(a) A Bank has a bond with a maturity of 4 years. The coupon rate of the bond is 8%, the yield to maturity is 9%, and the face value is 1 million dollars. Interest payment will be paid annually. Determine the price (present value) and duration of the bond. (9 marks)

(b) Predict the change in the bond price if interest rates rise by 100 basis points based on the duration of the bond that you have calculated in part (a). (5 marks)

(c) Calculate the leverage adjusted duration gap (DGAP) if the ratio of total equity to total asset is 0.14, and the duration of all its liabilities is 1.88. (Assume that the Bank holds the bond in part (a) as its only asset) (5 marks)

(d) It is expected that the market interest rate will increase in the future. Assume that the ratio of total equity to total asset, and the duration of all the liabilities are both fixed, compute a new value of duration of all the assets so that immunization can be carried out. (4 marks)