Solutions_ch5_ch6 - Chapter5 Solutions to Questions and...

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Chapter5: 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
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CHAPTER 5 B-2 4. 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 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 FV = $364,518 = $18,400(1.17) t ; t = ln($364,518 / $18,400) / ln 1.17 = 19.02 years FV = $173,439 = $21,500(1.15) t ; t = ln($173,439 / $21,500) / ln 1.15 = 14.94 years 6. 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 r , we get: r = (FV / PV) 1 / t – 1 r = ($290,000 / $55,000) 1/18 – 1 = .0968 or 9.68%
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CHAPTER 5 B-3 7. To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. 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 ) The length of time to double your money is: FV = $2 = $1(1.07) t t = ln 2 / ln 1.07 = 10.24 years The length of time to quadruple your money is: FV = $4 = $1(1.07) t t = ln 4 / ln 1.07 = 20.49 years Notice that the length of time to quadruple your money is twice as long as the time needed to double
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This note was uploaded on 04/25/2010 for the course IE 654 taught by Professor Smith during the Spring '10 term at 카이스트, 한국과학기술원.

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Solutions_ch5_ch6 - Chapter5 Solutions to Questions and...

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