Provide solutions to the following questions. Explain your answers fully.

An employer provides the following benefits for his 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 $2,000 pa for each complete year of service, payable monthly in advance from age 65 for 5 years certain and life thereafter. The independent rates of decrement for the employees are as follows: Age x 62 0.018 0.10 0.020 63 0.020 0.15 0.015 64 0.023 0.20 0.010 where d represents death, / ill-health retirement and w withdrawal. Each decrement occurs uniformly over each year of age in its single decrement table. (i) Construct a multiple decrement table with radix (a/)62 = 100,000 to show the numbers of deaths, ill-health retirements and withdrawals at ages 62, 63 and 64, and the number remaining in employment until age 65. [6] (ii) Calculate the expected present value of each of the above benefits for a new entrant aged exactly 62. Assume that interest is 6% pa before retirement and 4% pa thereafter, and that mortality after retirement follows the PMA92C20 table. [10] [Total 16]A continuous cashflow is to be paid at a rate p() =10+2t, OS/$ 10. The force of interest applicable during the period is: 6(1) = 0.05 +0.01, Ost$ 10 Find the accumulated value of the cashflow at the end of the ten-year period. [6]