# 5 ans - 30-year term insurance on(25 that pays 1000 at the...

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MATH 471: Actuarial Theory I Homework #5: Fall 2010 Assigned September 22, due September 29 1. Mortality follows the select-and-ultimate life table: x l [ x ] l [ x ]+ 1 l x + 2 x + 2 30 9,906 9,904 9,901 32 31 9,902 9,900 9,897 33 32 9,898 9,896 9,892 34 33 9,894 9,891 9,887 35 34 9,889 9,886 9,882 36 Calculate 1 | q [30] . ( 0.0003028 ) 2. A select-and-ultimate life table with a select period of 2 years is based on probabilities that satisfy the following relationship: q [ x - i ]+ i = 2 4 - i × q x for i = 0, 1. You are given that l 68 = 10,000, q 66 = 0.026, and q 67 = 0.028. Calculate: (a) l 67 . ( 10,288.07 ) (b) l [65]+1 . ( 10,469.53 ) 3. You are given: (i) x l [ x ] l [ x ]+ 1 l x + 2 x + 2 65 8,200 67 66 8,000 68 67 7,700 69 (ii) 3 q [ x ]+1 = 4 q [ x +1] (iii) 4 q x +2 = 5 q [ x +1]+1 Calculate l [67] . ( 8056.04 ) ————THERE ARE MORE PROBLEMS ON THE BACK ————

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4. Suppose mortality follows l x = 110 - x for 0 x 110 and i = 0.08. (a) Calculate 1000 ¯ A 1 25: 30 . (137.67) (b) Calculate var ( Z ), where Z is the present value random variable for a

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Unformatted text preview: 30-year term insurance on (25) that pays 1000 at the moment of death. (56,723.81) 5. Assume μ x ( t ) = μ and δ t = δ for t ≥ 0. Show that: ¯ A 1 x : n = μ μ + δ [1-exp[-( μ + δ ) n ]]. 6. A continuous n-year term insurance of 1 on (x) has an actuarial present value of 0.070579. You are given: (i) μ x ( t ) = 0.007 for t ≥ (ii) δ t = 0.05 for t ≥ Calculate: n. (15) 7. For a special 10-year term insurance on (x), payable at the moment of death: (i) μ x + t = 0.05 for t ≥ (ii) δ = 0.08 (iii) The death beneﬁt at time t is b t = e . 06 t for t ≤ 10; b t = 0 for t > 10. (iv) Z is the present value random variable for this insurance at issue. Calculate: var ( Z ). (0.2004)...
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5 ans - 30-year term insurance on(25 that pays 1000 at the...

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