Q4-S-2010W - 80 4(a The present value of the payments is 4...

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SOLUTIONS TO QUIZ 4 – ACTSC 232, WINTER 2010 1. Question 1 has been removed from this quiz. 2. We have ¨ a ( m ) x = 1 - A ( m ) x d ( m ) = 1 - i i ( m ) A x d ( m ) = 1 - i i ( m ) (1 - d ¨ a x ) d ( m ) = α ( m ) ¨ a x - β ( m ) where α ( m ) = id i ( m ) d ( m ) and β ( m ) = i - i ( m ) i ( m ) d ( m ) . 3. (a) The APV of the premiums is 12 × 150 × ¨ a (12) 60: 10 . (b) The APV of the death benefit is b × A (12) 60 . (c) We have 12 × 150 × ¨ a (12) 60: 10 = 1 . 15 × b × A (12) 60 . Now, A (12) 60 = i i (12) (1 - d ¨ a 60 ) = 0 . 378909 , ¨ a 60: 10 = ¨ a 60 - ¨ a 70 10 E 60 = 7 . 28322 . Thus, ¨ a (12) 60: 10 = α (12)¨ a 60: 10 - β (12)(1 - 10 E 60 ) = 7 . 02805 . Hence, b = 29031
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Unformatted text preview: . 80. 4. (a) The present value of the payments is 4 K x + J x X j =0 1 4 v j 4 = 1-v K x + Jx +1 4 d (4) . (b) The number of quarters lived by ( x ) in the death year is [( T x-K x )4] = [4 R x ] . (c) The expectation is E ([4 R x ]) = Z 1 [4 t ] dt = Z 1 4 dt + Z 2 4 1 4 1 dt + Z 3 4 2 4 2 dt + Z 1 3 4 3 dt = 1 . 5 . 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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