11 marks] You are one month into your actuarial internship at Marvellous Life. This morn- ling, your manager greets you with an extract from a select and ultimate life table. T + 2 27 12+2 25 99,892.52 99,842.38 99,815.86 26. 99.838.28 99.814.41 99,787.20 27 99,810.20 99,785.70 99,757.71 28 99,781.36 99,756.17 99.727.29 28 29 30 (a) (3 marks] "I would like to know the actuarial present value (APV) of a term insurance policy issued to (25) and just selected": says your manager, "assume a 3-voar policy with sum insured $20.000, payable at the end of the year of death". Compute this value assuming i = 0.03. Express this value using actuarial notation, (0) [3 marks] Your manager then asks for the APV of a whole life insurance issued to (25) and just selected, with a $20,000 benefit payable at the end of year of death. You are given A27 = 0.1279 and i = 0.03. Compute the APV using recursion. Express this value using actuarial notation. (d) (4 marks) Derive a relationship between Aq:a) and 41261:a assuming uniformly dis- tributed deaths between integer ages. Show all steps. 11 marks] You are one month into your actuarial internship at Marvellous Life. This morn- ling, your manager greets you with an extract from a select and ultimate life table. T + 2 27 12+2 25 99,892.52 99,842.38 99,815.86 26. 99.838.28 99.814.41 99,787.20 27 99,810.20 99,785.70 99,757.71 28 99,781.36 99,756.17 99.727.29 28 29 30 (a) (3 marks] "I would like to know the actuarial present value (APV) of a term insurance policy issued to (25) and just selected": says your manager, "assume a 3-voar policy with sum insured $20.000, payable at the end of the year of death". Compute this value assuming i = 0.03. Express this value using actuarial notation, (0) [3 marks] Your manager then asks for the APV of a whole life insurance issued to (25) and just selected, with a $20,000 benefit payable at the end of year of death. You are given A27 = 0.1279 and i = 0.03. Compute the APV using recursion. Express this value using actuarial notation. (d) (4 marks) Derive a relationship between Aq:a) and 41261:a assuming uniformly dis- tributed deaths between integer ages. Show all steps