ct010s12 - UNSW ACTL1001 Actuarial Studies and Commerce...

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UNSW ACTL1001 Actuarial Studies and Commerce Solutions 12 and Revision Exercise 1 Expected salary at age 65 for a 20 year old. Actual salary will be 45 ; 000 e P 45 i =1 & i where & i & Normal (0 : 04 ; 0 : 01) and we use the & ( ±;² ) notation. Since each & i is independent we know that P 45 i =1 & i & (45 ± 0 : 04 ; p 45 ± 0 : 01) Therefore expected salary is 45 ; 000 e 45 & 0 : 04+ 1 2 & 45 & 0 : 01 2 = 45 ; 000 e 1 : 80225 = 45 ; 000 ± 6 : 0632745 = 272 ; 847 Exercise 2 Expected present value. First determine expected retirement ben- e&t at age 65 in 20 years time (age 45 currently). Expected salary is 55 ; 000 e 20 & 0 : 04+ 1 2 & 20 & 0 : 01 2 = 55 ; 000 e 0 : 801 = 55 ; 000 ± 2 : 2277676 = 122 ; 527 : 22 Service to age 65 will be 40 years so (20 years current service plus 20 years future service). Expected bene&t at age 65 will be 8 ± 40 60 ± 122 ; 527 : 217 = 653 ; 478 : 49 and the present value factor will be 1 (1 : 06) 20 = 0 : 311805 Hence the expected present value of the retirement bene&t is 0 : 75 ± 0 : 311805 ± 653 ; 478 : 49 = 152 ; 818 since 0.75 is the probability of payment of the bene&t at retirement. 1
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Exercise 3 An actuarial review of a de&ned bene&t superannuation fund usually involves determining if the assets that are accumulating in the fund will be su¢ cient, along with future contributions, to meet the bene&t pay- ments. It also will involve an assessment of the adequacy of the contribution
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ct010s12 - UNSW ACTL1001 Actuarial Studies and Commerce...

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