Year Spot Interest Rates 1 1% 2 2% 3 3% 4 4% a) Calculate the discount factors for maturities 1, 2, 3 and 4-years. (3 marks) b) Calculate, in basis points, the 2-year implied forward rate, 2 years from now. (That is the forward rate starts at 24 months from now and ends at 48 months from now) (3 marks) c) Consider "bond A, with a face value of 100 and a 4-year remaining time to maturity, which pays coupons annually with a coupon rate of 5%. Calculate the price of bond A. (5 marks) d) What is the unmodified duration (sometimes called the Macauley duration) of bond A? (5 marks) e) Suppose that you observe the market price of bond A is 107. Is there any arbitrage opportunity? If so, write down the detailed strategy of how you would like to exploit the arbitrage profit. (4 marks)