Solutions to Lab Problems for Chapter 05

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Unformatted text preview: Solutions to Lab Problems for Chapter 5 7. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Medium Solution: A. FV = PV(1+k)n 17,000 = 10,000(1+ k)8 8ln(1+k) = ln(1.7), therefore k = 6.86% Or using a financial calculator (TI BAII Plus), N = 8, PV = – 10,000, PMT = 0, FV = 17,000, CPT I/Y = 6.86% 8. Section: 5.3 Compound Interest Learning Objective: 5.3 Level of difficulty: Medium Solution: C. FV = PV(1+k)n Assume that the initial investment is \$1. 3 = 1(1.09) n ln(3) = (n)ln(1.09) n = 12.7 years Or using a financial calculator (TI BAII Plus), I/Y = 9, PV = – 1, PMT = 0, FV = 3, CPT N = 12.7 26. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Easy Find the present value of the four ­year annuity at year 3: Now, find the present value of this amount today: 27. Section: 5.4 Annuities and Perpetuities Learning outcome: 5.4 Level of difficulty: Medium To be indifferent between the two options means that the present value of the annuity must equal \$40 million (the immediate payout). . Solving this using a financial calculator is the easiest way. N = 10, PMT =  ­ 5, PV = 40, CPT I/Y. We find an interest rate of 4.28%. If the interest rate is greater than 4.28%, I prefer the immediate payout of \$40 million. The present value of the 10 ­year annuity is less than \$40 million. If the interest rate is less than 4.28%, I prefer the annuity because the present value will be greater than \$40 million. 51. Section: 5.6 Loan or Mortgage Arrangements Learning Objective: 5.6 Level of Difficulty: Difficult Part 1: determine the principal outstanding after the 60th payment (i.e., How much will the next mortgage be for?) Step 1: determine effective monthly rate: Step 2: determine the monthly payments: Step 3: determine Present Value of remaining (300 – 60) payments of \$1,919.4194 Part 2: determine new payments Step 1: determine new effective monthly rate Step 2: determine the new monthly payment ⎡ 1 ⎢1 − (1 + 0.00655820)300 − 60 \$269, 510.0994 = PMT × ⎢ 0.00655820 ⎢ ⎢ ⎣ PMT = \$2, 232.507688 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ Franklin’s new payment is \$2,232.51, an increase of \$313.09. ...
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