Tutorial02_-_soln

Tutorial02_-_soln - Problem Set 2 ACTSC 231 Mathematics of...

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Unformatted text preview: Problem Set 2: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. Roy deposits $10 into a fund today and $20 fifteen years later. Interest is credited at a nominal discount rate of d (4) compounded quarterly for the first 10 years, and at a nominal interest rate of 6% compounded semiannually thereafter. The accumulated balance in the fund at the end of 30 years is $100. Calculate d (4) . Q1. The value at the end of 30 years of the $10 deposited now is equal to 10 " 1 1- d (4) 4 # 40 1 + 6% 2 40 = 32 . 620378 1 1- d (4) 4 ! 40 . The value at the end of 30 years of the $20 invested at the end of the fifteenth year is equal to 20 1 + 6% 2 (2)(15) = 48 . 545249 . Thus, we end up with the following equation: 32 . 620378 1 1- d (4) 4 ! 40 + 48 . 545249 = 100 , by which we have 1 1- d (4) 4 ! 40 = 1 . 577381 , whence, d (4) = 4 . 531789%. Q2. Simplify the following expression (in terms of the annual effective interest rate i only)....
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Tutorial02_-_soln - Problem Set 2 ACTSC 231 Mathematics of...

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