A pension fund has to pay out benefits at the end of each of the next 40 years. The benefits payable at the end of the first year total 1 million. Thereafter, the benefits are expected to increase at a fixed rate of 3.8835% per annum compound. (i) Calculate the discounted mean term of the liabilities using a rate of interest of 7% per annum effective. (5] The pension fund can invest in both coupon-paying and zero-coupon bonds with a range of terms to redemption. The longest-dated bond currently available in the market is a zero-coupon bond redeemed in exactly 15 years. (iiExplain why it will not be possible to immunise tnis pension fund against small changes in the rate of interest. [2]