I really need help with the math on parts c) and d). I've provided the answers from a) and b) to help with solving.

Consider two treasury bonds, A and B. Both mature in 10 years and both are priced now to have the same interest rate. Bond A is a zero coupon bond while bond B has an annual coupon rate of 4%.

(a) Suppose bond A is trading at a price of $82 per $100 face value, what is the interest rate? (hint: for a zero coupon bond, interest can be easily solved because bond price only has one term).

i = 2.0044%

(b) Price bond B by using the interest rate you computed from (a) since bond B has the same interest rate as described in the problem.

P_B = $117.93

(c) You and your friend both want to invest in 10 year treasuries and you both intend to hold them to maturity. Suppose that you invested in bond A while your friend invested in bond B by paying the respective prices in the market. Suppose the interest rates of the bonds is expected to stay at the same as today's level over the next 10 years, what is your average annual return over the 10 years? What is your friend's? You need to justify your answers.

(d) Suppose the interest rate is expected to rise steadily from today's level over the ensuing 10 years. What is your average annual return over the 10 years? Does it differ from your answer to (c)? What about your friend's? Is your friend's average annual return over the 10 years in this situation higher or lower than yours? Explain.