Answer all questions correctly

Question 2.22 A life office sold a portfolio of 10,000 term assurance policies on 1/1/2003. The policies had a term of 2 years, with premiums paid annually in advance and were sold to a group of males aged 60 exactly at that date. Each policy had a sum assured of $50,000, which is payable at the end of the year of death. The company prices the product assuming AM92 Ultimate mortality. (i) The same premium was charged for each year. The premium was calculated by setting the expected present value of the premiums equal to the expected present value of the benefit payments plus 10% of the standard deviation of this present value. Calculate the premium assuming 4% pa interest. [7] (ii) During the first policy year 75 policyholders died. Calculate the net premium reserve at the end of 2003 and hence the mortality profit for the portfolio for calendar year 2003. [5] (iii) A director of the company has calculated the profit of the business as premiums received less sum assured paid on death less the net premium reserve. He calculates the profit as "just under $3.5m" and writes to ask why this conflicts with the mortality profit set out above. Show that the director's figures are numerically correct and then explain why the two figures differ. [6] [Total 18] Question 2.23 On 1 January 2010 a pension scheme had 100 members aged 75 exact, each eligible for a pension of f10,000 pa, payable annually in advance. In addition, the members were entitled to a death benefit of f20,000 payable at the end of the year of death. No premiums were being paid in respect of these contracts after January 2010. Given that 4 of the lives died during 2010, calculate the mortality profit for these contracts for calendar year 2010 using the following basis: Mortality: PFA92C20 Interest: 4% pa Expenses: none [5]Question 2.24 (i) Express in the form of symbols, and also explain in words, the expressions "death strain at risk", "expected death strain" and "actual death strain" [3] (1i) On 1 January 2001 an office issued a number of annual premium policies to a group of lives, each of whom was then aged exactly 45. All policies were for a term of 20 years and were of the following types: endowment assurances under which the sum assured was payable on survival to the end of the term or at the end of the year of earlier death temporary assurances under which the sum assured was payable only at the end of the year of death within the policy term pure endowments under which the only benefit payable is the sum assured on survival to the end of the policy term Assuming that there is no source of decrement other than death, calculate the profit or loss from mortality for the calendar year 2010 in respect of the policies issued to this group of lives, given the following information: Type of policy Sums assured in force Sums assured on 1 January 2010 by death during 2010 discontinued Endowment assurance E600,000 $4,000 Temporary assurance E200,000 E2,000 Pure endowment $80,000 E500 Reserving basis: AM92 Ultimate mortality, 4% pa interest. Ignore expenses