BMM_TVM_Solutions

BMM_TVM_Solutions - Solutions to Chapter 4 The Time Value...

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Solutions to Chapter 4 The Time Value of Money 1. a. $100/(1.08) 10 = $46.32 b. $100/(1.08) 20 = $21.45 c. $100/(1.04) 10 = $67.56 d. $100/(1.04) 20 = $45.64 2. a. $100 × (1.08) 10 = $215.89 b. $100 × (1.08) 20 = $466.10 c. $100 × (1.04) 10 = $148.02 d. $100 × (1.04) 20 = $219.11 3. $100 × (1.04) 113 = $8,409.45 $100 × (1.08) 113 = $598,252.29 4. With simple interest, you earn 4% of $1,000 or $40 each year. There is no interest on interest. After 10 years, you earn total interest of $400, and your account accumulates to $1,400. With compound interest, your account grows to: $1,000 × (1.04) 10 = $1480.24 Therefore $80.24 is interest on interest. 5. PV = $700/(1.05) 5 = $548.47 6. Present Value Years Future Value Interest Rate* a. $400 11 $684 % 0 . 5 1 400 684 ) 11 / 1 ( = b. $183 4 $249 % 0 . 8 1 183 249 ) 4 / 1 ( = c. $300 7 $300 % 0 1 300 300 ) 7 / 1 ( = To find the interest rate, we rearrange the basic future value equation as follows: 4-1
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FV = PV × (1 + r) t r = 1 PV FV ) t / 1 ( 7. You should compare the present values of the two annuities. Discount Rate 10-year, $1,000 annuity 15-year, $800 annuity a. 5% $7,721.73 $8,303.73 b. 20% $4,192.47 $3,740.38 c. When the interest rate is low, as in part (a), the longer (i.e., 15-year) but smaller annuity is more valuable because the impact of discounting on the present value of future payments is less significant. 8. $100 × (1 + r) 3 = $115.76 r = 5.0% $200 × (1 + r) 4 = $262.16 r = 7.0% $100 × (1 + r) 5 = $110.41 r = 2.0% 9. PV = ($200/1.06) + ($400/1.06 2 ) + ($300/1.06 3 ) = $188.68 + $356.00 + $251.89 = $796.57 10. In these problems, you can either solve the equation provided directly, or you can use your financial calculator, setting: PV = ( )400, FV = 1000, PMT = 0, i as specified by the problem. Then compute n on the calculator. a. $400 × (1.04) t = $1,000 t = 23.36 periods b. $400 × (1.08) t = $1,000 t = 11.91 periods c. $400 × (1.16) t = $1,000 t = 6.17 periods 11. APR Compounding period Effective annual rate a. 12% 1 month (m = 12/yr) 1.01 12 1 = 0.1268 = 12.68% b. 8% 3 months (m = 4/yr) 1.02 4 1 = 0.0824 = 8.24% c. 10% 6 months (m = 2/yr) 1.05 2 1 = 0.1025 = 10.25% 4-2
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12. Effective Rate Compounding period Per period rate APR a. 10.00% 1 month (m = 12/yr) 1.10 (1/12) 1 = 0.0080 0.096 = 9.6% b. 6.09% 6 months (m = 2/yr) 1.0609 (1/2) 1 = 0.0300 0.060 = 6.0% c. 8.24% 3 months (m = 4/yr) 1.0824 (1/4) 1 = 0.0200 0.080 = 8.0% 13. Solve the following for t: 1.08 t = 2 t = 9.01 years On a financial calculator, enter: PV = ( )1, FV = 2, PMT = 0, i = 8 and then compute n. 14.
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This note was uploaded on 11/21/2011 for the course FIN 3134 taught by Professor Ddklock during the Spring '08 term at Virginia Tech.

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BMM_TVM_Solutions - Solutions to Chapter 4 The Time Value...

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