When a bond sells for less than its face value, as in this case at 98 1/2 (or 98.5% of face value), it implies that the market interest rate must be higher than the bond's stated (coupon) interest rate. This occurs because the bond's fixed interest payments seem less attractive when compared to the higher market interest rates available elsewhere, thus investors are only willing to buy the bond at a 'discount' to its face value.
This is reflected in the given example, where investing $964 at a market interest rate of 12% returns the same $1,080 that the bond will pay in its last year. Since the bond is selling for less than its face value, we can infer that the market rate of interest must be above the bond's coupon rate.
In summary, the market interest rate is what dictates the bond's selling price. If a bond with a fixed coupon rate is selling for less than its face value (as in this case), the market rates have increased beyond the bond's coupon rate.