Final answer:
The price of the bond can be found by calculating the present value of the bond's future cash flows and comparing it to its face value. The bond in question, with a coupon rate higher than the current yield to maturity, will sell for more than its face value and is hence a premium bond.
Step-by-step explanation:
The question deals with calculating the price of a bond with given characteristics: a 10% semiannual coupon, a face value of $1,000, 20 years to maturity, and a yield to maturity (YTM) of 8%. To determine the price, we need to calculate the present value of all future coupon payments plus the present value of the face value. As the interest rate (YTM) is lower than the coupon rate, this bond will sell for more than its face value, making it a premium bond.
To calculate the bond's price, we would use the present value of an annuity formula for the semiannual coupon payments and the present value formula for the face value. Since the coupon rate is higher than the YTM, the investor will receive semiannual interest payments that are greater than what the current market requires, which results in a bond price over $1,000.
When comparing the calculated bond price against its face value, if the bond price is higher than the face value, it is considered a premium bond. Conversely, if it were lower, it would be a discount bond. The fact that this bond sells for more than face value is reflective of the condition where the market interest rates have fallen since the bond was issued.