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RelativeResourceManager9 - π 2 upon survival to age...

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MATH 471: Actuarial Theory I Homework #9: Fall 2009 Assigned October 28, due November 4 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. Consider a special whole life annuity-due 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 APV 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) 3. Suppose mortality follows the Illustrative Life Table and i = 0.06. Calculate the net single premium, π , for a 35-year temporary life annuity-due issued to (30) with an annual payment of 1000 that pays an additional benefit of
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Unformatted text preview: π 2 upon survival to age 65. (15,641.99) 4. Suppose, at time 0, that: (i) 30 lives age 65 purchase a whole life annuity-immediate with an annual payment of 1 and (ii) 20 lives age 75 also purchase a whole life annuity-immediate with an annual payment of 1. Assume all lives are independent, mortality follows the Illustrative Life Table, and i = 0.06. Let S be the total present value of the payments for all 50 annuities. (a) Calculate E ( S ). (391.25) (b) Calculate var ( S ). (629.58) 5. Using the Illustrative Life Table, the assumption of UDD in each year of age, and i = 0.06, calculate: (a) ¨ a (2) 40 . (14.56) (b) 30 | ¨ a (2) 40 . (1.03)...
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