Question

Consider a bond paying a coupon rate of 9.00% per year semiannually when the market interest rate is only 3.6% per half-year. The bond has six years until maturity. a. Find the bond's price today and six months from now after the next coupon is paid.

Answer 1

To calculate the bond's price today and six months from now, you need to find the present values of all the future cash flows. This involves calculating the present value of each coupon payment and the final principal payment using the present value formula.

Step-by-step explanation:

To calculate the price of the bond, we need to find the present values of all the future cash flows. The bond pays a coupon rate of 9.00% per year, semiannually, and has a market interest rate of 3.6% per half-year. The bond has six years until maturity.

Bond's Price Today:

1. Calculate the present value of each coupon payment using the formula: PV = C / (1 + r/n)^(nt), where C is the coupon payment, r is the market interest rate, n is the number of coupon payments per year, and t is the number of years until maturity.
2. Calculate the present value of the final principal payment using the formula: PV = F / (1 + r/n)^(nt), where F is the face value of the bond.
3. Add all the present values calculated in steps 1 and 2 to find the bond's price today.

Bond's Price Six Months from Now:

1. Calculate the present value of each remaining coupon payment using the formula: PV = C / (1 + r/n)^(nt), where C is the coupon payment, r is the market interest rate, n is the number of coupon payments per year, and t is the remaining number of years until maturity.
2. Calculate the present value of the final principal payment using the formula: PV = F / (1 + r/n)^(nt), where F is the face value of the bond.
3. Add all the present values calculated in steps 1 and 2 to find the bond's price six months from now.