Final answer:
The bond will trade at a new price below its face value when the yield to maturity rises due to an increase in market interest rates. The bond's price is recalculated to give a yield that is competitive with current rates, in this case, 12%. This adjustment accounts for the fact that investors have alternative investment opportunities paying higher returns.
Step-by-step explanation:
If the yield to maturity (YTM) of a bond rises with semiannual compounding, the price at which the bond will trade must be recalculated. The YTM is a measure of the total return anticipated on a bond if the bond is held until it matures. A bond's price will vary inversely with the yield: as the yield goes up, the price goes down, and vice versa.
To determine the new trading price, we consider that the investor will receive the $1,000 face value plus $80 for the last year's interest payment. If interest rates in the market rise such that the YTM becomes 12%, then the bond, originally paying 8%, becomes less attractive compared to new bonds paying higher rates. As a result, the bond's seller will need to lower its price below the face value to induce investors to buy it. In this circumstance, the new price could be calculated using a bond pricing formula which incorporates the new required yield of 12%.
For example, if the bond is selling for $964 and the investor receives a total of $1080 after the last payment, the yield on the bond is ($1080 - $964) / $964 = 12%. Here, the interest or coupon rate at 8% has not changed, but the effective yield has due to changes in the bond's price. When interest rates rise, previously issued bonds at lower interest rates will generally sell for less than face value, adjusting the price to reflect the current market conditions.