Final answer:
The price of the two-year bond can be calculated using the present value formula and the yield to maturity. By comparing the calculated present value to the face value, we can determine whether the bond is trading at a discount, premium, or at par.
Step-by-step explanation:
The price of a two-year, default-free security can be calculated using the present value formula. The bond has a face value of $1000 and an annual coupon rate of 5.75%. The yield to maturity (YTM) is given as 5.5%. To calculate the price of the bond, we need to discount the future cash flows generated by the bond at the YTM.
Using the present value formula, we can calculate the present value of the annual coupon payments and the face value of the bond:
PV = C/ (1 + r)^1 + C/ (1 + r)^2 + ... + C/ (1 + r)^n + F/ (1 + r)^n
Where PV is the present value, C is the coupon payment, r is the discount rate (YTM), and F is the face value of the bond. Plugging in the values, we get:
PV = 57.5/ (1 + 0.055)^1 + 57.5/ (1 + 0.055)^2 + 1057.5/ (1 + 0.055)^2
Simplifying this equation gives us the present value of the bond. To determine if the bond is trading at a discount, premium, or at par, we compare the calculated present value to the face value of $1000:
If the calculated present value is less than $1000, the bond is trading at a discount. If the calculated present value is more than $1000, the bond is trading at a premium. If the calculated present value is equal to $1000, the bond is trading at par.
By calculating the present value using the formula and YTM of 5.5%, we can determine the price of the two-year bond and whether it is trading at a discount, premium, or at par.