Present Value of an Annuity Determine the present value of $340,000 to be received at the end of each of four years, using an interest rate of 6%, compounded annually, as follows: a. By successive computations, using the present value of $1 table in Exhibit 5. Round to the nearest whole dollar. First year Second Year Third Year Fourth Year Total present value b. By using the present value of an annuity of $1 table in Exhibit 7. Round to the nearest whole dollar c. Why is the present value of the four $340,000 cash receipts less than the $1,360,000 to be received in the future? over the 4 years. The present value is less due to Present Value of $1 at Compound Interest Due In n Perlods 7% 6% 6.5% 5.5% 4.5% 5% Perlods 4.0% 0.93897 0.88166 0.93458 0.94340 0.94787 0.95238 0.95694 0.96154 0.87344 0.89000 0.89845 0.91573 0.90703 0.92456 2 0.81630 0.82785 0.83962 0.85161 0.88900 0.87630 0.86384 0.77732 0.76290 0.79209 0.82270 0.80722 4 0.85480 0,83856 0.71299 0.74726 0.72988 0.76513 0.78353 0.82193 0.80245 0.66634 0.70496 0.68533 0.76790 0.74622 0.72525 0.79031 6 0.62275 0.66506 0.64351 0.73483 0.70319 0.71068 0.68744 7 0.75992 0.58201 0.60423 0.65160 0.62741 8 0.67684 073069 0.54393 0.59190 0.56735 0.64461 0.61763 0.70259 0.67290 0.50835 0.53273 0.58543 0.55839 10 0.67556 0.64393 0.61391 0.50021 0.47509 0.55491 0.52679 11 0.64958 0.61620 0.58468 0.46968 0.44102 0.44401 0.52598 0.49697 0.62460 0.58966 0.55684 12 0.46884 0.41496 0.56427 0.53032 0.49856 13 0.60057 0.44230 0.41727 0.41410 0.38782 0.36245 0.57748 0.55526 0.53997 0.50507 0.47257 0.44793 14 0.48102 0.38883 0.51672 15 0.42458 0.39365 0.36510 0.33873 0.31657 0.49447 0.45811 16 0.53391 0.43630 0.40245 0.38147 0.37136 0.34281 0.47318 17 0.51337 0.35034 0.49363 0.45280 0.41552 0.32189 0.29586 18 0.43330 0.36158 0.33051 0.30224 0.39573 0.27651 19 0.47464 0.34273 0.45639 041464 0.37689 0.31180 0.28380 0.25842 20 0.35894 0.29416 0.32486 0.30793 0.29187 0.27666 0.26648 21 0.43883 0.42196 0.40573 0.39679 0.24151 0.25021 0.23494 0.37970 0.36335 0.34185 0.32557 0.27751 0.26180 0.24698 0.22571 22 23 0.21095 0.19715 0.18425 24 0.39012 0.34770 0.31007 0.22060 0.20714 25 0.37512 0.33273 0.29530 0.26223 0.23300 0.36069 0.24856 26 0.28124 0.21981 0.31840 0.19450 0.17220 0.30469 27 28 0.34682 0.33348 0.32065 0.26785 0.25509 0.24295 0.23560 0.22332 0.21168 0.20737 0.18263 0.17148 0.16101 0.16093 0.29157 0.19563 0.15040 29 0.27902 0.18456 0.14056 30 0.30832 0.26700 0.23138 0.20064 0.17411 0.15119 0.13137 CeTnjagje.c0my gey.. 0.12277 0.14196 0.16425 0.19018 0.18027 0.17087 0.22036 0.25550 0.29646 0.11474 31 0.13329 0.15496 0.20987 0.19987 0.24450 0.28506 32 0.10723 0.12516 0.11752 0.11035 0.14619 0.13791 0.13011 0.27409 0.26355 0.25342 0.23397 33 0.10022 0.16196 0.19035 0.22390 34 0.09366 0.15352 0.18129 0.21425 35 0.06678 0.08054 0.09722 0.11746 0.14205 0.20829 0.17193 40 0.04761 0.05879 0,07265 0.08988 0.11130 0.13796 0.17120 45 0.03395 0.04291 0.05429 0.06877 0.11071 0,08720 0.14071 50 Present Value of $1 at Compound Interest Due in n Periods 14% 13% 12% 8 % 11% 10% 9% Periods a87719 0.88496 090909 089286 090090 0.91743 0.92593 076947 0.78315 0.79719 081162 082645 0.84168 0,85734 067497 0.71178 0.69305 073119 075131 079383 073503 0.77218 0.61332 059208 065873 0.63552 068301 0.70843 4 a51937 0.56743 0.54276 062092 059345 0.68058 064993 5 0.50663 045559 O48032 059627 054703 0.50187 a53464 a56447 063017 0.39964 048166 045235 0.42506 a51316 058349 040388 0.37616 035056 043393 0.46651 0.54027 0.36061 0.33288 030751 039092 042410 0.46043 0.50025 0.32197 026974 0.35218 0.29459 0.38554 0.42241 10 046319 031728 0.28748 0.26070 023662 042888 0.35049 0.38753 11 0.25668 0.23071 020756 031863 028584 0.35553 12 0.39711 025751 0.22917 0.20416 0.18207 0.28966 0.32618 13 0.36770 015971 023199 0.20462 0.18270 0.18068 0.29925 0.26333 0.34046 14 0.20900 0.15989 0.14010 0.27454 0.23939 15 0.31524 018829 0.16312 0.29189 0.25187 021763 0.14150 0.12289 16 0.14564 0.12522 0.10700 17 0.27027 0.23107 0.19784 0.16963 0.13004 009456 18 0.25025 021199 0.17986 0.15282 0.11081 0.16351 0.13768 0.11611 0.09806 0.08295 19 023171 0.19449 0.29459 0.26974 0.35218 0.32197 038554 042241 10 046319 0.28748 0.26070 0.23662 0.31728 0.38753 035049 11 042888 028584 0.23071 0.20756 0.25668 0.35553 031863 0.39711 12 0.22917 0.20416 0.18207 0.28966 0.25751 0.32618 13 0.36770 0.18068 0.23199 0.20462 0.15971 0.34046 0.29925 0.26333 14 0.15989 0.14010 0.20900 0.18270 031524 0.27454 023939 15 0.18829 0.16312 0.14150 0.12289 0.25187 0.21763 16 0.29189 0.16963 0.14564 0.19784 0.12522 010780 17 0.27027 0.23107 0.25025 0.21199 0.15282 0.13004 0.11081 009456 0.17986 18 0.11611 0.09806 0.08295 0.23171 0.19449 016351 013768 19 0.17843 007276 20 0.21455 0.14864 012403 0.10367 0.08678 0.19866 0.06383 21 0.16370 0.13513 011174 0.09256 0.07680 0.18394 22 0.15018 0.12285 0.08264 0.06796 0.05599 0.10067 0.17032 23 0.13778 0.11168 0.07379 0.06014 0.04911 0.09069 0.12640 24 0.15770 0.10153 0.04308 0.08170 0.06588 0.05323 25 0.14602 0.11597 0.04710 0.09230 0.07361 0.05882 0.03779 26 0.13520 0.10639 0.08391 0.06631 0.05252 0.04168 0.03315 27 0.12519 0.02908 0.09761 007628 0.05974 0.04689 0.03689 28 0.11591 008955 006934 006304 0.04187 0.02551 0.05382 0.03264 29 0.10733 0,08215 0.02889 0.03738 004849 002237 30 0.09938 0.07537 0.05731 0.04368 001963 0.03338 0.02557 31 0.09202 0.06915 0.05210 0.02980 003935 0.02262 0.01722 32 0.08520 0,07889 0.06344 004736 0.02661 003545 0.02002 001510 33 0.05820 0.04306 003194 0.02376 0.01772 0.01325 34 0.07305 0.05339 0.03914 002878 0.02121 0.01568 0.01162 35 0.06763 0.04899 0.03558 0.02592 001894 0.01388 0.01019 40 0.04603 0.03184 002209 001538 0.01075 0,00753 0.00529 45 0.03133 0.02069 0.01372 000913 0,00610 0,00409 000275 50 002132 001345 0.00852 0,00542 0,00346 0.00222 0,00143 Present Value of Ordinary Annuity of $1 per Period Periods 4.0% 4.5% 6% 6.5% 5% 5.5% 7% 1 0.96154 0.95694 0.95238 0.94787 0.94340 0.93897 0.93458 1.88609 1.87267 1.80802 2 1.85941 1.84632 183339 182063 3 2.77509 2.74896 2.72325 2.69793 2.67301 2.64848 2.62432 3.62990 4 3.58753 346511 3.54595 3.50515 342580 3.38721 5 445182 438998 4.10020 4.32948 427028 421236 4.15568 6 5.24214 5.15787 5.07569 4.84101 S48452 4.99553 4.91732 4.76654 5.89270 7 6.00205 568297 5.78637 5.58238 5.38929 8 6.73274 6.59589 646321 5.97130 6.33457 620979 6.08875 743533 7.26879 7.10782 6.95220 6.80169 6.65610 651523 10 8.11090 7.91272 72173 753763 7.36009 7.02358 7.18883 11 8.76048 8.52892 8.30641 8.09254 7.68904 7.88687 7.49867 9.38507 12 9.11858 8.38384 8.86325 8.61852 8.15873 7.94269 13 9.98565 9.68285 9.39357 9.11708 885268 8.59974 8.35765 14 10.56312 10.22283 9.89864 9.58965 9.29498 9.01384 8.74547 15 11.11839 10.73955 10.37966 10.03758 9.71225 940267 9.10791 16 11.65230 11.23402 10.83777 10.46216 10.10590 9.76776 9.44665 17 11.70719 1127407 12.16567 10.86461 10.47726 10.11058 9.76322 18 12.65930 12.15999 11.68959 11.24607 10.82760 1043247 10.73471 10.05909 12.08532 19 13.13394 12.59329 11.60765 10.33560 11.15812 20 13.59033 13.00794 1246221 11.95038 11.46992 11.01851 10.59401 21 14.02916 13.40472 12.82115 12.27524 1176408 11.28498 10.83553 22 14.45112 13.78442 14.14777 13.16300 12.58317 12.04158 11.53520 11.06124 14.85684 23 13 48857 12.87504 12.30338 11.77014 11.27219 24 1524696 14.49548 13.79864 13.15170 12.55036 11.99074 11.46933 14.82821 25 1562208 14.09394 1341393 12.78336 12.19788 11.65358 26 15.98277 15.14661 14.37519 13.66250 13.00317 12.39237 11.82578 27 1632959 1545130 1464303 13.89810 13.21053 12.57500 11.98671 1666306 28 14.89813 15.74287 14.12142 1340616 12.74648 12.13711 29 16.98371 14.33310 16.02189 15.14107 13.59072 12.90749 12.27767 30 17.29203 16.28889 15.37245 14.53375 13.76483 13.05868 1240904 13.20063 12.53181 13.92909 1472393 14.90420 15.59281 16.54439 17.58849 12.64656 1333393 14.08404 31 15.80268 16.78889 17.87355 12.75379 32 1345909 14.23023 15.07507 16.00255 17.02286 18.14765 1841120 12.85401 33 13.57661 14.36814 15.23703 16.19290 17.24676 12.94767 34 13.68696 14.49825 15.39055 16.37419 1746101 18.66461 35 13.33171 14.14553 15.04630 16.04612 17.15909 18.40158 19.79277 40 13.60552 14.48023 15A5583 16.54773 1777407 19.15635 20.72004 45 13.80075 14.72452 15.76186 16.93152 19.76201 18.25593 2148218 50 Present Value of Ordinary Annuity of $1 per Period 14% 13% 12% 119% 10% Periods 99% 8% 088496 0.87719 0.89286 0.90090 0.91743 0.90909 092593 1.64666 1.66810 169005 1.71252 1.73554 1.75911 1.78326 7 2.32163 2.36115 240183 2.44371 2.48685 2.53129 2.57710 3 297447 2.91371 3.03735 3.16987 3.10245 3.23972 3.31213 343308 3.51723 3.60478 3.69590 3.79079 3.99271 3.88965 5 3.88867 3.99755 4.23054 4.11141 4.48592 4.35526 4.62288 6 442261 4.28830 456376 4.86842 4.71220 5.03295 7 5.20637 4.63886 4.96764 4.79677 S.14612 5.53482 5.33493 5.74664 5.53705 5.32825 5.13166 494637 5.99525 641766 5.75902 6.24689 5.65022 5.42624 5.21612 6.14457 5.88923 6.71008 10 593770 5.68694 545273 649506 620652 680519 7.13896 11 5.66029 6.81369 6.19437 5.91765 649236 7.16073 12 7,53608 642355 6.12181 5.84236 7.10336 6.74987 748690 13 7.90378 7.36669 6.62817 6.30249 6.00207 6.96187 7.78615 14 822424 7.19087 681086 6.46238 6.14217 7.60608 8.55948 806069 15 697399 782371 737916 660388 6.26506 885137 831256 16 754879 7.11963 6.37286 8.54363 802155 6.72909 17 9.12164 7.70162 724967 6.83991 6.46742 937189 8.75563 820141 18 8.95011 836492 7 83929 736578 693797 655037 19 960360 5.13166 4.94637 5.53705 5,32825 5.75902 6.24689 5.99525 5.42624 521612 5.88923 5,65022 6.14457 6.71006 6.41766 10 649506 5.93770 5.68694 S45273 6.20652 7.13896 6.80519 11 6.81369 6.19437 5.91765 5.66029 7.16073 649236 12 7.53608 6.12181 642355 584236 748690 7.10336 6.74987 13 7.90378 6.00207 7.78615 6,62817 6.30249 8.22424 736669 6.96187 14 646238 6.14217 15 8.55948 8.06069 7.60608 7.19087 6.81086 6.60388 6.26506 16 8.85137 8.31256 7.82371 737916 6.97399 17 9.12164 6.72909 6.37286 8.54363 8.02155 754879 7.11963 6.83991 8.75563 18 9.37189 7.24967 6.46742 8.20141 7.70162 19 9.60360 8.95011 8.36492 736578 6.93797 6.55037 783929 20 9.81815 662313 9.12855 851356 7.96333 746944 7.02475 10.01680 21 864869 9.29224 7.56200 764465 6.68696 8.07507 7.10155 22 10.20074 7.16951 944243 877154 8.17574 6.74294 23 10.37106 9.58021 888322 8.26643 7.71843 7.22966 679206 24 10.52876 9.70661 8.98474 8.34814 7.78432 7.28288 683514 25 10.67478 9.82258 9.07704 842174 7.84314 7.32998 6.87293 100998 26 9.92897 9.16095 848806 7.89566 7.37167 6.90608 27 10.93516 1002658 923722 740856 8.54780 7.94255 6.93515 28 11.05108 10.11613 930657 860162 798442 744120 7A7009 6.96066 29 11.15841 10.19828 936961 8.65011 8.02181 6.98304 30 11.25778 1027365 942691 8.69379 8.05518 749565 7.00266 31 1134980 1034280 947901 8.73315 8.08499 751828 7.01988 32 1143500 10.40624 952638 8.76860 8.11159 7.53830 7.03498 33 1151389 10.46444 956943 8.80054 8.13535 7.55602 7.04823 34 11.58693 1165457 1051784 960857 8.82932 8.15656 7.57170 7.05985 35 1056682 964416 8.85524 8.17550 7.58557 7.07005 40 11.92461 1075736 9.77905 8.95105 824378 763438 7.10504 45 12.10840 18120 9.86281 9.00791 828252 7.66086 7.12322 50 1223348 10.96168 991481 830450 9.04165 7.67524 7.13266