Answer the following question

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 )'s 16 10,000 0 0 750 5 17 9,245 0 0 600 5 18 8,640 0 0 500 5 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 $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]A special 3-year temporary assurance will pay f100,000 on the first death of a man aged 60 exact and a woman aged 58 exact. The benefit is paid at the end of the year of death. A level annual gross premium of 1,299 is paid in advance for as long as the policy remains in force. You are given the following information about the pricing basis for this contract: Risk discount rate: 20% pa Profit criterion: Net present value of profit to equal zero Renewal expenses: $50 pa In addition, you are told that reserves of $175 were assumed to be held per policy in force at the end of the first year, for the purpose of projecting future profit flows for the pricing of this contract. (i) Calculate the actual reserve that would be held for a policy in force at the end of the first year, immediately before the second premium is paid, according to each of the following two bases: Basis A Reserve type: Prospective net premium reserve Mortality: Male life - PMA92C20 plus five years to the actual age Female life - PFA92C20 plus five years to the actual age Interest: 4% pa Basis B Reserve type: Prospective gross premium reserve Expenses: $75 incurred at the start of each year Mortality and interest as for Basis A [8] (ii) Comment on your answers to part (i). [3] [Total 11]