9ans - MATH 471 Actuarial Theory I Homework#9 Fall 2010 Assigned October 27 due November 3 1 Assume mortality follows de Moivres Law with = 110 and

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MATH 471: Actuarial Theory I Homework #9: Fall 2010 Assigned October 27, due November 3 1. Assume mortality follows de Moivre’s Law with ω = 110 and d = 0.05. Calculate: (a) ¨ a 45 . (14.36) (b) ¨ a 45: 15 . (9.73) (c) 15 | ¨ a 45 . (4.63) (d) ¨ a 45: 15 . (15.36) 2. Allen, age 15, has been cursed by the dreaded Hattendorf. Consequently, he now has the following survival probabilities: p 15 = 0.95, p 16 = 0.80, p 17 = 0.50, p 18 = 0. Assuming i = 0.06, calculate: (a) ¨ a 15 . (2.89) (b) a 15 . (1.89) (c) a 15: 2 . (1.57) 3. Consider a special whole life annuity on (x) which pays R at the beginning of the ﬁrst year, 2 R at the beginning of the second year, and 3 R at the beginning of each year thereafter. You are also given: (i) The actuarial present value of this annuity is 3333. (ii) i = 0.05 (iii) p x = 0.98 and p x +1 = 0.97 (iv) ¨ a x +2 = 31.105 Calculate: R . (40) 4. Suppose Z is the present value random variable for a 2-year pure endow- ment of 1 on (x). You are given:

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This note was uploaded on 02/02/2011 for the course MATH 471 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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9ans - MATH 471 Actuarial Theory I Homework#9 Fall 2010 Assigned October 27 due November 3 1 Assume mortality follows de Moivres Law with = 110 and

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