T3-331F09

# T3-331F09 - 5 V and 15 V 2 For a fully discrete h-Payment...

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Tutorial 3 – ACTSC 331, FALL 2009 October 14, Wednesday, 3:30-4:20, MC 4021 1. Consider a fully discrete 10-Payment year, whole life insurance on (50). For the ﬁrst 5 years, beneﬁt premiums are 1 . 5 π per year and a death beneﬁt of 2 will be paid at the end of the year of death. For the next 5 years, beneﬁt premiums are π per year and a death beneﬁt of 1 will be paid at the end of the year of death. After year 10, the death beneﬁt remains 1. Let k V denote the beneﬁt reserve at the end of year k . (a) Derive the formula for π in terms of actuarial functions. (b) Write prospective formulas for 5 V and 15 V . (c) Write retrospective formulas for
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Unformatted text preview: 5 V and 15 V . 2. For a fully discrete h-Payment year, whole life insurance on ( x ). Let k V denote the beneﬁt reserve 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 . Derive formulas for (a) π ; and (b) k V when k = 0 , 1 , ..., h-1 . 3. 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 . 1...
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