4. (a) () Imagine you have 1000 to invest and AIB bank offers you either an in- terest rate of 4.50% compounded quarterly or 4.475% contimously com- pounded both for a five-year investment. Which investment would you profor? Why? What can you deduce about the two rates? [3] (ii) You work for Bank of Ireland and a customer asks you to lend him 1000 today and he will repay back 100 one year from now, 500 two years from now, and 600 three years from now. If the rate of interest you are using to evaluate this stream of cashflow is 4% simple compounded, should you agree on the lending? Does your bank gain or loss on this financial operation? [3] (ii) You invest 1000 this year, 1500 one year from now, and 2500 two years from now to use the accumulated funds six years from now to cover the 10000 down payment on a house. Will you achieve your objective if the investments earns 7% compounded monthly? (b) (i) What is the bond vield to maturity? Which is the relation between bond price and its yield to maturity? What is the bond par vield? [2] (ii) Let us consider a 4-year coupon bond, with anmal coupon of 6%, no- tional N = 100 and market price 112.11. Using the zero rates in Table 1, compute the bond par yield assuming that the ZC rates are continuously compounded. Do you expect that the par yield is greater or lower than 6%. Why? Maturity (years) ZC rate (%) 1.2 2 1.7 1 3 22 2.8 (c) () Consider the CC rates in Table 1 and assume again they are continuously compounded. Without doing any calculation, do you expect that the forward rate for a period of time ending at T is greater or lower than the Ti zero rate? Why? Calculate the forward interest rates Fit (1) Consider the Crates in Table 1 and assume now they are annually com- pounded. Show that if the forward interest rate F12 were 2.5%, there would be an arbitrage opportunity. Describe the arbitrage strategy and determine the net profit