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app_a - APPENDIX A THE TIME VALUE OF MONEY EXERCISES EA1...

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APPENDIX A THE TIME VALUE OF MONEY EXERCISES EA–1 Time Periods (Years) Compound Interest Rates 5 10 15 5% $150 × 1.27628 $150 × 1.62889 $150 × 2.07893 = $191.44 = $244.33 = $311.84 10% $150 × 1.61051 $150 × 2.59374 $150 × 4.17725 = $241.58 = $389.06 = $626.59 15% $150 × 2.01136 $150 × 4.04556 $150 × 8.13706 = $301.70 = $606.83 = $1,220.56 EA–2 Time Periods (Years) Compound Interest Rates 5 10 15 5% $10,000 =$7,835.26 $10,000 =$6,139.15 $10,000 =$4,810.17 1.05^5 1.05^10 1.05^15 10% $10,000 =$6,209.21 $10,000 =$3,855.44 $10,000 =$2,393.92 1.10^5 1.10^10 1.10^15 15% $10,000 =$4,971.76 $10,000 =$2,471.85 $10,000 =$1,228.94 1.15^5 1.15^10 1.15^15 The above problem has also been attempted in an alternate way to demonstrate the use of formulas. 1
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EA–3 Time Periods (Years) Compound Interest Rates 5 10 15 5% $150 × 5.52563 $150 × 12.57789 $150 × 21.57856 = $828.84 = $1,886.68 = $3,236.78 10% $150 × 6.10510 $150 × 15.93743 $150 × 31.77248 = $915.77 = $2,390.61 = $4,765.87 15% $150 × 6.74238 $150 × 20.30372 $150 × 47.58041 = $1,011.36 = $3,045.56 = $7,137.06 EA–4 Time Periods (Years) Compound Interest Rates 5 10 15 5% $150 × 5.80191 $150 × 13.20679 $150 × 22.65749 = $870.29 = $1,981.02 = $3,398.62 10% $150 × 6.71561 $150 × 17.53117 $150 × 34.94973 = $1,007.34 = $2,629.68 = $5,242.46 15% $150 × 7.75374 $150 × 23.34928 $150 × 54.71747 = $1,163.06 = $3,502.39 = $8,207.62 EA–5 Time Periods (Years) Compound Interest Rates 5 10 15 5% $10,000 × 4.32948 $10,000 × 7.72173 $10,000 × 10.37966 = $43,294.80 = $77,217.30 = $103,796.60 10% $10,000 × 3.79079 $10,000 × 6.14457 $10,000 × 7.60608 = $37,907.90 = $61,445.70 = $76,060.80 15% $10,000 × 3.35216 $10,000 × 5.01877 $10,000 × 5.84737 = $33,521.60 = $50,187.70 = $58,473.70 2
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EA–6 Time Periods (Years) Compound Interest Rates 5 10 15 5% $10,000 × 4.54595 $10,000 × 8.10782 $10,000 × 10.89864 = $45,459.50 = $81,078.20 = $108,986.40 10% $10,000 × 4.16987 $10,000 × 6.75902 $10,000 × 8.36669 = $41,698.70 = $67,590.20 = $83,666.90 15% $10,000 × 3.85498 $10,000 × 5.77158 $10,000 × 6.72448 = $38,549.80 = $57,715.80 = $67,244.80 EA–7 a. ($50 × .85734) + ($100 × .68058) + ($80 × .54027) = $42.87 + $68.06 + $43.22 = $154.15 b. ($100 × 3.31213) + ($100 × .54027) = $331.21 + $54.03 = $385.24 c. ($60 × .68058) + ($60 × .63017)+ ($60 × .58349)+ ($60 × .54027) + ($100 × .46319) = $40.83 + $37.81 + $35.01 + $32.42 + $46.32 = $192.39 d. ($90 × .58349) + ($90 × .54027) + ($90 × .50025) = $52.51 + $48.62 + $45.02 = $146.15 EA–8 a. ($50 × .85734) + ($100 × .68058) + ($80 × .58349) = $42.87 + $68.06 + $46.68 = $157.61 b. ($100 × 3.57710) + ($100 × .58349) = $357.71 + $58.35 = $416.06 c. ($60 × .73503) + ($60 × .68058) + ($60 × .63017) + ($60 × .58349) + ($100 × .50025) = $44.10 + $40.83 + $37.81 + $35.01 + $50.03 = $207.78 d. ($90 × .63017) + ($90 × .58349) + ($90 × . 54027) = $56.72 + $52.51 + $48.62 = $157.85 3
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EA–9 a. Dollar amount = $25,000 × Future value factor for i = 10% and n = 4 = $25,000 × 1.46410 (from Table 1) = $36,603 Dollar amount = $36,603 × Future value factor for i = 12% and n = 3 = $36,603 × 1.40493 (from Table 1) = $51,425 Dollar amount = $51,425 × Future value factor for i = 15% and n = 5 = $51,425 × 2.01136 (from Table 1) = $103,434 b. Ben should not accept $36,000 for $25,000 at the end of 4 years. Why not? Because if he invests the initial $25,000 at 10 percent per annum compounded annually, he will have a total of $36,603, $603 more than the amount the person offered him. EA–10 a. Dollar amount = ($40,000 × Present value factor for an ordinary annuity factor for i = 10% and n = 10) + ($500,000 × Present value factor for i = 10% and n = 10) = ($40,000 × 6.14457 from Table 5) + ($500,000 × .38554 from Table 4) = $245,782.80 + $192,770.00 = $438,552.80 b. There are two different ways to calculate the dollar amount. The two ways are shown below. Dollar amount = ($40,000 × Present value factor for an annuity due for i = 10% and n = 10) + ($500,000 × Present value factor for i = 10% and n = 10) = ($40,000 × 6.75902 from Table 6) + ($500,000 × .38554 from Table 4) = $270,360.80 + $192,770.00 = $463,130.80 Dollar amount = $40,000 + ($40,000 × Present value factor for an ordinary annuity factor for i = 10% and n = 9) + ($500,000 × Present value factor for i = 10% and n = 10) = $40,000 + ($40,000 × 5.75902 from Table 5) + ($500,000 × .38554 from Table 4) = $40,000 + $230,360.80 + $192,770.00 = $463,130.80 4
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EA–11 Option 1 Present value = $500,000 × Present value factor for an ordinary annuity for i = 10% and n = 20) = $500,000 × 8.51356 (from Table 5) = $4,256,780 Option 2 Present value = $4,500,000 Option 3 Present value = $1,000,000 + [($2,100,000 × Present value factor for an ordinary annuity for i = 10% and n = 3) × Present value factor for i = 10% and n = 4] = $1,000,000 + [($2,100,000 × 2.48685 from Table 5) × .68301 from Table 4] = $1,000,000 + $3,566,941 = $4,566,941 Option 3 should be chosen because it has the highest present value. In other words, if receiving the equivalent amounts for each of the 3 payment patterns, alternative 3 would yield the largest payout today.
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