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RelativeResourceManager7

RelativeResourceManager7 - (ii k p x =(0 95 k for k = 0 1...

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MATH 471: Actuarial Theory I Homework #7: Fall 2009 Assigned October 14, due October 21 1. A discrete 15-year endowment insurance of 10,000 is issued to (30). Assume mortality follows de Moivre’s Law with ω = 90, and i = 0.05. (a) Calculate the actuarial present value of this insurance. (5337.57) (b) Calculate the standard deviation of Z for this insurance. (1166.85) 2. A special term insurance policy pays 1000 at the end of the year of death for the first ten years and 2000 at the end of the year of death for the next 10 years. Mortality follows the Illustrative Life Table, and i = 0.06. Calculate the single benefit premium for this policy on (40). (92.60) 3. Suppose: (i) Z is the present value random variable for a whole life insurance of 1 payable at the end of the year of death.

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Unformatted text preview: (ii) k p x = (0 . 95) k for k = 0, 1, 2, . .. (iii) i = 0.10 Calculate A x . [Hint: Deﬁne v * = 0.95/1.10, and recall from MATH 210 the present value of a perpetuity-due of 1 per year.] (1/3) 4. You are given: (i) For a standard life, A 1 45: 10 = 0.15 (ii) A standard life has mortality rate q 45 = 0.01 (iii) v = 0.95 Due to an extra hazard at age 45, a certain life has q 45 = 0.02, but has standard mortality at all other ages. Calculate A 1 45: 10 for this life. (0.1581) 5. Using the Illustrative Life Table, the UDD assumption over each year of age, and i = 0.06, calculate the actuarial present value of a continuous 30-year deferred whole life insurance of 100,000 on (35). (6305.74)...
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RelativeResourceManager7 - (ii k p x =(0 95 k for k = 0 1...

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