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AK/ADMS 3530.03 Finance Midterm Exam Winter 2008 February 17, 2008 Solutions Type A Exam Numerical questions (4 points each) 1. (Q. 2 in B) Janet owes her friend some money. She is given the following alternatives of payment. If the discount rate is 6%, which of the following alternatives of payment is best for her? A) Pay \$9,750 now. B) \$2,000 per year for 5 years, each payable at the end of the year. C) \$1,950 per year for 5 years, each payable at the beginning of the year. D) \$2,000 at the end of year 1, \$5,000 at the end of year 2, \$3,000 at the end of year 3 and \$1,200 at the end of year 4. Answer B PV (A) = \$9,750; PV (B) is the PV of a 5-year annuity = \$8,424.73; PV (C) is the PV of a 5-year annuity due = \$8,706.96; and PV (D) = \$9,806.14. She should choose (B) since alternative (B) has the lowest PV today. 2. (Q. 1 in B) Jeff Hanson wants to have \$1,000,000 at the end of 15 years. He has \$10,000 to invest now, and his father will give him \$100,000 in 5 years from today. In addition, he is planning to invest an equal amount of X at the end of every year for the next 15 years to reach his goal. If the rate of interest is 8%, how much is X ? A) \$25,657 B) \$27,710 C) \$30,249 D) \$31,978 Answer B First, his goal is \$1,000,000 – \$10,000(1.08) 15 – \$100,000(1.08) 10 = \$752,385.81. Then, n = 15, I/Y = 8%, FV = 752,385.81, PV = 0, CPT PMT= \$27,710. 3. (Q. 7 in B) Walter wants to save \$5,000 nominal dollars per year (at the end of each year) for the next 30 years for his retirement. The expected annual nominal rate of interest is 6% for the first ten years, 7% for the next ten years and 8% for the last ten years. The expected annual rate of inflation is 3% for the first ten 1

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years, 2.5% for the next ten years and 2% for the last ten years. At the end of 30 years, how much in real dollars will he have? A) \$239,127 B) \$329,214 C) \$472,038 D) \$501,466 Answer A First, in 30 years he will have in nominal dollars the amount of FVAF (\$5,000, 10 years, 6%) × (1.07) 10 × (1.08) 10 + FVAF (\$5,000, 10 years, 7%) × (1.08) 10 + FVAF (\$5,000, 10 years, 8%) = \$501,466. Then, in terms of real dollars, (\$501,466) / [(1.03) 10 (1.025) 10 (1.02) 10 ], which is equal to \$239,127 in real dollars. Please note : there are several ways to solve this question. 4. (Q. 8 in B) If \$165,000 is borrowed for a home mortgage, to be repaid monthly at a 6.25% APR semiannually compounded over 20 years. Assuming that monthly payments begin in one month from now, how much interest will you pay (in dollars) over the life of the mortgage loan? A) \$122,614 B) \$159,106 C) \$165,000 D) \$287,614 Answer A The semiannual rate = 0.0625 / 2 = 0.03125. EAR = (1.03125) 2 – 1 = 0.063477. The monthly rate i m = (1+ 0.063477) 1/12 -1 = 0.005142. The number of months in the mortgage: n = 20yrs × 12mths/yr = 240 months.
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