Tutorial05_-_soln

Tutorial05_-_soln - Problem Set 5: ACTSC 231 Mathematics of...

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Unformatted text preview: Problem Set 5: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. Find the present value of a ten-year annuity which pays $500 at the end of each month for the first 4 years and $2,000 at the end of each quarter for the last 6 years. Annual effective interest rate is 7%. Q1. The present value of this annuity is (500 12) a (12) 4 e 7% + (2 , 000 4) a (4) 6 e 7% (1 . 07)- 4 = 20 , 967 . 341 + 29 , 84 . 837 = $50 , 811 . 18 . Thus, the present value is $50,811.18. You may want to use formulae to find the values of a (12) 4 e 7% and a (4) 6 e 7% as follows, but it is more time-saving if you use calculator find them directly. (500 12) a (12) 4 e 7% + (200 4) a (4) 6 e 7% (1 . 07)- 4 = 6 , 000 1- (1 . 07)- 4 i (12) + 8 , 000 1- (1 . 07)- 6 i (4) (1 . 07)- 4 = = 20 , 967 . 341 + 29 , 84 . 837 = $50 , 811 . 18 , where i (12) = 12 (1 + i ) 1 / 12- 1 = 6 . 78497% and i (4) = 4 (1 + i ) 1 / 4- 1 = 6 . 82341%. Q2. A family puts $2,000 every two years in a fund that earns a 5% annual rate. On the day of the 10th payment, they transfer the accumulated amount into a fund that pays X at the beginning of each month for four years, and that earns 4% annual effective rate. Determine X . Q2. On the day of the last payment, the accumulated amount in the fund is 2 , 000 s 10 e j = 35 , 259 . 47 , where j = (1 . 05) 2- 1 = 0 . 1025. We should set the accumulated value 2 , 000 s 10 e j equal to 12 X a (12) 4 e 4% , i.e., X...
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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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Tutorial05_-_soln - Problem Set 5: ACTSC 231 Mathematics of...

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