Tutorial01_-_soln

Tutorial01_-_soln - Solution to Problem Set 1 Q1. AK (0) =...

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Solution to Problem Set 1 Q1. A K (0) = 16. So, a ( t ) = A K ( t ) /A K (0) = ( t 3 +2 t 2 +4 t ) / 16+1, and 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. At t = 10 the accumulated value of Tom’s savings is 900(1 + %2) 2 (1 + %3) 3 (1 + %4) 5 = 1 , 244 . 86. Q4. 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 , 113(1 + 0 . 01 × 7) = 1 , 190 . 91 . Or, A K (7) = A K (4)(1 + i 5 )(1 + i 6 )(1 + i 7 ) = 1 , 000(1 + 0 . 05)(1 + 0 . 06)(1 + 0 . 07) = 1 , 190 . 91. Q5. The fact that $500 will accumulate to $566 in five years implies that 500(1+ i ) 5 = 566. Thus, v 5 = (1 +
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This note was uploaded on 07/13/2011 for the course ACTSC 231 taught by Professor Chisholm during the Winter '09 term at Waterloo.

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Tutorial01_-_soln - Solution to Problem Set 1 Q1. AK (0) =...

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