(a) [5 marks] Prove that when the simple discount I and the simple bank discount I are the same, the annual simple interest rate i (computed by the simple discount method) and the annual simple discount rate d (computed by the simple bank diount method) satisfy d=1+ini here n is the period of discount (expressed in years). (b) [4 marks] (i). Find the annual effective discount rate d if d12 is 12%. (ii). Find the discounted value of 1000 due in 2 years at d12=12% (c) [5 marks] Niamh borrowed some money from Aoife as follows: 100 due in 2 years and 300 due in 3 years. If money is worth 4% compounded semiannually when can Niamh discharge all of her debts with a single payment of 400