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# A2 - ACTSC 232 Spring 2010 Assignment 2 Due Friday June 25...

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ACTSC 232 - Spring 2010 - Assignment 2 Due: Friday, June 25 at 11:30 am 1. (a) Describe in words the insurances with the present values given. i. Z 1 = b 20000 v T x , T x 10 10000 v T x , T x 10 ii. Z 2 = 0 , T x 15 10000 v T x , 15 T x 25 10000 v 25 , T x 25 (b) Write down in integral form the formula for the expected value for Z 1 and Z 2 . (c) Derive expressions in terms of standard actuarial functions for the expected values in (b). (d) Derive an expression in terms of standard actuarial functions for the covariance of Z 1 and Z 2 . 2. Given A 20 = 0 . 35, A 40 = 0 . 55, and A 20: 20 = 0 . 485 Calculate (a) A 1 20: 20 (b) A 1 20: 20 3. You are given the following extract from a select life table: [ x ] l [ x ] l [ x ]+1 l [ x ]+2 l [ x ]+3 l x +4 x + 4 [30] 100,000 99,899 99,724 99,520 99,288 34 [31] 99,802 99,689 99,502 99,283 99,033 35 [32] 99,597 99,471 99,268 99,030 98,752 36 [33] 99,365 99,225 99,007 98,747 98,435 37 [34] 99,120 98,964

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A2 - ACTSC 232 Spring 2010 Assignment 2 Due Friday June 25...

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