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Tutorial05_-_soln

# Tutorial05_-_soln - Problem Set 5-solution ACTSC 231...

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Problem Set 5-solution: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. The present value of this perpetuity-due is 1 , 000 v n ¨ a = 6 , 561; where v = 9 / 10 i.e. d = 1 / 10. We know that ¨ a = 1 /d = 10. Thus, n = ln(6 , 561 / 10 , 000) ln 0 . 9 = 4 . Q2. We first need to find the interest rate i on the loan, which solves 50 , 000 = 7 , 426 . 39a 8 i. Using the financial calculator, we find i = 4%. (a) We can then compute OLB 3 = 7 , 426 . 39a 5 4% = 33 , 060 . 98. (b) The interest paid in the fourth payment is i · OLB 3 = 1 , 322 . 44. Q3. (a) The loan amount L is 10,000 and the payment P is such that L = P a 5 6% . Solving this equation, we obtain P = 2 , 373 . 96. Consequently, OLB 2 = P · a 3 6% = 6 , 345 . 63. (b) The additional payment at time 5 is the accumulated value of the missed payment at time 3, and hence is given by P (1 . 06) 2 = 2 , 667 . 39. Q4. This annuity is the sum of the annuity with payment \$1,000 from t = 0 to t = 3 and the annuity with the first payment \$1,000 at t = 4 and increasing by 5% per year up to t = 9. The accumulated value at t = 4 is 1 , 000¨ s 4 8% + 1 , 000 1 + (1 . 05) v + [(1 . 05) v ] 2 + · · · + [(1 . 05) v ] 5 = 1 , 000¨ s 4 8% + 1 , 000¨ a 6 i * = 4 , 866 . 601 + 5 , 598 . 447 = 10 , 465 . 048 ,

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Tutorial05_-_soln - Problem Set 5-solution ACTSC 231...

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