b. $20,000 received at the beginning of each semiannual period for six years with 16% interest, compounded semiannually. The present value (PV) for this scenario is $ Present Value of an Ordinary Annuity - X Present Value of an Ordinary Annuity Periods 1% 29 39 491 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 2099 Periods 1 0.99010 0.98039 0.97087 0.96154 0.95238 0.94340 0.93458 0.92593 0.917430.909090.900900-892880.884980.877190.889570.86207 0.8547010.847460.840340.83333 2 1.97040 1.94156 1.91347 1.88809 1.85941 1.83339 1.80802 1.78328 1.759111.735541.71252 1.69005 1.668101.648881.625711.605231.58521 1.56584 1.54850 1.52778 2 3 2.94098 2.88388 2.82861 2.77500 2.72325 2.87301 2.62432 2.57710 2.531292.48885|2.443712.40183|2.36115|2.321632.283232.245892.20958|2.17427 2.13992 2.10848 4 3 3.90197 3.80773 3.71710 3.62990 3.54595 3.46511 3.38721 3.31213 3.23972 3.16987|3. 10245|3.03735|2.97447|2.91371 2.85498|2.79818|2.74324269006|2.63850 2.58873 4 5 4.85343 471348 4.57971 4.45182 4.32948 4.21238 4.10020 3.99271 3.88985 3.790793.89590 3.80478 3.517233.433083.35216|3.274293.19935 3.12717 3.057632.99061 5 8 5.79548 5.60143 5.41719 5.24214 5.07560 4.91732 4.76654 4.62288 4.48592/4 35526 4.23054 4.111413.99755|3.88867 3.78448|3.684743.58918|3.49760 3.40978|3.32551 8 7 6.72819 6.47199 6.23028 6.00205 5.78637| 5.58238 5.38929 5.20637 5.03295 4.86842 4.712204563764.42261 4.28830 416042 4.03857 3.92238 3.81153|3.70570 3.60450 7 8 7.85168 7.32548 7.01980 6.73274 6.46321 6.20979 5.97130 5.74684 5.534825.334935. 146124987644.79877|4.638884.48732 4.34350 420716 4.07757 3.95437 3.83716 8 9 8.56602 8.162247.78811 7.43533 7.10782 6.80169 6.51523 6.24680 5.99525 5.75902 5.537055.328255.13168494637 4.77158 4.60654 4.45057|430302 4.16333|4.03097 9 10 9.47130 8.98250 8.53020 8.11090 7.72173 7.38000 7.02358 6.71008 0.417666.144575.889235.850225.426245.216125.01877|4.83323 4.658804 49409 4338934 19247 10 11 10.36763 9.78885 9.25262 8.78048 8.30841 7.88887 7.49887 7.13898 6.805198.49506 8.206525.937705.688945.452735.23371 5.028644 838414.656014.488504 32708 11 12 11.25508 10.57534 9.95400 9.38507 8.86325 8.38384 7.94269 7.53608 7.16073|6.813896.492388.19437|5.91765 5.660295.42062 5.197114.98839 4.79322 4.61050 4.43922 13 12 12.13374 11.34837 10.63498| 9.98585 9.39357 8.85268 8.35765 7.90378 7.4880017.103386.749876.423556.121815.84238 5.58315 5.34233 5.11828 4.90951 4.71471 4.53268) 14 13 13.00370 12.10625 11.2960710.56312 9.89864 9.294988.74547| 8.24424 7.786157.366696.981876.6281716.302498.00207 5.724485.467535.229305.008064 80228|4.61057 15 14 13.88505 12.84926 11.93794 11.11839 10.37966 9.71225 9.10791 8.55948 8.060897.606087.190878.81086 8.46238 6.14217/5.847375.575465.32419 5.09158 4.87588 4.67547 15 16 1471787 13.57771 12.56110 11.65230 10.83777 10.10500 9.44685 8.851378.312587.823717.379168.973998.603888.265065.954235688505.405295.16235 4.937701472958 16 17 15.562251429187|13.1661212.1658711.2740710.47726 9.76322 9.12164 8.54363 3.02155 7.54879|7.119638.72909 8.37286/6.047165.748705.474615.22233498966 4.77463 17 18 16.39827 14.99203/13.7535112.65930 11.68959 10.82760 10.05909 9.37189 8.7566318.20141 7.701627.24967 8.83991 8.46742 6. 12797 5.817855.53385 5.273165.03333 4.81219 18 19 17.22601 15.678461432380 13.1339412.08532 11.1581210.33560 9.60360 8.95011 8.36492 7.839297365786.93797 6.55037 6. 19823 5.877465.584405.316245.070034 84350 20 19 18.04555 16.35143/14.87747 13.59033|12.46221 11.46992 10.59401 9.81815 9.128558.513567.983337.48944 7.024758.62313|6.259335.928845.62777 5.35275 5.10086/4.86958 20 25 22.0231619.52346|17.4131515.6220814.0939412.7833611.65358 10.674780 9.822589.07704 8.421747.843147.32998|6.872936.484158.097095.766235.46691 5. 19515 4.94759 25 30 25.8077122.39648|19.8004417.2920315.37245 13.76483|12.4090411.25778 10.273659.42691 8.693798.055187.49565 7.002666.565986. 177205.829305.516815.234664.97894 30 35 29.40858|24.99862/21.48722 18.6646116.37419|14.4982512.9476711.65457 10.58882|9.644168.85524 8. 175507.58557 7.070056.61661 8.21534 5.858205.53862 5.25122 4.99154 40 35 32.8346927.35548 23.11477|19.79277 17.15909|15.04630 13.3317111.92461 10.757369.779058.95105 8.243787.63438 7.105048.841786.23350 5.871335.548155.25815 4.99860 45 40 36.0945129.490162451871 20.72004 17.77407|15.4558313.60552 12. 10840 10.881209.86281 9.00791 8.282527.660867.123226.654298.242145.877335.55232 5.28108 4.99863 50 45 39. 1961231.42381|25.72976 21.48218 18.25593|15.7618813.80075 12.23348 10.961689.91481 9.04165 3.30450 7.67524 7.132666.88051 8.24626 5.880065.554145.26228|4.99945 50 80 44.95504 34 76089 27.67558|22.62349 18.9292916.16143 14.0391812 37655 11.04799|9.987169.073568.324057.68728 7.140116.685156.249155.881885.555295.26300 4.99991 80 Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 119 13% 1496 15% 16% 17% 18% 19% 20%Periods 129 Print Done Present Value of $1 Present Value of $1 Periods 1981 294 4% 594 6% 7981 8901 998 10% 11% 1290 1391 1594 16% 1791 18% 1994 2091 Periods 1 10.990100.980390.970870.961540.952380.94340 0.934580.925930.917430.909090.90090 0.892880.884980.877190.869570.862070.854700.84748 10.83333 1 10.84034) 2 0.98030 0.9611710.9426010.924580.9070310.890000.87344 0.85734 0.8416810.82845.0.811620.797190.783150.769470.75614 0.743160.73051 0.718180.706160.69444 2 3 0.970590.942320.915140.889000.86384 0.83962 0.81630|0.79383|0.772180.75131 0.73119 0.711780.693050.674970.657520.840660.624370.60863 0.59342|0.57870 3 4 0.96098|0.92385 0.888490.854800.822700.792090.76290 0.735030.708430.68301 0.658730.63552|0.613320.592080.57175 0.552290.533650.515790.498670.48225 4 5 10.951470.905730.86261 0.821930.783530.747260.712990.680580.849930.6209210.593450.567430.542760.51937 0.497180.47611 0.45611 0.437110.419050.40188 5 6 0.942050.887970.837480.79031 0.74622 0.704960.666340.630170.5962710.56447/0.534840.50663/0.480320.455590.43233/0.41044 0.38984 0.37043/0.352140.33490 6 7 0.93272 0.87056 0.813090.75992 0.710680.665060.622750.583490-547030.513160.481660.452350.425060.399840.375940.353830.333200.31393|0.29592 0.27908| 7 8 0.923480.853490.789410.73069 0.676840.627410.582010.54027 0.501870.46651 0.433930.40388|0.376160.350560.32690|0.305030.284780.266040.24867 0.23257| 8 9 0.914340.836760.768420.702590.84481 0.59190|0.543930.50025 0.48043|0.424100.39092 0.360810.33288|0.30751 0.284260.262950.243400 2254810.208970.19381 9 10 0.905290.820350.744090.675560.613910.558390.508350.463190.422410.385540.3521810.32197 0.29459 0.269740.247180.22668|0.20804 0.19106 0.17560 0.16151 10 11 0.89632|0.80426 0.722420.849580.58468 0.526790.475090.4288810.387530.350490.317280.2874810.26070 0.236620-214940.19542 0.17781 0.16192 0.147570.13459| 11 12 0.887450.788490.701380.624600.556840.496970.44401 0.397110.355530-31863|0.28584 0.256680.23071 0.207560.186910.168460.151970.137220.124000.11216 12 13 0.878660.773030.680950.800570.53032 0.46884 0.414960.36770|0.3261810.289660.25751 0.22917 0.204160.18207|0.162530.145230.12989 0.116290.104210.09346 13 14 0.869960.75788 0.681120.577480.50507 0.44230|0.387820.340460.299250.263330.231990-20462|0.18068|0.15971 0.141330.12520 0.11102 0.098550.08757 0.07789 14 15 0.861350.743010.841860.555260.48102 0.417270.362450-315240.27454 0.239390 209000.18270|0.15989 0.140100.12289 0.107930.09489 0.083520.07359 0.08491 15 18 0.85282 0.72845|0.623170.53391 0.45811 0.39365 0.338730.291890.251870.21763|0.188290.16312 0.141500.122890.106860.09304 0.081100.07078 0.081840.05409 16 17 0.84438|0.714160.80502 0.513370.43630 0.371360.316570.27027|0.2310710.19784 0.16963 0.145840.125220.107800.092930.080210.06932 0.05998|0.05196|0.04507|| 17 18 0.836020.700160.587390.493630.41552 0.350340.29586|0.25025 0.211990.17986 0.15282 0.130040.110810.094560.08081 0.069140.059250.050830.04367 0.03756|| 18 19 0.827740.68643|0.570290.474840.395730.33051 0.27651 0.231710.194400.16351 0.13768 0.11611 0.09806|0.082950.070270.059610.05064 0.04308 0.03670|0.03130 19 20 0.819540.67297 0.55368|0.456390.37689 0.311800.258420.21455 0.17843|0.14864 0.124030.10367 0.08678|0.07276 0.081100.051390.04328 0.03651 0.030840.02608|| 20 25 0.779770.609530.477610.375120.29530 0.233000.184250.14802 0.11597 0.092300.07361 0.05882 0.047100.037790.03038 0.02447 0.01974 0.01598 0.01292 0.01048 25 30 0.74192 0.55207 0.411990.308320.23138/0.17411 0.131370.09938|0.075370.057310.04368 0.03338 0.025570.01963|0.01510 0.01165 0.00900 0.00697 0.00541 0.00421 30 35 0.70591 0.50003|0.35538|0.253420.18129 0.13011 0.09368 0.08763|0.048990.035580.025920.01894 0.01388 0.010190.007510.00556 0.00411 0.003050.00227 0.00169 35 40 10.671650.452890.30656|0.208290.14205 0.09722 0.066780.048030.031840.022090.01538|0.010750.007530.005290.003730.002840.001870.001330.000950.00068 40 45 0.639050.410200.284440.171200.111300.072650.04781 0.031330.020690.013720.009130.006100.00409 0.002750.001860.001260.00085 0.000580.000400.00027 45 50 10.608040.37153 0.22811 0.14071 0.087200.05429 0.03395 0.02132 0.013450.00852 0.005420.003480.00222 0.001430.00092 0.000600.00039 0.00025 0.0001710.00011 50 80 0.550450.30478 0.189730.095060.05354 0.030310.017280.009880.00568|0.00328 0.00191 0.00111 0.000650.000390.000230.000140.00008 0.00005 0.00003 0.00002 80 Periods 1% 2941 3% 49% 5% 6941 7% 9% 109 11% 12% 13% 149 15% 16% 17% 18% 19% 20%Periods Print Done Presen Value of an Annuity Due - X DOO Present Value of an Annuity Due Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% Periods 1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.99010 1.98039 1.97087 1.96154 1.95238 1.94340 1.93458 1.92593 1.91743 1.90909 1.90090 1.892881.884961.877191.889571.86207 1.85470|1.84748 1.840341.83333 2 3 2.97040 2.94156 2.91347 2.88809 2.85941 2.83339 2.80802 2.78326 2.75911 2.73554 2.712522.69005|2.688102.648882.825712.805232.585212.585642.548502.52778 3 4 3.94099 3.88388 3.82881 3.77509 3.72325 3.67301 3.82432 3.57710 3.53129 3.48885 3.443713.40183|3.36115|3.32163|3.283233.24589|3.20958|3.17427 3.13992|3.10648 4 5 4.90197 4.80773 4.71710 4.82990 4.54595 4.46511 4.38721 4.31213| 4.23972 4.18987| 4.10245|4.03735 3.97447 3.91371 3.85498|3.79818|3.74324 3.69008 3.638593.58873 5 6 5.85343 5.71348 5.57971 5.45182 5.32948 5.21238 5.100204.99271 4.88985 4.79079 4.69590|4.60478 4.517234.43308 4 35216 4.27429 4. 199354.12717|405783|3.99061 7 6.79548 6.80143 6.41719 6.24214 6.07589 5.91732 5.78854 5.62288 5.48592 5.35528 5.23054 5.111414.99755 4.88887 4.78448 4.884744.58918|4.49780 4.40978 4.32551 7 8 7.72819 7.471997.23028 7.00205 6.78637 6.58238 6.38929 1.20637 6.03295 5.88842 5.7122015.583765.422815.288305.180425.03857 4.92238 4.811534.70570 4.60459 8 9 8.85168 8.32548 8.01989 7.73274 7.46321 7.20979 6.97130 6.74684 6.53482 6.33493 6.146125.967645.798775.838865.48732 5.343595.207165.07757 4.95437 4.83718 9 10 9.58802 9.16224 8.78611 8.43533 8.10782 7.801697.51523 7.24689 6.99525 6.75902 6.537056.32825|6.131685.948375.771585.606545.45057 5.303025.183335.03097 10 11 10.47130 9.98259 9.53020 9.11090 8.72173 8.360098.02358 7.71008 7.41768 7.14457 6.889238.85022 8.42624 8.2161218.018775.833235.658805.494095.338935.19247 11 12 11.36763|10.78885 10.25262 9.76048 9.30641 8.88887 8.49887 8.13896 7.80519 7.49506 7.206526.937706.888948.452736.233716.028645.836415.658015.488505.32708 12 13 12.2550811.57534 10.95400 10.38507 9.88325 9.38384 8.94269 8.53608 8.16073 7.81389 7.492387.194376.91765 8.680298.420626.19711 5.988395.793225.610505.43922 13 14 13.13374 12.3483711.6349610.9858510.39357 9.85288 9.35765 8.90378 8.48890 8.10338 7.749877.42355 7.121818.84236 6.58315|6.342336.11828|5.909515.714715.53268 15 14 14.00370 13.10625 12.2980711.56312 10.89864 10.29498 9.745471 9.24424 8.78815 8.36889 7.981877.628177.302497.00207|6.724488.467536.229306.008065.80228|5.61057 15 18 14.8850513.8492812.93794 12.1183911.3796610.7122510.10791 9.55948 9.06089 8.80808 8.19087 7.81086/7.46238 7.142178.847378.575468.32419|6.091585.875885.67547 16 17 15.71787|14.57771 13.56110 12.85230 11.83777 11.10590 10.44665 9.85137) 9.31256 8.82371 8.379167.973997.60388 7.265068.954238.68850 6.405296.162355.937705.72958 18 17 16.5622515.29187|14.18812 13.16567 12.2740711.4772810.78322 10.12164 9.54363 9.02155 8.54879 8.11983 7.72909 7.37288 7.047166.748706.474818.222335.989685.77463 18 19 17.3982715.99203 14.7535113.65930 12.6895911.82760 11.05909 10.37189 9.75583 9.20141 8.70162 8.24967 7.83991 7.467427. 127976.817856.53385|6.273168.033335.81219 19 20 18.2260116.6784615.3238014.13394 13.08532 12.15812 11.33560 10.60360 9.95011 9.38492 8.839298.36578|7.93797 7.55037 7.198236.87746 8.584496.316246.070035.84350 25 22.2433919.9139317.9355416.24696 14.7986413.5503812.4693311.52876 10.70681 9.98474 9.348148.784328.28288 7.83514 7.43377|7.072636.748496.450956.182235.93710 25 30 28.0657922.84438|20.18845 17.9837116.1410714.59072 13.27787 12.1584111.1982810.38961 9.650119.021818.470097.98304 7.550887.165556.82039 6.509838.22924 5.97472 30 35 29.70267 25.49859|22.1318419.4112017.19290 15.36814 13.85401 12.5869311.51784 10.60857 9.829329.156568.571708.05985 7.809107.209796.854096.53557|6.248955.98984 35 40 33.1830327.9025923.8082220.5844818.0170415.94907 14.2849312.87858 11.72552 10.758969.935679.233038.626843.099757.638057.230868.88946 6.548825.257205.99592 40 45 38.45545 30.07998|25.25427 21.5488418.6627716.38318|14.55791 13.0770711.86051 10.84909 9.99878|9.278428.658788.12047 7.85244 7.240896.876476.551746.260685.99838 50 45 39.58808|32.05208|26.5016622.34147|19.16872 16.70757 14.7888013.2121611.94823 10.9063010.036249301048.67302 8.131237.85959 7.24588 6.879676.553896.262115.99934 50 60 45.40459 35.45610128.5058323.5284319.87575 17.1311115.02192 13.36888 12.0423110.98387 10.071659.322948.686838.13972 7.884927.24902 6.881806.555246.262975.99989 60 Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 1991 20%Periods Print Done