Test1-S11 - ACTSC 331 - Life Contingencies I Test 1 1. (18...

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ACTSC 331 - Life Contingencies I Test 1 1. (18 marks) Consider a special fully discrete whole life insurance with: b K +1 = 400 e 0 : 02( K +1) , K = 0 ; 1 ;::: premium k payable at time k (if survival): k = , k = 0 ; 1 ; 2 ;::: A force of interest of 4% is assumed. Given that ± A @ x A @ x +15 0 : 02 0 : 669 0 : 726 0 : 04 0 : 492 0 : 564 0 : 06 0 : 382 0 : 456 0 : 08 0 : 308 0 : 380 0 : 1 0 : 256 0 : 324 (a) (3 marks) (b) (3 marks) calculate the time- 15 policy value. (c) (7 marks) determine V ar ( 15 L j K ± 15) . (d) (5 marks) Assume 100 policies were issued at time 0 to a group of identical (and independent) policyholders. At time 14 , 60 5 deaths, and the e/ective force of interest was 2% . Given that q x +14 = 0 : 044 , i. (3 marks) ii.
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