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# 000 payable at the end of the five years or at the

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000, payable at the end of the five years, or at the end of the year of death, if earlier. Premiums of 19847 . 84 are payable annually in advance throughout the term of the policy. The insurer assumes that initial expenses will be \$300 and renewal expenses, which are incurred at the beginning of the second and subsequent years of the policy, will be \$30 plus 2 . 5% of the premium. The funds invested for the policy are expected to earn 7 . 5% p.a., and mortality is expected to follow the AM92 Select life table. The company holds net premium reserves, calculated using AM92 Ultimate mortality and interest of 4% p.a. Find the profit vector of this policy and explain the procedure in detail. 2. (Cashflow projection for convectional products) Explain how to set premiums, using a risk discount rate of 12%, so that the total expected present value of the profit is 15% of the total expected present value of premiums for the following 2-year term endowment insurance to a life aged 55 : Sum assured: S , payable at the end of the two years, or at the end of the year of death, if earlier. Premiums are payable annually in advance throughout the term of the policy 3

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First year expense: e 0 . Expense for the second year: 100 e 3 % of the annual premium plus e 2 The funds invested for the policy earn 7 . 5% p.a. and mortality follows AM92 Select The company holds net premium reserves calculated using AM92 Ultimate and interest of 4% p.a.. Moreover, state with brief reasons, without carrying out any further calculations, what the effect on the premium would be in each of the following cases: (i) The reserves are calculated using a lower rate of interest; (ii) The insurer uses a risk discount rate of 15%; and (iii) Mortality is assumed to be AM92 Ultimate. 3. (Unit linked contracts- Unit account cashflow projection) What are the key features of a unit linked contract? Explain in detail how to project the cashflows of the unit fund for the following contract and show that the values of the unit fund at the end of each year for a policy in force at the start of that year is: 510 . 435 for year 1, 2 , 641 . 297 for year 2, 4 , 931 . 121 for year 3, and 7 , 391 . 766 for year 4. A life office issues a 4-year unit linked endowment policy to a life aged 50 exact under which level premiums of \$2 , 000 per annum are payable in advance. In the first year, 25% of the premium is allocated to units and 102 . 5% in the second and subsequent years. There is a bid/offer spread in the prices of the units of 5% of the offer price. A management charge of 0 . 5% per annum of the bid value of the units is deducted at the end of each year. If the policyholder dies during the term of the policy, the death benefit of \$5 , 000 or the bid value of the units after the deduction of the management charge, whichever is higher, is payable at the end of the year of death. On surrender or on survival to the end of the term, the bid value of the units is payable at the end of the year of exit.
• Fall '19
• Endowment policy

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