PQ-2-Answer-331-2011-F

PQ-2-Answer-331-2011-F - (b) Multiplying by v h on both...

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Answers to Practice Questions 2 – ACTSC 331, Fall 2011 1. (a) By the equivalence principle, π ¨ a 80: 4 = 3 h =0 b h +1 v h +1 h p 80 q 80+ h . Hence, π = 1 . 2106 . (b) By the recursion relationship, we have 3 V = b 4 v q 83 - π = 1 . 4108 . 2. By the recursion equation, we have 10 V = ( 9 V + π 9 ) (1 + i ) - ( b 10 - 10 V ) q 49 and hence q 49 = 0 . 0125 . 3. (a) By the recursion equation, we have π = v j +1 V - j V for j = 0 , 1 ,...,h - 1 . (1) On multiplication by v j on both sides of the equation (1) and then summing the equation over j = 0 , 1 ,...,h - 1, we get π = v h A x + h ¨ a h = A x + h ¨ s h (b) On multiplication by v j on both sides of the equation (1) and then summing the equation over j = 0 , 1 ,...,k - 1, we obtain k V = π ¨ a k v k = A x + h ¨ s h ¨ s k 4. (a) By the recursion equation, we obtain π = 60 + v h +1 V - h V, for h = 0 , 1 ,...,n - 1 . Multiplying by v h on both sides of the equation and then taking summation with respect to h from 0 to n - 1 yield π = 150.
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Unformatted text preview: (b) Multiplying by v h on both sides of the equation and then taking summation with respect to h from 0 to k-1 yield k V = 90 s k for k = 1 ,...,n . 5. (a) By the equivalence principle, we have a 60: 3 = vq 60 + 4 v 2 p 60 q 61 + 9 v 3 2 p 60 q 62 . Thus = 0 . 96676. (b) By the recursion equation, we have 2 V = 9 vq 62- = 1 . 60. (c) By the recursion equation, we have 0 = vq 60- + vp 60 1 V . Hence, 1 V = 1 . 02. (d) The policy value is 1 . 25 V = . 75 q 61 . 25 4 v . 75 + . 75 p 61 . 25 v . 75 2 V = 1 . 96. 6. Under the given conditions, we have 10 7 12 V 60 = 1-7 12 10 V 60 + 10 + 7 12 11 V 60 = 0 . 25904 . 1...
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