Case A Case B Case C Number of Annual Rate Years Involved 8% 9% 10% Discounts per Year Annually Annually Semiannually (a) (b) Case A periods Case B Case C periods periods (2) In Table 4 (present value of an annuity of 1): Case A Case B Case C Number of Number of Annual Rate Years Involved Payments Involved 9% 10% 6% Frequency of Payments Annually Annually Semiannually 14 (a) Case A periods Case B periods Case C periods D) Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% 196154 95238 94340 93458 92593 91743 90909 90090 89286 86957 192456 90703 89000 87344 85734 84168 .82645 81162 79719 75614 88900 186384 83962 81630 79383 77218 75132 73119 71178 65752 185480 82270 79209 176290 73503 170843 68301 65873 63552 57175 182193 78353 74726 171299 68058 64993 .62092 59345 56743 49718 179031.74622 70496 .66634 .63017 59627 56447 53464 50663 43233 175992 71068 66506 62275 58349 54703 51316 48166 45235 37594 173069 67684 62741 58201 54027 50187 46651 43393 .40388 32690 170259 64461 59190 54393 50025 46043 42410 39092 36061 28426 67556 61391 55839 50835 46319 .42241 38554 35218 32197 24719 64958 58468 52679 47509 42888 38753 35049 31728 28748 21494 62460 55684 49697 44401 39711 35554 31863 28584 25668 .18691 .60057 53032 .46884 41496 36770 32618 28966 25751 22917 16253 57748 50507 44230 38782 34046 29925 2633 23199 20462 14133 5526 48102 41727 36245 31524 27454 23939 20900 18270 11289 53391 45811 39365 33873 29189 25187 21763 18829 16312 10687 51337 43630 37136 31657 27027 23107 19785 16963 14564 09293 149363 41552 35034 29586 25025 21199 17986 15282 13004 08081 .47464 39573 33051 27615 23171 19449 16351 13768 11611 07027 19 - 1, - , n, 19 |-- , , , ,, , TABLE 4 Present Value of an Annuity of 1 m) Payments 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% 96154 95238 94340 934589259391743 90909 9009089286 86957 1.88609 1.85941 1.83339 1.80802 1.78326 1.75911 1.73554 1.71252 1.69005 1.62571 2.77509 2.72325 2.67301 2.62432 2.57710 2.53130 2.48685 2.44371 2.40183 2.28323 3.62990 3.54595 3.46511 3.38721 3.31213 3.23972 3.16986 3.10245 3.03735 2.85498 4.45182 4.32948 4.21236 4.10020 3.99271 3.88965 3.79079 3.69590 3.60478 3.35216 5.24214 5.075694.91732 4.76654 4.62288 4.48592 4.35526 4.23054 4.11141 3.78448 6.00205 5.78637 5.58238 5.38929 5.20637 5.03295 4.86842 4.71220 4.56376 4.16042 6.73274 6.46321 6.20979 5.97130 5.74664 5.53482 5.33493 5.14612 4.96764 4.48732 7.43533 7.10782 6.80169 6.51523 6.24689 5.99525 5.759025.53705 5.32825 4.77158 8.11090 7.721737.36009 7.02358 6.71008 6.41766 6.14457 5.88923 5.650225.01877 8.76048 8.30641 7.88687 7.49867 7.13896 6.80519 6.49506 6.20652 5.93770 5.23371 9.38507 8.86325 3.38384 7.94269 7.53608 7.16073 6.81369 6.49236 6.19437 5.42062 9.98565 9.39357 8.852688.35765 7.90378 7.48690 7.10336 6.74987 6.42355 5.58315 10.56312 9.89864 9.294988.74547 8.24424 7.78615 7.36669 6.981876.62817 5.72448 11.11839 10.37966 9.71225 9.10791 8.55948 8.060697.60608 7.19087 6.81086 5.84737 11.65230 10.83777 10.105909.44665 8.85137 8.31256 7.82371 7.37916 6.97399 5.95424 12.16567 11.27407 10.47726 9.76322 9.12164 8.54363 3.02155 7.54879 7.11963 6.04716 12.65930 11.68959 10.82760 10.059099.37189 8.75563 8.20141 7.701627.24967 6.12797 13.13394 12.08532 11.15812 10.33560 9.60360 8.95012 8.36492 7.839297.36578 6.19823 13.59033 12.46221 11.46992 10.59401 9.81815 9.12855 3.51356 7.96333 7.46944 6.25933