test2_01 - ACT348F - TERM TEST 2 - NOVEMBER 21, 2001 Print...

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ACT348F - TERM TEST 2 - NOVEMBER 21, 2001 Print your name and student number clearly on each page This is a closed book test . Do all work on this question paper, with work for question 1 on this page (use both sides if necessary), work for question 2 on the next page, etc. All calculations should be done to . Answers are expected to have at least 4 digit accuracy. at least 6 digit accuracy 1. A fully discrete 2-year endowment insurance issued at age has a equal % death benefit to Terminal Reserve: . The endowment ±²²² b ³ ~ ±²²² b = Á ³ ~ ±²²² b = benefit paid to survivors at age is 1000. You are given that the annual effective %b´ interest rate is , and . µ ~ À± ¶ ~ À´ Á ¶ ~ À· % %b (a) Show that the annual benefit premium for the policy is 658 . (b) Find and . == (c) Formulate the unconditional 2nd year net cash loss random variable, . * BONUS: Formulate and show that the unconditional expectation . * ,¸* b#*Μ~² Solution: (a) ¨ ± ¹~) h # ¶ b #= O c ~ c b %b ± S º± b #» ~ ±²²²º#¶ b # ¶ » b ±²²²# S ±À¼²¼± ~ ±Á ´½¾À´² S ~ ¾½¿ ±± ± % %b . Or, and ; ¾½¿º± b #» ~ ±´½¾À´ ±²²²º#¶ b # ¶ » b ±²²²# ~ ±´½¾À´ % %b since they are equal 658 is the benefit premium. ± ~ (b) ±
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test2_01 - ACT348F - TERM TEST 2 - NOVEMBER 21, 2001 Print...

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