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2 Pages

### 331F03A1-S

Course: ACTS 331, Fall 2009
School: W. Alabama
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Word Count: 255

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TO SOLUTIONS ASSIGNMENT #1 A 1. (a) By the EP, b A40 = 230 a40 = 230 1- 40 . We have = ln1.06 and A40 = 0 v t t p40 40 (t) dt = 60 0 e-t dt = 0.2773594. 60 [5 marks] [5 marks] Hence, b = 10, 284.20. (b) The benefit reserve = b A60 - 230 a60 = 1565.07. (c) Given T (40) &gt; 20, 20 L = b v T (40)-20 - 230 aT (40)-20 . Thus, 2 230 V ar(20 L|T (40) &gt; 20) = b + ( 2 A60 - (A60 )2 ) =...

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TO SOLUTIONS ASSIGNMENT #1 A 1. (a) By the EP, b A40 = 230 a40 = 230 1- 40 . We have = ln1.06 and A40 = 0 v t t p40 40 (t) dt = 60 0 e-t dt = 0.2773594. 60 [5 marks] [5 marks] Hence, b = 10, 284.20. (b) The benefit reserve = b A60 - 230 a60 = 1565.07. (c) Given T (40) > 20, 20 L = b v T (40)-20 - 230 aT (40)-20 . Thus, 2 230 V ar(20 L|T (40) > 20) = b + ( 2 A60 - (A60 )2 ) = 12651925.25. [5 marks] 2. (a) By the EP, a50:10 = A50:20 . Thus, = 0.0555. (b) Given T (50) > 15, 15 L 15 L [5 marks] = v T (50)-15 , =v , 5 if T (50) 20, if T (50) > 20. [4 marks] (c) A65:5 . (d) 1 15 E 50 [3 marks] ( a50:10 - A1 ). [3 marks] 50:15 (e) By (a), a50:10 - A1 = A50:20 - A1 . Hence, the formulas in (c) and (d) are 50:15 50:15 equal since A50:20| = A1 + A65:5 15 E 50 . [5 marks] 50:15 [5 marks] (f) By (c), the benefit reserve is A65:5 = 1 - a65:5 = 0.7840. 20 L 3. (a) Given K(65) 20, = aK(65)-19 . [3 marks] [4 marks] (b) E [20 L | K(65) 20] = a85 (c) V ar L [20 | K(65) 20] = 1 d2 ( 2 A85 - (A85 )2 ) . 12 E68 [5 marks] - P (15| a65 ) a68: 12 [4 marks] [4 marks] (d) The prospective formula: 3 V (15| a65 ) = a80 (e) The retrospective formula: 3 V (15| a65 ) = 1 3 E65 P (15| a65 ) a65: 3 . 1 4. 5 V60 = P60 s60: 5 - 5 k60 s60: 5 = 15.227 = P60:15 s60: 5 - 5 k 60 = 0.5053. [5 marks] 5 V60:15 5. (a) 1 V100:3| =1- a101:2| , a100:3| v = e- , a101:2| = 1 + v p101 = 1 + v a100:3| 1 V100:3| l102 = 1.411767, l101 = 1 + v p100 + v 2 2 p100 = 1.9494875, = 0.275827. [5 marks] (b) 1 1 V100: 3 1 = A1 2 - P100: 3 a101: 2 , 101: 1 P100: 3 ...

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W. Alabama - ACTS - 331
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W. Alabama - ACTS - 331
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W. Alabama - ACTS - 331
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W. Alabama - ACTS - 331
W. Alabama - ACTS - 331
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W. Alabama - ACTS - 331
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W. Alabama - ACTS - 331
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