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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