ACTSC 231 Tutorial01_-_soln

ACTSC 231 Tutorial01_-_soln - Solution to Problem Set 1 Q1....

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Solution to Problem Set 1 Q1. A K (0) = 16. So, K = 16 and a ( t ) = A K ( t ) /A K (0) = ( t 3 + 2 t 2 + 4 t ) / 16 + 1. Thus, i 3 = [ A K (3) - A K (2)] /A K (2) = [73 - 40] / 40 = 0 . 825, or i 3 = [ a (3) - a (2)] /a (2) = (4 . 5625 - 2 . 5) / 2 . 5 = 0 . 825. Q2. Let i be the simple interest rate, then we have 1 , 200(1 + iT ) = 1 , 320, so iT = 0 . 1. Thus, A 100 ( T/ 2) = $100(1 + i · T/ 2) = $100(1 . 05) = $105 Q3. Let i be the compound interest rate per year, then 600(1 + i ) 2 - 600 = 264, so i = 0 . 2. Therefore, the amount of interest earned from $2,000 for three years is $2 , 000(1 . 2) 3 - 2 , 000 = $1 , 456. Q4. At t = 10 the accumulated value of Tom’s savings is 900(1 + %2) 2 (1 + %3) 3 (1 + %4) 5 = 1 , 244 . 86. Q5. First note that A K ( n ) = A K ( n - 1)(1 + i n ). Thus, A K (5) = A K (4)(1 + i 5 ) = 1 , 000(1 + 0 . 01 × 5) = 1 , 050; A K (6) = A K (5)(1 + i 6 ) = 1 , 050(1 + 0 . 01 × 6) = 1 , 113; A K (7) = A K (6)(1 + i 7 ) = 1 , 050(1 + 0 . 01 × 6) = 190 . 91 . Or,
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This note was uploaded on 01/21/2011 for the course ACTSC 231 taught by Professor Chisholm during the Fall '09 term at Waterloo.

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