answer all the questions with though explanations

Question 4.4 The active male membership of a large pension scheme enjoys the experience of the multiple decrement table below. 5" in Age Active lives Age retirements H ass. e and HI I: '3' H E I.u-I-u... u no en to U1 3. c-a E: M u. M I: M s I n n - n - - - El E You may assume that decrements occur uniformly in each single decrement table. except for age retirements at age 65 which all {seem an the 65th birthday. Calculate the following: {a} The probability that a man who joins the scheme on his lth birthday, will retire after his 63rd birthday. [2] (b) The independent rate of withdrawal between the ages of l? and 18. [3] (c) The expected present value of a lump sum retiremem benet of 10,000 payable on retirement at age 65, for a member now aged exactly l8, calculated using 4% pa interest. [1] (d) The expected present value of a lump stun death benet 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]