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ch5hw - FV = \$4 = \$1(1.09)t t = ln 4 ln 1.09 = 16.09 years...

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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 = (\$280,000 / \$50,000) 1/18 – 1 = 10.04% 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(1.09)t t = ln 2 / ln 1.09 = 8.04 years The length of time to quadruple your money is:
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Unformatted text preview: FV = \$4 = \$1(1.09)t t = ln 4 / ln 1.09 = 16.09 years Notice that the length of time to quadruple your money is twice as long as the time needed to double your money (the difference in these answers is due to rounding). This is an important concept of time value of money. 11. To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = \$1,000,000 / (1.09)80 = \$1,013.63 12. To find the FV of a lump sum, we use: FV = PV(1 + r)t FV = \$50(1.045)102 = \$4,454.84 15. 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 = (\$10,311,500 / \$12,377,500)1/4 – 1 = – 4.46% Notice that the interest rate is negative. This occurs when the FV is less than the PV....
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