T2-331F09

# T2-331F09 - 4 Write the retrospective formula for the...

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Tutorial 2 – ACTSC 331, FALL 2009 October 7, Wednesday, 3:30-4:20, MC 4021 Problem 1 Consider a 20-Payment years, 30-year endowment insurance on (40). In this insurance, a death beneﬁt of 1500 is payable at the time of death if death occurs during the 30-year period. A maturity value of 1000 will be paid if (40) is still alive at the end of the 30-year term. Premiums are charged continuously at an annual rate of c as long as (40) survives during the 20-year period. Assume that the force of mortality is a constant of 0.01 and the force of interest is δ = 0 . 03. 1. Calculate c by the equivalence principle. 2. Write the prospective loss function 25 L for this insurance, given T (40) > 25. 3. Write the prospective formula for the beneﬁt reserve at the end of the 25th policy year.
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Unformatted text preview: 4. Write the retrospective formula for the beneﬁt reserve at the end of the 25th policy year. 5. Prove that the two formulas in (c) and (d) are equal. 6. Calculate the beneﬁt reserve at the end of the 25th policy year. 7. Calculate the beneﬁt reserve at the end of the 10th policy year. Problem 2 You are given i = 0 . 05 and the following life table x l x 95 1000 96 920 97 550 98 120 99 50 100 Calculate 1 V 1 97: 3 , i.e. the beneﬁt reserve at the end of the ﬁrst policy year of a fully discrete 3-year term insurance issued to (97). Problem 3 You are given: 5 ¯ k x = 0 . 261747; ¯ P ( ¯ A x ) = 0 . 031797; ¯ P ( ¯ A x : 15 ) = 0 . 039312; 5 ¯ V ( ¯ A x : 15 ) = 0 . 336861 . Calculate 5 ¯ V ( ¯ A x ). 1...
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