Answers the following questions.

The active male membership of a large pension scheme enjoys the experience of the multiple decrement table below. Age Active lives Age retirements Ill-health Withdrawals Deaths (al), (ad )x retirements (ad)" (ad), (ad )' 16 10,000 0 0 750 5 17 9.245 0 0 600 5 18 8,640 0 0 500 5 30 3,150 0 2 30 7 40 3,111 0 3 20 .. . 63 2,200 100 25 0 20 64 2,055 200 30 0 25 65 1,800 1,800 You may assume that decrements occur uniformly in each single decrement table, except for age retirements at age 65 which all occur on the 65th birthday. Calculate the following: (a) The probability that a man who joins the scheme on his 18th birthday, will retire after his 63rd birthday. [2] (b) The independent rate of withdrawal between the ages of 17 and 18. [3] (c) The expected present value of a lump sum retirement benefit of $10,000 payable on retirement at age 65, for a member now aged exactly 18, calculated using 4% pa interest. [1] (d) The expected present value of a lump sum death benefit of $20,000 payable immediately on death in service after a member's 63rd birthday, for a member now aged exactly 40, using 4% pa interest. [2] [Total 8]Consider an economy in which there are only two goods, Good X and Good Y, which currently cost 50 and 20 respectively. Total consumer income is 1000, which is currently used to purchase 10 units of Good X and 25 units of Good Y. Suppose that the price of Good X falls to 40 and that consumption of Good X increases to 12 units. (i) Calculate the price elasticity of demand for Good X. [1] (ii) Calculate the cross-price elasticity of demand for Good Y with respect to the price of Good X and comment on your answer. [3] [Total 4]