Final answer:
The price of a zero-coupon bond is determined by discounting the $1,000 maturity value by the market interest rate. If the market interest rate is 12%, then the price of the bond would be $964 since this is the amount that would grow to $1,080 in one year at 12%, matching the bond's payment at maturity.
Step-by-step explanation:
The question concerns the calculation of a bond's price assuming semiannual compounding, given its time to maturity and a zero-coupon feature. To determine the price of a zero-coupon bond that pays $1,000 at maturity, we need to consider the yield to maturity (YTM), which represents the bond's internal rate of return if held until maturity. The concept is that the bond's market price adjusts to changes in interest rates to make the bond's yield equal to the market yield. If market interest rates rise above the bond's YTM, as in the given example where rates rise to 12%, the bond's price will fall below its face value in order to offer a competitive return to investors.
Assuming there is only one year left to maturity and the market interest rate is 12%, the calculation would be based on the fact that $964 invested at a 12% interest rate for one year would yield $1,080. Therefore, an investor would not pay more than $964 for the bond to match the market interest rate. This type of analysis helps to understand the relationship between bond prices, interest rates, and the yield to maturity.