test1_01 - ACT348F - TERM TEST 1 - OCTOBER 17, 2001 Print...

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ACT348F - TERM TEST 1 - OCTOBER 17, 2001 Print your name and student number clearly on each page 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 at least 6 digit accuracy . Answers are expected to have at least 4 digit accuracy. THIS IS A CLOSED BOOK TEST - NO BOOKS OR NOTES ARE ALLOWED. A calculator may be used 1. (a) Express in each of the following forms: ! %¢ O =²( ³ c c (i) prospective, (ii) retrospective, (iii) premium difference, (iv) paid-up insurance (v) annuity-only, (vi) insurance only, (vii) premium only (b) Formulate the prospective and retrospective form of the reserve ! %¢ O = . Starting with one of these formulations, show that if , !± then ! %¢ O 7c 7 7 =~ %¢ O c %¢! O c %¢! O c .
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2.(a) With and assuming DeMoivre's Law with ( ) ± ~ À² ~ ²³³ ´ ~ !% c%c! c% find . =µ( ¶ c c (b) With (force of interest) and assuming for all (constant force of ±² ~À² µ&¶~À³· & mortality at all ages), find .
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test1_01 - ACT348F - TERM TEST 1 - OCTOBER 17, 2001 Print...

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