Present Value of an Annuity Determine the present value of $110,000 to be received at the end of each of four years, using an interest rate of 5%, 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 $110,000 cash receipts less than the $440,000 to be received in the future? The present value is less due to over the 4 years. Present Value of $1 at Compound Interest Due in n Periods Exhibit 5 Periods 4.0% 4.5% 5% 5.5% 6% 6.5% 7% 1 0.96154 0.95694 0.95238 0.94787 0.94340 0.93897 0.93458 2 0.92456 0.91573 0.90703 0.89845 0.89000 0.88166 0.87344 3 0.88900 0.87630 0.86384 0.85161 0.83962 0.82785 0.81630 4 0.85480 0.83856 0.82270 0.80722 0.79209 0.77732 0.76290 5 0.82193 0.80245 0.78353 0.76513 0.74726 0.72988 0.71299 6ABRO 2315 62222 22222 22222 2333 0.79031 0.76790 0.74622 0.72525 0.70496 0.68533 0.66634 7 0.75992 0.73483 0.71068 0.68744 0.66506 0.64351 0.62275 8 0.73069 0.70319 0.67684 0.65160 0.62741 0.60423 0.58201 9 0.70259 0.67290 0.64461 0.61763 0.59190 0.56735 0.54393 10 0.67556 0.64393 0.61391 0.58543 0.55839 0.53273 0.50835 11 0.64958 0.61620 0.58468 0.55491 0.52679 0.50021 0.47509 0.62460 0.58966 0.55684 0.52598 0.49697 0.46968 0.44401 0.60057 0.56427 0.53032 0.49856 0.46884 0.44102 0.41496 14 0.57748 0.53997 0.50507 0.47257 0.44230 0.41410 0.38782 0.55526 0.51672 0.48102 0.44793 0.41727 0.38883 0.36245 16 0.53391 0.49447 0.45811 0.42458 0.39365 0.36510 0.33873 17 0.51337 0.47318 0.43630 0.40245 0.37136 0.34281 0.31657 18 0.49363 0.45280 0.41552 0.38147 0.35034 0.32189 0.29586 19 0.47464 0.43330 0.39573 0.36158 0.33051 0.30224 0.27651 20 0.45639 0.41464 0.37689 0.34273 0.31180 0.28380 0.25842 21 0.43883 0.39679 0.35894 0.32486 0.29416 0.26648 0.24151 0.42196 0.37970 0.34185 0.30793 0.27751 0.25021 0.22571 23 0.40573 0.36335 0.32557 0.29187 0.26180 0.23494 0.21095 24 0.39012 0.34770 0.31007 0.27666 0.24698 0.22060 0.19715 25 0.37512 0.33273 0.29530 0.26223 0.23300 0.20714 0.18425 26 0.36069 0.31840 0.28124 0.24856 0.21981 0.19450 0.17220 27 0.34682 0.30469 0.26785 0.23560 0.20737 0.18263 0.16093 28 0.33348 0.29157 0.25509 0.22332 0.19563 0.17148 0.15040 29 0.32065 0.27902 0.24295 0.21168 0.18456 0.16101 0.14056 30 0.30832 0.26700 0.23138 0.20064 0.17411 0.15119 0.13137 31 0.29646 0.25550 0.22036 0.19018 0.16425 0.14196 0.12277 0.28506 0.24450 0.20987 0.18027 0.15496 0.13329 0.11474 0.27409 0.23397 0.19987 0.17087 0.14619 0.12516 0.10723 34 0.26355 0.22390 0.19035 0.16196 0.13791 0.11752 0.10022 35 0.25342 0.21425 0.18129 0.15352 0.13011 0.11035 0.09366 40 0.20829 0.17193 0.14205 0.11746 0.09722 0.08054 0.06678 45 0.17120 0.13796 0.11130 0.08988 0.07265 0.05879 0.04761 50 0.14071 0.11071 0.08720 0.06877 0.05429 0.04291 0.03395 Present Value of $1 at Compound Interest Due in n Periods Exhibit 5 Periods 8% 9% 10% 11% 12% 13% 14% 1 0.92593 0.91743 0.90909 0.90090 0.89286 0.88496 0.87719 2 0.85734 0.84168 0.82645 0.81162 0.79719 0.78315 0.76947 3 0.79383 0.77218 0.75131 0.73119 0.71178 0.69305 0.67497 4 0.73503 0.70843 0.68301 0.65873 0.63552 0.61332 0.59208 5 0.68058 0.64993 0.62092 0.59345 0.56743 0.54276 0.51937 6 0.63017 0.59627 0.56447 0.53464 0.50663 0.48032 0.45559 7 0.58349 0.54703 0.51316 0.48166 0.45235 0.42506 0.39964 8 0.54027 0.50187 0.46651 0.43393 0.40388 0.37616 0.35056 9 0.50025 0.46043 0.42410 0.39092 0.36061 0.33288 0.30751 10 0.46319 0.42241 0.38554 0.35218 0.32197 0.29459 0.26974 12315 0.42888 0.38753 0.35049 0.31728 0.28748 0.26070 0.23662 0.39711 0.35553 0.31863 0.28584 0.25668 0.23071 0.20756 0.36770 0.32618 0.28966 0.25751 0.22917 0.20416 0.18207 14 0.34046 0.29925 0.26333 0.23199 0.20462 0.18068 0.15971 0.31524 0.27454 0.23939 0.20900 0.18270 0.15989 0.14010 67602 16 0.29189 0.25187 0.21763 0.18829 0.16312 0.14150 0.12289 17 0.27027 0.23107 0.19784 0.16963 0.14564 0.12522 0.10780 18 0.25025 0.21199 0.17986 0.15282 0.13004 0.11081 0.09456 19 0.23171 0.19449 0.16351 0.13768 0.11611 0.09806 0.08295 20 0.21455 0.17843 0.14864 0.12403 0.10367 0.08678 0.07276 22222 22223 21 0.19866 0.16370 0.13513 0.11174 0.09256 0.07680 0.06383 0.18394 0.15018 0.12285 0.10067 0.08264 0.06796 0.05599 23 0.17032 0.13778 0.11168 0.09069 0.07379 0.06014 0.04911 24 0.15770 0.12640 0.10153 0.08170 0.06588 0.05323 0.04308 25 0.14602 0.11597 0.09230 0.07361 0.05882 0.04710 0.03779 26 0.13520 0.10639 0.08391 0.06631 0.05252 0.04168 0.03315 27 0.12519 0.09761 0.07628 0.05974 0.04689 0.03689 0.02908 28 0.11591 0.08955 0.06934 0.05382 0.04187 0.03264 0.02551 29 0.10733 0.08215 0.06304 0.04849 0.03738 0.02889 0.02237 30 0.09938 0.07537 0.05731 0.04368 0.03338 0.02557 0.01963 mmmmm 31 0.09202 0.06915 0.05210 0.03935 0.02980 0.02262 0.01722 32 0.08520 0.06344 0.04736 0.03545 0.02661 0.02002 0.01510 33 0.07889 0.05820 0.04306 0.03194 0.02376 0.01772 0.01325 34 0.07305 0.05339 0.03914 0.02878 0.02121 0.01568 0.01162 35 0.06763 0.04899 0.03558 0.02592 0.01894 0.01388 0.01019 40 0.04603 0.03184 0.02209 0.01538 0.01075 0.00753 0.00529 45 0.03133 0.02069 0.01372 0.00913 0.00610 0.00409 0.00275 50 0.02132 0.01345 0.00852 0.00542 0.00346 0.00222 0.00143 Present Value of Ordinary Annuity of $1 per Period Exhibit 7 Periods 4.0% 4.5% 5% 5.5% 6% 6.5% 7% 1 0.96154 0.95694 0.95238 0.94787 0.94340 0.93897 0.93458 2 1.88609 1.87267 1.85941 1.84632 1.83339 1.82063 1.80802 3 2.77509 2.74896 2.72325 2.69793 2.67301 2.64848 2.62432 4 3.62990 3.58753 3.54595 3.50515 3.46511 3.42580 3.38721 5 4.45182 4.38998 4.32948 4.27028 4.21236 4.15568 4.10020 10 16849 5.24214 5.15787 5.07569 4.99553 4.91732 4.84101 4.76654 6.00205 5.89270 5.78637 5.68297 5.58238 5.48452 5.38929 6.73274 6.59589 6.46321 6.33457 6.20979 6.08875 5.97130 7.43533 7.26879 7.10782 6.95220 6.80169 6.65610 6.51523 8.11090 7.91272 7.72173 7.53763 7.36009 7.18883 7.02358 12345 628920 11 8.76048 8.52892 8.30641 8.09254 7.88687 7.68904 7.49867 9.38507 9.11858 8.86325 8.61852 8.38384 8.15873 7.94269 9.98565 9.68285 9.39357 9.11708 8.85268 8.59974 8.35765 10.56312 10.22283 9.89864 9.58965 9.29498 9.01384 8.74547 11.11839 10.73955 10.37966 10.03758 9.71225 9.40267 9.10791 16 11.65230 11.23402 10.83777 10.46216 10.10590 9.76776 9.44665 17 12.16567 11.70719 11.27407 10.86461 10.47726 10.11058 9.76322 18 12.65930 12.15999 11.68959 11.24607 10.82760 10.43247 10.05909 19 13.13394 12.59329 12.08532 11.60765 11.15812 10.73471 10.33560 13.59033 13.00794 12.46221 11.95038 11.46992 11.01851 10.59401 22222 21 14.02916 13.40472 12.82115 12.27524 11.76408 11.28498 10.83553 14.45112 13.78442 13.16300 12.58317 12.04158 11.53520 11.06124 23 14.85684 14.14777 13.48857 12.87504 12.30338 11.77014 11.27219 24 15.24696 14.49548 13.79864 13.15170 12.55036 11.99074 11.46933 25 15.62208 14.82821 14.09394 13.41393 12.78336 12.19788 11.65358 22222 2333 26 15.98277 15.14661 14.37519 13.66250 13.00317 12.39237 11.82578 27 16.32959 15.45130 14.64303 13.89810 13.21053 12.57500 11.98671 28 16.66306 15.74287 14.89813 14.12142 13.40616 12.74648 12.13711 29 16.98371 16.02189 15.14107 14.33310 13.59072 12.90749 12.27767 30 17.29203 16.28889 15.37245 14.53375 13.76483 13.05868 12.40904 31 17.58849 16.54439 15.59281 14.72393 13.92909 13.20063 12.53181 17.87355 16.78889 15.80268 14.90420 14.08404 13.33393 12.64656 18.14765 17.02286 16.00255 15.07507 14.23023 13.45909 12.75379 34 18.41120 17.24676 16.19290 15.23703 14.36814 13.57661 12.85401 35 18.66461 17.46101 16.37419 15.39055 14.49825 13.68696 12.94767 40 19.79277 18.40158 17.15909 16.04612 15.04630 14.14553 13.33171 45 20.72004 19.15635 17.77407 16.54773 15.45583 14.48023 13.60552 50 21.48218 19.76201 18.25593 16.93152 15.76186 14.72452 13.80075 Present Value of Ordinary Annuity of $1 per Period Exhibit 7 Periods 8% 9% 10% 11% 12% 13% 14% 1 0.92593 0.91743 0.90909 0.90090 0.89286 0.88496 0.87719 2 1.78326 1.75911 1.73554 1.71252 1.69005 1.66810 1.64666 3 2.57710 2.53129 2.48685 2.44371 2.40183 2.36115 2.32163 4 3.31213 3.23972 3.16987 3.10245 3.03735 2.97447 2.91371 3.99271 3.88965 3.79079 3.69590 3.60478 3.51723 3.43308 10 67849 4.62288 4.48592 4.35526 4.23054 4.11141 3.99755 3.88867 5.20637 5.03295 4.86842 4.71220 4.56376 4.42261 4.28830 5.74664 5.53482 5.33493 5.14612 4.96764 4.79677 4.63886 6.24689 5.99525 5.75902 5.53705 5.32825 5.13166 4.94637 6.71008 6.41766 6.14457 5.88923 5.65022 5.42624 5.21612 12315 7.13896 6.80519 6.49506 6.20652 5.93770 5.68694 5.45273 7.53608 7.16073 6.81369 6.49236 6.19437 5.91765 5.66029 7.90378 7.48690 7.10336 6.74987 6.42355 6.12181 5.84236 14 8.22424 7.78615 7.36669 6.96187 6.62817 6.30249 6.00207 8.55948 8.06069 7.60608 7.19087 6.81086 6.46238 6.14217 61898 8.85137 8.31256 7.82371 7.37916 6.97399 6.60388 6.26506 17 9.12164 8.54363 8.02155 7.54879 7.11963 6.72909 6.37286 9.37189 8.75563 8.20141 7.70162 7.24967 6.83991 6.46742 9.60360 8.95011 8.36492 7.83929 7.36578 6.93797 6.55037 20 9.81815 9.12855 8.51356 7.96333 7.46944 7.02475 6.62313 21 10.01680 9.29224 8.64869 8.07507 7.56200 7.10155 6.68696 2222 22 10.20074 9.44243 8.77154 8.17574 7.64465 7.16951 6.74294 23 10.37106 9.58021 8.88322 8.26643 7.71843 7.22966 6.79206 24 10.52876 9.70661 8.98474 8.34814 7.78432 7.28288 6.83514 25 10.67478 9.82258 9.07704 8.42174 7.84314 7.32998 6.87293 22228 26 10.80998 9.92897 9.16095 8.48806 7.89566 7.37167 6.90608 27 10.93516 10.02658 9.23722 8.54780 7.94255 7.40856 6.93515 11.05108 10.11613 9.30657 8.60162 7.98442 7.44120 6.96066 29 11.15841 10.19828 9.36961 8.65011 8.02181 7.47009 6.98304 30 11.25778 10.27365 9.42691 8.69379 8.05518 7.49565 7.00266 31 11.34980 10.34280 9.47901 8.73315 8.08499 7.51828 7.01988 32 11.43500 10.40624 9.52638 8.76860 8.11159 7.53830 7.03498 33 11.51389 10.46444 9.56943 8.80054 8.13535 7.55602 7.04823 34 11.58693 10.51784 9.60857 8.82932 8.15656 7.57170 7.05985 35 11.65457 10.56682 9.64416 8.85524 8.17550 7.58557 7.07005 40 11.92461 10.75736 9.77905 8.95105 8.24378 7.63438 7.10504 45 12.10840 10.88120 9.86281 9.00791 8.28252 7.66086 7.12322 50 12.23348 10.96168 9.91481 9.04165 8.30450 7.67524 7.13266