An investment fund has future liabilities of 11 million due in 7 years' time and 8.084 million in 11 years' time. The manager of the fund has sold the assets previously held and is creating a new portfolio by investing in the zero-coupon bond market. The manager is able to buy zero-coupon bonds for whatever term is required and has adequate funds at to be used for this purpose. (i) Explain whether it is possible for the manager to immunise the fund against small changes in the rate of interest by purchasing a single zero-coupon bond. [2 marks] (ii) In fact, the manager purchases two zero-coupon bonds, one paying 15.36 million in 7.5 years' time and the other paying 3.791 million in exactly 14.25 years' time. The current interest rate is 5.5% per annum effective. Investigate whether the investment fund satisfies the necessary conditions to be immunised against small changes in the rate of interest.