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chap004solutions

# chap004solutions - Solutions to Chapter 4 The Time Value of...

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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 4-1

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6. Present Value Years Future Value Interest Rate a. \$400 11 \$684 % 00 . 5 1 400 684 ) 11 / 1 ( = - b. \$183 4 \$249 % 00 . 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: FV = PV × (1 + r) t r = 1 PV FV ) t / 1 ( - 7. You should compare the present values of the two annuities. a. 73 . 721 , 7 \$ (1.05) 0.05 1 0.05 1 \$1,000 PV 10 = × - × = 73 . 303 , 8 \$ (1.05) 0.05 1 0.05 1 \$800 PV 15 = × - × = b. 47 . 192 , 4 \$ (1.20) 0.20 1 0.20 1 \$1,000 PV 10 = × - × = 38 . 740 , 3 \$ (1.20) 0.20 1 0.20 1 \$800 PV 15 = × - × = c.When the interest rate is low, as in part (a), the longer (i.e., 15-year) but smaller annuity
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