5. A life office issues a 25-year endowment assurance policy to a life aged 40 exact. The sum assured of 100,000 is payable at maturity or at the end of the year of death if earlier. Level premiums are payable monthly in advance until the policyholder is 60 or death if earlier. (a) Calculate the monthly premium (to 2 decimal places) using the following pricing basis: Mortality: AM92 Ultimate Interest: 4% per annum effective Initial expenses: 300 Renewal expenses: 2.5% of all the premiums excluding first monthly premiums Claim expenses: 0.2% of the sum assured on death or maturity [16 marks] (b) Write down (do not evaluate) the prospective gross premium reserve exactly 20 years after issue, assuming the reserving basis is the same as pricing basis. [3 marks] [Total: 19 marks] 5. A life office issues a 25-year endowment assurance policy to a life aged 40 exact. The sum assured of 100,000 is payable at maturity or at the end of the year of death if earlier. Level premiums are payable monthly in advance until the policyholder is 60 or death if earlier. (a) Calculate the monthly premium (to 2 decimal places) using the following pricing basis: Mortality: AM92 Ultimate Interest: 4% per annum effective Initial expenses: 300 Renewal expenses: 2.5% of all the premiums excluding first monthly premiums Claim expenses: 0.2% of the sum assured on death or maturity [16 marks] (b) Write down (do not evaluate) the prospective gross premium reserve exactly 20 years after issue, assuming the reserving basis is the same as pricing basis. [3 marks] [Total: 19 marks]