(a) Sonoran Bank has assets consisting of $4.5 billion in cash, $60.0 billion of 5.5% fixed rate interest only mortgages (with annual payment and compounding) with an average life of 12.0 years (and currently trading at par) and $30.0 billion of other loans with a modified duration of 3.78. Sonoran also has $80.0 billion of 2.0% fixed rate liabilities consisting entirely of 3-year (annual pay) certificates of deposit, currently trading at par. (i) Using the duration gap (DG) method, calculate Sonoran Bank's exposure to an unexpected 40bp parallel increase in interest rates. Explain your answer. State any assumptions. (15 marks) (ii) Using the DG method, calculate what unexpected parallel increase in interest rates would completely eradicate Sonoran Bank's equity? (b) (5 marks) Sonoran Bank wishes to immunise its balance sheet against unexpected interest rate changes with a classic T-bond futures contract currently priced at $118.32 (in decimal form). The cheapest to deliver bond against this contract is a 16-year, 2.85% coupon bond currently priced to yield 4.5%. (i) Calculate the cost of the cheapest to deliver bond. (7 marks) (ii) How many futures contracts are necessary to immunise Sonoran Bank's balance sheet? (8 marks)