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Math 472 HW 1 Solutions

# Math 472 HW 1 Solutions - (i Beneﬁt premiums are such...

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MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #1: Spring 2011 Assigned January 19, due January 26 1. Consider a fully discrete whole life insurance on (35): (i) The death benefit is such that: b j = 1000(1 . 03) j for j = 1, 2, ... (ii) Benefit premiums are such that: π j = π (1 . 01) j for j = 0, 1, .... (iii) Mortality follows de Moivre’s Law with ω = 95, and i = 0.06. (a) Determine π . (32.51) (b) Calculate the benefit reserve at the end of policy year 10 using a prospective approach. (221.92) (c) Calculate the benefit reserve at the end of policy year 10 using a retrospective approach. (221.92) 2. Consider a fully discrete 40-payment whole life insurance of 10,000 on (25):

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Unformatted text preview: (i) Beneﬁt premiums are such that: π j = π (1 . 025) j for j = 0, 1, . .., 39; π j = 0 for j = 40, 41, . ... (ii) l x = 100 -x for 0 ≤ x ≤ 100, and i = 0.07. Calculate: π . (119.34) 3. For a fully discrete 2-year term insurance of 10,000 on (63): (i) The beneﬁt premium payable at the beginning of the ﬁrst year is P , and the beneﬁt premium payable at the beginning of the second year is 1.02 P . (ii) Mortality follows the Illustrative Life Table, and i = 0.06. Calculate the beneﬁt reserve at the end of the ﬁrst year. (6.23)...
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