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A company provides the following benefits for its employees: immediately on death in service, a lump sum of $20,000 immediately on withdrawal from service (other than on death or in ill-health), a lump sum equal to f1,000 for each completed year of service immediately on leaving due to ill-health, a benefit of $5,000 pa payable monthly in advance for 5 years certain and then ceasing, and on survival in service to age 65, a pension of E2,000 po for each complete year of service, payable monthly in advance from age 65 for 5 years certain and life thereafter. The forces of decrement for the employees at each age, assumed to be constant over each year of age, are as follows: Age X Hy 62 0.018 0.10 0.020 63 0.020 0.15 0.015 64 0.023 0.20 0.010 where wy is the (assumed constant) force of decrement by cause / over (x, x +1) , d represents death, / represents ill-health retirement and w represents withdrawal. (i) Construct a multiple decrement table with radix (a/)62 =100,000 to show the numbers of deaths, ill-health retirements and withdrawals at ages 62, 63 and 64, and the number remaining in employment until age 65. [5] (ii) Calculate the expected present value of each of the above benefits for a new entrant aged exactly 62. Assume that interest is 6% po effective before retirement and 4% po effective thereafter, and that mortality after retirement follows the PMA92C20 table. [10] [Total 15].1 Describe the main features of a unit-linked policy. .2 Explain the terms 'unit fund' and 'non-unit fund' in the context of a unit-linked life assurance contract, listing the various items that make up the non-unit fund. .3 A woman now aged exactly 64 has paid $20,000 a year into an accumulating with-profits contract style at the start of each of the last four years. The policy has incurred the following charges: f1,000 deducted at the start of year 1 E100 deducted at the start of each subsequent year. The following rates of regular bonus interest have been applied: Year t 1 2 3 4 Bonus interest by 2.9% 3.1% 3.2% 3.4% Additionally, there is a terminal bonus on contractual claim, currently payable at the rate of 0.015x(t -1) of the fund value, where t is the number of years the policy has been in force at the time of claim. The policy is now maturing, and the woman is using all of the maturity proceeds to buy a level annuity from the insurance company. The annuity will be payable monthly in advance for a minimum of 5 years and for the whole of life thereafter. Calculate the monthly amount of annuity that the woman will receive, if the insurance company uses the following basis in its annuity pricing: Mortality: PFA92C20 with a 3-year age deduction Interest: 4% pa Expenses: E400 initial plus 0.35% of each annuity payment. [7]
