On 1st January 2013 a life office sold a large number of 18-year Endowment policies to lives then aged 42 exact. The benefit is 100,000 payable on survival to age 60 or at the end of year of earlier death. Premiums are payable annually in advance throughout the term of the policy or until death if earlier. a) Calculate the annual premium. [5 marks] b) Calculate the retrospective value per policy in force as at 31st December 2020 assuming that all items of experience are exactly as expected in the basis given. [9 marks] c) Using the recursive relationship, roll your answer to b) forward one year to calculate the value per policy in force as at 31st December 2021. [2 marks] d) Verify your answer by to c) by calculating the prospective value per policy in force as at 31st December 2021. [4 marks] On 31st December 2020 there were 756 policies in force, and during the year 7 policyholders died. e) Calculate the mortality profit or loss to the life office over 2021 assuming that all other elements of the basis were as expected. [4 marks] f) A colleague has commented that there's a slight discrepancy between your figures for prospective and retrospective reserves, whereas they have done a similar calculation using a spreadsheet and calculating all functions from the qx figures on the mortality table. They have no such discrepancy and their figures are similar (though not quite identical) to yours. Comment on this observation. [2 marks] [Total: 26 marks] Basis AM92 Select mortality 6% per annum interest Initial Expenses 250 Renewal expenses 15 per annum from policy year 2 onwards Initial Commission 120% of annual premium Renewal Commission 5% of annual premium from policy year 2 onwards On 1st January 2013 a life office sold a large number of 18-year Endowment policies to lives then aged 42 exact. The benefit is 100,000 payable on survival to age 60 or at the end of year of earlier death. Premiums are payable annually in advance throughout the term of the policy or until death if earlier. a) Calculate the annual premium. [5 marks] b) Calculate the retrospective value per policy in force as at 31st December 2020 assuming that all items of experience are exactly as expected in the basis given. [9 marks] c) Using the recursive relationship, roll your answer to b) forward one year to calculate the value per policy in force as at 31st December 2021. [2 marks] d) Verify your answer by to c) by calculating the prospective value per policy in force as at 31st December 2021. [4 marks] On 31st December 2020 there were 756 policies in force, and during the year 7 policyholders died. e) Calculate the mortality profit or loss to the life office over 2021 assuming that all other elements of the basis were as expected. [4 marks] f) A colleague has commented that there's a slight discrepancy between your figures for prospective and retrospective reserves, whereas they have done a similar calculation using a spreadsheet and calculating all functions from the qx figures on the mortality table. They have no such discrepancy and their figures are similar (though not quite identical) to yours. Comment on this observation. [2 marks] [Total: 26 marks] Basis AM92 Select mortality 6% per annum interest Initial Expenses 250 Renewal expenses 15 per annum from policy year 2 onwards Initial Commission 120% of annual premium Renewal Commission 5% of annual premium from policy year 2 onwards