Answer all the questions below

Question 4.4 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)x (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 # # 4 . . . . . . . . . . . . 39 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 f10,000 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]