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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
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
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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