H & M Insurance Company has liabilities to pay RM100 million annually for the next 40 years. In order to meet these liabilities, this insurance company can invest in zero coupon bonds with terms to redemption of five years and 40 years.

a) State the conditions that are necessary for an Insurance company to be immunized from small, uniform changes in the rate of interest. (3 Marks)

b) Calculate the present value of the liabilities at a rate of interest of 4% per annum. (2 Marks)

c) Calculate the duration of the liabilities at a rate of interest of 4% per annum. (3 Marks)

d) Calculate the nominal amount of each bond that the fund needs to hold so that the first two conditions for immunization are met at a rate of interest of 4% per annum. (10 Marks)

e) Illustrate using your answer in (c), the revised present value of the liabilities if there were a reduction in interest rates by 1.5% per annum. (3 Marks)