PQ-2-331-2011-F

# PQ-2-331-2011-F - n years if x is alive then(a Show that...

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Practice Questions 2 – ACTSC 331, FALL 2011 1. Consider a fully discrete 4-year term insurance on (80). You are give i = 0 . 03, the following table h π h b h +1 q 80+ h 0 π 3 0.15 1 π 5 0.20 2 π 7 0.25 3 π 9 0.30 (a) Calculate the annual premium of π . (b) Calculate the policy value at the end of the third policy year. 2. For a fully discrete whole life insurance on (40), you are given i = 0 . 05 , b 10 = 2000, and 9 V + π 9 = 10 V = 400. Calculate q 49 . 3. For a fully discrete h -Payment year, whole life insurance on ( x ). Let k V denote the policy value at the end of year k . The death benefit in the j -th policy year is equal to j V for j = 1 , 2 , ..., h and 1 for j = h + 1 , h + 2 , ... . The benefit premium in the j -th policy year is π , j = 1 , 2 , ..., h . (a) Show that π = A x + h ¨ s h . (b) Show that k V = ¨ s k A x + h ¨ s h for k = 0 , 1 , ..., h - 1 . 4. For a fully discrete n -year endowment insurance on ( x ), let h V denote the benefit reserve at the end of year h . The death benefit in year h is equal to h V + 60(1+ i ) q x + h - 1 for h = 1 , ..., n . The benefit premium in year h is π for h = 1 , ..., n . A maturity value of 90¨ s n will be paid to ( x ) at the end of

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Unformatted text preview: n years if ( x ) is alive then. (a) Show that the premium π = 150. (b) Show that k V = 90¨ s k for k = 1 ,...,n . 5. For a fully discrete 3-year term insurance on (60), the death beneﬁt in year h is h 2 for h = 1 , 2 , 3, and the premium in year h is π for h = 1 , 2 , 3. You are given that i = 0 . 05, q 60 = 0 . 15, q 61 = 0 . 20, q 62 = 0 . 30, and . 75 q 61 . 25 = 0 . 18 . (a) Calculate the premium π . (b) Calculate the policy value at the end of the second year. (c) Calculate the policy value at the end of the ﬁrst year. 1 (d) Calculate the policy value at the end of the 15th month. 6. For a fully discrete whole life insurance on (60), you are given (a) 10 V = 0 . 23114 (b) 11 V = 0 . 25540 (c) π 10 = 0 . 03300 Calculate 10 7 12 V under the assumptions of a uniform distribution of deaths between integral ages and i = 0 and q 70 = 0. 2...
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