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ACTSC232-Tut4

# ACTSC232-Tut4 - assumption calculate E Z 4 Z 1 is the PV of...

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ACTSC 232 Introduction to Actuarial Mathematics Tutorial 4, Winter 2012 1. Assume the force of mortality satisfy De Moivre’s Law with ω = 100, that is μ x = 1 100 - x , for 0 x < 100. Let i = 0 . 05, calculate (a) A (2) 50 (b) A (2) 1 50: 20 2. Given that ¯ A 20 = 0 . 35, ¯ A 40 = 0 . 55, ¯ A 20: 20 = 0 . 485, 2 ¯ A 20 = 0 . 2, 2 ¯ A 40 = 0 . 32, and i = 0 . 04. Calculate (a) A 1 20: 20 (b) ¯ A 1 20: 20 (c) 2 ¯ A 20: 20 3. For a 20-year term life insurance issued to (30), \$1,000,000 will be paid at the end of the death year. Let Z be the present value of this insurance beneﬁt. Using the SOA illustrative life table, calculate (a) E [ Z ] (b) V ar ( Z ) (c) If the death beneﬁt is paid at the end of the death month, under the UDD fractional age
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Unformatted text preview: assumption, calculate E [ Z ]. 4. Z 1 is the PV of a continuous n-year term insurance beneﬁt, issued to ( x ). Z 2 is the PV of a continuous whole life insurance beneﬁt, issued to the same life. What is the covariance of Z 1 and Z 2 ? Express in actuarial functions, simpliﬁed as far as possible. 5. (a) Show that ( IA ) 1 x : n = vq x + vp x ± ( IA ) 1 x +1: n-1 + A 1 x +1: n-1 ² (b) You are given that ( IA ) 50 = 4 . 99675, A 1 50: 1 = 0 . 00558, A 51 = 0 . 24905 and i = 0 . 06. Calculate ( IA ) 51 1...
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