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CHAPTER 5

# CHAPTER 5 - answer since they are the inverse of each other...

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CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Solutions to Questions and Problems Basic 1. The simple interest per year is: \$5,000 × .08 = \$400 So after 10 years you will have: \$400 × 10 = \$4,000 in interest. The total balance will be \$5,000 + 4,000 = \$9,000 With compound interest we use the future value formula: FV = PV(1 + r ) t FV = \$5,000(1.08) 10 = \$10,794.62 The difference is: \$10,794.62 – 9,000 = \$1,794.62 2. To find the FV of a lump sum, we use: FV = PV(1 + r ) t FV = \$2,250(1.10) 11 = \$ 6,419.51 FV = \$8,752(1.08) 7 = \$ 14,999.39 FV = \$76,355(1.17) 14 = \$687,764.17 FV = \$183,796(1.07) 8 = \$315,795.75 3. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = \$15,451 / (1.07) 6 = \$ 10,295.65 PV = \$51,557 / (1.13) 7 = \$ 21,914.85 PV = \$886,073 / (1.14) 23 = \$ 43,516.90 PV = \$550,164 / (1.09) 18 = \$116,631.32 4. To answer this question, we can use either the FV or the PV formula. Both will give the same
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Unformatted text preview: answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r ) t Solving for r , we get: r = (FV / PV) 1 / t – 1 FV = \$297 = \$240(1 + r ) 2 ; r = (\$297 / \$240) 1/2 – 1 = 11.24% FV = \$1,080 = \$360(1 + r ) 10 ; r = (\$1,080 / \$360) 1/10 – 1 = 11.61% FV = \$185,382 = \$39,000(1 + r ) 15 ; r = (\$185,382 / \$39,000) 1/15 – 1 = 10.95% FV = \$531,618 = \$38,261(1 + r ) 30 ; r = (\$531,618 / \$38,261) 1/30 – 1 = 9.17% 5. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r ) t Solving for t , we get: t = ln(FV / PV) / ln(1 + r ) FV = \$1,284 = \$560(1.09) t ; t = ln(\$1,284/ \$560) / ln 1.09 = 9.63 years FV = \$4,341 = \$810(1.10) t ; t = ln(\$4,341/ \$810) / ln 1.10 = 17.61 years...
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