Question 4 (a) A bank offers a two-year bond with par value $1,000 with 5% coupon rates, semi-annually. The yield rate of this bond is 7% convertible semi-annually. Investor borrows the amount at an effective interest rate of 2% p.a. to buy this two-year bond, and each coupon payment will be put into an account earning interest at the effective interest rate of 6%. This investor will redeem the bond after two years and repay all the principle and interest in a lump sum. (i) Determine the price and current rate of the two-year bond. (ii) Calculate the Macaulay duration of the two-year bond. (iii) Is the two-year bond selling at par, premium, or discount? Briefly explain. (iv) Determine the net gain of the investor. [4 marks] [4 marks] [1 mark] [4 marks]