Q2-Answer-2010W

Q2-Answer-2010W - x = ¯ A 1 x n Z ∞ n v t-n n t-n n p x...

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ANSWERS TO QUIZ 2 – ACTSC 232, WINTER 2010 1. (a) 2 p [83]+1 = l [83]+3 l [83]+1 = 0 . 7243. (b) The probability is 2 p [80]+3 = l 85 l [80]+3 = 0 . 8333 . (c) 3 | 2 q [81]+1 = l 85 l [81]+1 - l 87 l [81]+1 = 0 . 119. 2. (a) Z = 1000 v T 40 . (b) The single benefit premium of the insurance is E ( Z ) = 1000 Z 70 0 e - 0 . 02 t 1 70 dt = 538 . 145 . (c) We have E ( Z 2 ) = 1000 2 Z 70 0 e - 2 × 0 . 02 t 1 70 dt = 335424 . 978 . Thus, the variance of the present value of the death benefit is 45824.94. (d) The probability is Pr { 1000 v T 40 > 600 } = Pr { T 40 < 25 . 5413 } = 0 . 3649 . 3. The formula comes from ¯ A
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Unformatted text preview: x = ¯ A 1 x : n + Z ∞ n v t-n + n t-n + n p x μ x + t dt = ¯ A 1 x : n + v n n p x Z ∞ n v t-n t-n p x + n μ x + t dt = ¯ A 1 x : n + v n n p x Z ∞ v s s p x + n μ x + n + s ds. 4. (a) It follows from A 30 = A 1 30: 20 + v 20 20 p 30 A 50 and A 30: 20 = A 1 30: 20 + v 20 20 p 30 that A 1 30: 20 = 0 . 071 . (b) 20 | A 30 = A 30-A 1 30: 20 = 0 . 145. 1...
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This note was uploaded on 03/20/2011 for the course ACTSC 232 taught by Professor Matthewtill during the Summer '08 term at Waterloo.

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