# ps3sol[1] - 1/111 – 1 = 8.41 To find the FV of the first...

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Problem Set #3 – Solutions 1. The simple interest per year is: \$5,000 × .06 = \$300 So after 10 years you will have: \$300 × 10 = \$3,000 in interest. The total balance will be \$5,000 + 3,000 = \$8,000 With compound interest we use the future value formula: FV = PV(1 + r ) t FV = \$5,000(1.06) 10 = \$8,954.24 The difference is: \$8,954.24 – 8,000 = \$954.24 9. 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 ) t = ln (\$170,000 / \$40,000) / ln 1.062 = 24.05 years 13. To answer this question, we can use either the FV or the PV formula. 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 = (\$1,170,000 / \$150)

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Unformatted text preview: 1/111 – 1 = 8.41% To find the FV of the first prize, we use: FV = PV(1 + r ) t FV = \$1,170,000(1.0841) 34 = \$18,212,056.26 14. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = \$485,000 / (1.2590) 67 = \$0.10 19. We need to find the FV of a lump sum. However, the money will only be invested for six years, so the number of periods is six. FV = PV(1 + r ) t FV = \$25,000(1.079) 6 = \$35,451.97 20. To answer this question, 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 ) t = ln(\$100,000 / \$10,000) / ln(1.11) = 22.06 So, the money must be invested for 22.06 years. However, you will not receive the money for another two years. From now, you’ll wait: 2 years + 22.06 years = 24.06 years...
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