Final answer:
To calculate the value of the bond on January 15, 2022, we need to discount the future cash flows to present value. The value of the bond is $912.37, and it is a discount bond.
Step-by-step explanation:
To calculate the value of the bond on January 15, 2022, we need to discount the future cash flows to present value. The coupon payments of $80 will be received annually for 10 years, and the face value of $1,000 will be received at maturity. Since the interest rate in the market is 10%, we can use the present value formula to calculate the value of the bond:
Value of bond = (Coupon payment / Interest rate) * (1 - (1 / (1 + Interest rate)^n)) + (Face value / (1 + Interest rate)^n)
Substituting the values, we get:
Value of bond = (80 / 0.10) * (1 - (1 / (1.10)^10)) + (1000 / (1.10)^10)
Solving this equation, we find that the value of the bond on January 15, 2022, is approximately $912.37.
To determine whether the bond is a premium or discount bond, we compare its current value with its par value. If the current value is higher than the par value, it is a premium bond. If the current value is lower than the par value, it is a discount bond. In this case, since the current value of the bond is $912.37, which is lower than the par value of $1,000, the bond is a discount bond.