Consider three 26-year bonds, A, B and C, that mature on the same date (exactly 26 years from now) and pay annual coupons at the same point in time. All bonds have the same face value of $100. Bond A has an annual coupon of 13% with current price of $105. Bond B has an annual coupon of 9% with current price of $90. Use annual compounding in your analysis.

(a) If Bond C has an annual coupon of 8% per year, what should be its current price that is consistent with no arbitrage?

(b) Suppose the annualized rate of return on a zero (with face value $1) that is currently trading and maturing in 26 years is 2.7% (i.e., r26 = 2:7%). Is there an arbitrage opportunity? If so, show how to exploit it (i.e., derive a trading strategy leading to this arbitrage pro_t), and derive the pro_t to be made on each unit of this zero.