Actuarial Science

10 questions.

You are given: i) qx = 0.2 ii) qx+1 = 0.4 iii) qx+2 = 0.6 iv) qx+3 = 0.8 v) qx+4 = 1.0 vi) ? = 0.06 Calculate a) Ax; b) ??:3̅| 1 ; c) ??:3̅| 1 ; d)2Ax 2. You are given: i) qx = 0.2 ii) 1|?? = 0.2 iii) 2|?? = 3|?? = 4|?? = 0.2 i) ? = 0.06 Calculate a) Ax; b) ??:3̅| 1 ; c) ??:3̅| 1 ; d)2Ax 3. In problem #1, calculate ?̅ ? and 2?̅ ? under UDD 4. In problem #2, calculate ?̅ ?:3̅| and 2?̅ ? under UDD 5. You are given: i) ?50:20| ̅̅̅̅̅ = 0.42247 ii) ?50:20| ̅̅̅̅̅ 1 = 0.14996 iii) ?50 = 0.31266 Calculate ?70 6. You are given: i) ?? = 0.25 ii) ??+20 = 0.4 iii) ??:20| ̅̅̅̅̅ = 0.55 iv) ? = 0.03 Calculate 10000 ?̅ ?:20| ̅̅̅̅̅ under a) UDD and b) claims acceleration method 7. You are given: i) (IA)50 = 4.99675 ii) ?50:1̅| 1 = 0.00558 iii) ?51 = 0.24905 iv) ? = 0.06 Calculate (IA)51 8. You are given: i) X denotes the present value of the random variable for n-year endowment and Y denotes the present value of the random variable for n-year term insurance(X and Y are both continuous). ii) Var(X) = 0.0052 iii) v n = 0.3 iv) npx = 0.8 v) E(Y) = 0.04 Calculate Var(Y) 9. ?1 = { ? ??, ?? ≤ ? 0, ?? > ? and ?2 = { 0, ?? ≤ ? ? ? , ?? > ? Calculate Cov(Z1, Z2) 10. You are given: x lx Ax 35 100000.00 0.151375 36 99737.15 0.158245 37 99455.91 0.165386 38 99154.72 0.172804 39 98831.91 0.180505 40 98485.68 0.188492 ? = 6% Calculate a) 5E35; b) ?35:5̅| 1 ; c) 5|?35; d) ?̅ 35:5̅| under UDD

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