Test_1 _soln

Test_1 _soln - ACTSC 331 Test 1 - Winter 2010 Time: 90...

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ACTSC 331 Test 1 - Winter 2010 Time: 90 minutes Aids: calculator 1. For a 3-year select and ultimate table you are given: t 1 2 3 4 t p [20] 0.9999 0.9997 0.9994 0.9989 [4] a) Determine the following values p [20] , p [20]+1 , p [20]+2 , and p 23 . p [20] = : 9999 , p [20]+1 = 2 p [20] p [20] = 0 : 9997 0 : 9999 = 0 : 999 80 , p [20]+2 = 3 p [20] 2 p [20] = 0 : 9994 0 : 9997 = 0 : 999 70 , and p 23 = 4 p [20] 3 p [20] = 0 : 9989 0 : 9994 = 0 : 999 50 . [4] b) Given l 24 = 90 ; 000 calculate l 23 , l [20]+2 ; l [20]+1 ; and l [20] . l 23 = l 24 p 23 = 90000 0 : 999 50 = 90045 , l [20]+2 = l 23 p [20]+2 = 90045 0 : 999 70 = 90072 ; l [20]+1 = l [20]+2 p [20]+1 = 90072 0 : 999 80 = 90090 : 0 and l [20] = l [20]+1 p [20] = 90090 : 9999 = 90099 [2] c) Calculate 1 j q [20] and 2 j q [20] 1 j q [20] = p [20] 2 p [20] = 0 : 9999 & 0 : 9997 = 0 : 0002 or 1 j q [20] = l [20]+1 l [20]+2 l [20] = 90090 90072 90099 = 0 : 000200 and 2 j q [20] = 2 p [20] 3 p [20] = 0 : 9997 & 0 : 9994 = 0 : 0003 or 2 j q [20] = l [20]+2 l 23 l [20] = 90072 90045 90099 = : 000300 1
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2. A 2-year term insurance with sum insured $100,000 is issued to a select life age 40. Premiums are paid annually in advance for at most 2 years. The policy value basis is: Interest: 5% per year e/ective Initial Expense: 20% of gross premium Renewal Expense: 5% of gross premium Death claim expense: $100 payable when a death claim is paid Mortality based on the following table: [ x ] l [ x ] l [ x ]+1 l [ x ]+2 l [ x ]+3 l x +4 x + 4 [40] 100000 99899 99724
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Test_1 _soln - ACTSC 331 Test 1 - Winter 2010 Time: 90...

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