Math 472 HW 2 Solutions - annual benet premiums are level...

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MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Homework #2: Spring 2011 Assigned January 26, due February 2 1. Re-do Problem 3(b) in the “Chapter 8: Lecture Examples” handout, using a retrospective approach to calculate 2 ¯ V . (27.76) 2. For a special fully continuous life insurance on (40): (i) b t = 0 for 0 t < 15; b t = 1000 e 0 . 04 t for t 15. (ii) π t = π for 0 t < 15; π t = 0 for t 15. (iii) Mortality follows de Moivre’s Law with a limiting age of 90. (iv) δ = 0.06 (a) Calculate π , using the equivalence principle. (43.23) (b) Calculate 20 ¯ V , the benefit reserve at the end of the twentieth year. (1673.56) 3. For a fully discrete 10-payment whole life insurance of 100,000 on (x): (i) i = 0.05 and q x +9 = 0.011 (ii) The level benefit premium is 2078. (iii) The terminal benefit reserve for the ninth year is 32,535. Calculate the initial benefit reserve for year 11. (35,635.64) ————THERE ARE MORE PROBLEMS ON THE BACK ———— 1
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4. For a fully discrete whole life insurance of 1000 on (45), you are given that
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Unformatted text preview: annual benet premiums are level and: k 1000 k V 45 q 45+ k 22 235 0.015 23 255 0.020 24 272 0.025 Calculate the 25th year terminal benet reserve. (286.04) 5. For a fully discrete whole life insurance with non-level benets on (70): (i) The annual level benet premium for this insurance is equal to P 50 . (ii) q 70+ k = q 50+ k + 0.01 for k = 0, 1, . .., 19 (iii) q 60 = 0.01368 (iv) k V = k V 50 for k = 0, 1, . .., 19 (v) 11 V 50 = 0.16637 Calculate the net amount at risk for year 11. (0.4816) 6. For a special fully discrete 3-year endowment insurance on (65): (i) The death benet is 5000 plus the benet reserve at the end of the year of death. (ii) The pure endowment benet is 5000. (iii) The annual level benet premium is . (iv) p 65+ h = 0.97 for h = 0, 1, 2. (v) i = 0.06 Calculate: 1 V . (1570.55) 2...
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Math 472 HW 2 Solutions - annual benet premiums are level...

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