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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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