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RelativeResourceManager11 - π and is determined by the...

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MATH 471: Actuarial Theory I Homework #11: Fall 2009 Assigned November 18, due December 2 1. Consider a fully discrete whole life insurance of 1000 on (40). Assume mortality follows de Moivre’s Law with ω = 100, and i = 0.06 (a) Provide the expression for the loss-at-issue random variable, L , where P denotes each premium. (b) Find the annual benefit premium. (20.87) (c) Find the annual percentile premium so Pr ( L > 0) = 0.20. (49.96) 2. Assume that mortality follows the Illustrative Life Table and i = 0.06. Calculate the annual benefit premium for a 15-payment fully discrete 30-year term insurance of 1 on (35). (0.0067) 3. A special fully discrete whole life insurance on (x) pays a benefit of 10,000 plus the return of all premiums without interest. The annual premium is
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Unformatted text preview: π , and is determined by the equivalence principle. Show: π = 10 , 000[1-d ¨ a x ] ¨ a x-( IA ) x . 4. Show: n P x P 1 x : n-P 1 x : n P 1 x : n = A x + n . 5. Suppose mortality follows the Illustrative Life Table, deaths are uniformly distributed within each year of age, and i = 6%. Calculate the annual benefit premium for a 25-year endowment insurance of 50,000 on (40) where: (i) the benefit is payable at the moment of death (for the term part of the coverage) and (ii) (40) pays premiums at the beginning of each year. (1039.44) 6. Assume that mortality follows the Illustrative Life Table, i = 0.06, and deaths are uniformly distributed within each year of age. Calculate: P (4) 25: 20 . (0.0273)...
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