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Unformatted text preview: ACTSC 232  Spring 2010  Assignment 3 Due: Monday, July 26 at 11:30 am 1. Suppose that Makeham’s law applies with A = 0 . 001, B = 0 . 0007 and c = 1 . 082. Assume also that the effective rate of interest is 6% per year, and ω = 120. (a) Use Excel (your spreadsheet (or the solutions) from Assignment 2 can be a start) to find the exact values of ¨ a x , ¨ a (4) x , ¨ a (12) x , and ¨ a (52) x for x = 50 and 100. You do not have to submit your spreadsheet electronically. (b) Using the two approximations (UDD and simplified), estimate the values of the quarterly, monthly, and weekly annuities for x = 50 and 100. (c) Compare your estimated values to the actual ones. Comment on the differences. 2. (a) Describe the annuity with the following present value random variable: Y = braceleftbigg v T x ¯ a n T x , T x ≤ n , T x > n (This is called a Family Income Benefit) (b) Show (carefully) that E [ Y ] = ¯ a n ¯ a x : n (c) Explain the answer in (b) by a logical argument....
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 Summer '08
 MATTHEWTILL
 1 %, 15 years, $1000, 0 5%, 0 25%

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