1. VALOR ACTUAL DE UNA ANUALIDAD: (1 - (1 + i)-n) / i
i% N años
1 2 3 4 5 6 7 8 9 10
1 0,99010 1,97040 2,94099 3,90197 4,85343 5,79548 6,72819 7,65168 8,56602 9,47130
1 ¼ 0,98765 1,96312 2,92653 3,87806 4,81784 5,74601 6,66273 7,56812 8,46234 9,34553
1 ½ 0,98522 1,95588 2,91220 3,85438 4,78264 5,69719 6,59821 7,48593 8,36052 9,22218
1 ¾ 0,98280 1,94870 2,89798 3,83094 4,74786 5,64900 6,53464 7,40505 8,26049 9,10122
2 0,98039 1,94156 2,88388 3,80773 4,71346 5,60143 6,47199 7,32548 8,16224 8,98259
2 ¼ 0,97800 1,93447 2,86990 3,78474 4,67945 5,55448 6,41025 7,24718 8,06571 8,86622
2 ½ 0,97561 1,92742 2,85602 3,76197 4,64583 5,50813 6,34939 7,17014 7,97087 8,75206
2 ¾ 0,97324 1,92042 2,84226 3,73943 4,61258 5,46237 6,28941 7,09431 7,87768 8,64008
3 0,97087 1,91347 2,82861 3,71710 4,57971 5,41719 6,23028 7,01969 7,78611 8,53020
3 ¼ 0,96852 1,90656 2,81507 3,69498 4,54720 5,37259 6,17200 6,94625 7,69612 8,42240
3 ½ 0,96618 1,89969 2,80164 3,67308 4,51505 5,32855 6,11454 6,87396 7,60769 8,31661
3 ¾ 0,96386 1,89287 2,78831 3,65138 4,48326 5,28507 6,05790 6,80280 7,52077 8,21279
1 2 3 4 5 6 7 8 9 10
4 0,96154 1,88609 2,77509 3,62990 4,45182 5,24214 6,00205 6,73274 7,43533 8,11090
4 ¼ 0,95923 1,87936 2,76198 3,60861 4,42073 5,19974 5,94699 6,66378 7,35135 8,01089
4 ½ 0,95694 1,87267 2,74896 3,58753 4,38998 5,15787 5,89270 6,59589 7,26879 7,91272
4 ¾ 0,95465 1,86602 2,73606 3,56664 4,35956 5,11653 5,83917 6,52904 7,18762 7,81635
5 0,95238 1,85941 2,72325 3,54595 4,32948 5,07569 5,78637 6,46321 7,10782 7,72173
5 ¼ 0,95012 1,85284 2,71054 3,52545 4,29972 5,03536 5,73431 6,39840 7,02935 7,62884
5 ½ 0,94787 1,84632 2,69793 3,50515 4,27028 4,99553 5,68297 6,33457 6,95220 7,53763
5 ¾ 0,94563 1,83984 2,68542 3,48503 4,24117 4,95619 5,63233 6,27170 6,87632 7,44805
6 0,94340 1,83339 2,67301 3,46511 4,21236 4,91732 5,58238 6,20979 6,80169 7,36009
6 ¼ 0,94118 1,82699 2,66070 3,44536 4,18387 4,87894 5,53312 6,14882 6,72830 7,27369
6 ½ 0,93897 1,82063 2,64848 3,42580 4,15568 4,84101 5,48452 6,08875 6,65610 7,18883
6 ¾ 0,93677 1,81430 2,63635 3,40642 4,12779 4,80355 5,43658 6,02958 6,58509 7,10547
1 2 3 4 5 6 7 8 9 10
7 0,93458 1,80802 2,62432 3,38721 4,10020 4,76654 5,38929 5,97130 6,51523 7,02358
7 ¼ 0,93240 1,80177 2,61238 3,36818 4,07290 4,72997 5,34263 5,91388 6,44651 6,94313
7 ½ 0,93023 1,79557 2,60053 3,34933 4,04588 4,69385 5,29660 5,85730 6,37889 6,86408
7 ¾ 0,92807 1,78940 2,58877 3,33064 4,01916 4,65815 5,25118 5,80156 6,31236 6,78641
8 0,92593 1,78326 2,57710 3,31213 3,99271 4,62288 5,20637 5,74664 6,24689 6,71008
8 ¼ 0,92379 1,77717 2,56552 3,29378 3,96654 4,58803 5,16215 5,69252 6,18246 6,63507
8 ½ 0,92166 1,77111 2,55402 3,27560 3,94064 4,55359 5,11851 5,63918 6,11906 6,56135
8 ¾ 0,91954 1,76509 2,54262 3,25758 3,91501 4,51955 5,07545 5,58662 6,05666 6,48889
9 0,91743 1,75911 2,53129 3,23972 3,88965 4,48592 5,03295 5,53482 5,99525 6,41766
9 ¼ 0,91533 1,75316 2,52006 3,22202 3,86455 4,45268 4,99101 5,48376 5,93479 6,34764
9 ½ 0,91324 1,74725 2,50891 3,20448 3,83971 4,41983 4,94961 5,43344 5,87528 6,27880
9 ¾ 0,91116 1,74138 2,49784 3,18710 3,81512 4,38735 4,90875 5,38383 5,81670 6,21112
10 0,90909 1,73554 2,48685 3,16987 3,79079 4,35526 4,86842 5,33493 5,75902 6,14457
1

2. VALOR ACTUAL DE UNA ANUALIDAD: (1 - (1 + i)-n) / i
i% N años
11 12 13 14 15 16 17 18 19 20
1 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456
1 ¼ 10.2178 11.0793 11.9302 12.7706 13.6005 14.4203 15.2299 16.0295 16.8193 17.5993
1 ½ 10.0711 10.9075 11.7315 12.5434 13.3432 14.1313 14.9076 15.6726 16.4262 17.1686
1 ¾ 9,92749 10.7395 11.5376 12.3220 13.0929 13.8505 14.5951 15.3269 16.0461 16.7529
2 9,78685 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514
2 ¼ 9,64911 10.4148 11.1636 11.8959 12.6122 13.3126 13.9977 14.6677 15.3229 15.9637
2 ½ 9,51421 10.2578 10.9832 11.6909 12.3814 13.0550 13.7122 14.3534 14.9789 15.5892
2 ¾ 9,38207 10.1042 10.8070 11.4910 12.1567 12.8046 13.4351 14.0488 14.6460 15.2273
3 9,25262 9,95400 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775
3 ¼ 9,12581 9,80708 10.4669 11.1060 11.7249 12.3244 12.9049 13.4673 14.0119 14.5393
3 ½ 9,00155 9,66333 10.3027 10.9205 11.5174 12.0941 12.6513 13.1897 13.7098 14.2124
3 ¾ 8,87979 9,52269 10.1424 10.7396 11.3153 11.8702 12.4050 12.9205 13.4173 13.8962
11 12 13 14 15 16 17 18 19 20
4 8,76048 9,38507 9,98565 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903
4 ¼ 8,64354 9,25039 9,83251 10.3909 10.9265 11.4403 11.9332 12.4059 12.8594 13.2944
4 ½ 8,52892 9,11858 9,68285 10.2228 10.7395 11.2340 11.7072 12.1600 12.5933 13.0079
4 ¾ 8,41656 8,98956 9,53657 10.0588 10.5573 11.0332 11.4876 11.9213 12.3354 12.7307
5 8,30641 8,86325 9,39357 9,89864 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622
5 ¼ 8,19842 8,73959 9,25377 9,74230 10.2065 10.6475 11.0665 11.4646 11.8428 12.2022
5 ½ 8,09254 8,61852 9,11708 9,58965 10.0376 10.4622 10.8646 11.2461 11.6077 11.9504
5 ¾ 7,98870 8,49996 8,98341 9,44058 9,87289 10.2817 10.6683 11.0338 11.3795 11.7064
6 7,88687 8,38384 8,85268 9,29498 9,71225 10.1059 10.4773 10.8276 11.1581 11.4699
6 ¼ 7,78700 8,27012 8,72482 9,15277 9,55555 9,93463 10.2914 10.6272 10.9433 11.2407
6 ½ 7,68904 8,15873 8,59974 9,01384 9,40267 9,76776 10.1106 10.4325 10.7347 11.0185
6 ¾ 7,59295 8,04960 8,47738 8,87810 9,25349 9,60515 9,93456 10.2432 10.5322 10.8030
11 12 13 14 15 16 17 18 19 20
7 7,49867 7,94269 8,35765 8,74547 9,10791 9,44665 9,76322 10.0591 10.3356 10.5940
7 ¼ 7,40618 7,83793 8,24049 8,61585 8,96582 9,29214 9,59640 9,88010 10.1446 10.3912
7 ½ 7,31542 7,73528 8,12584 8,48915 8,82712 9,14151 9,43396 9,70601 9,95908 10.1945
7 ¾ 7,22637 7,63468 8,01362 8,36531 8,69170 8,99462 9,27575 9,53666 9,77880 10.0035
8 7,13896 7,53608 7,90378 8,24424 8,55948 8,85137 9,12164 9,37189 9,60360 9,81815
8 ¼ 7,05318 7,43943 7,79624 8,12586 8,43035 8,71164 8,97149 9,21154 9,43330 9,63815
8 ½ 6,96898 7,34469 7,69095 8,01010 8,30424 8,57533 8,82519 9,05548 9,26772 9,46334
8 ¾ 6,88633 7,25180 7,58786 7,89688 8,18104 8,44234 8,68261 8,90355 9,10671 9,29353
9 6,80519 7,16073 7,48690 7,78615 8,06069 8,31256 8,54363 8,75563 8,95011 9,12855
9 ¼ 6,72553 7,07142 7,38803 7,67783 7,94309 8,18590 8,40814 8,61157 8,79778 8,96822
9 ½ 6,64730 6,98384 7,29118 7,57185 7,82818 8,06226 8,27604 8,47127 8,64956 8,81238
9 ¾ 6,57049 6,89794 7,19630 7,46816 7,71586 7,94156 8,14721 8,33459 8,50532 8,66088
10 6,49506 6,81369 7,10336 7,36669 7,60608 7,82371 8,02155 8,20141 8,36492 8,51356
2

3. VALOR ACTUAL DE UNA ANUALIDAD: (1 - (1 + i)-n) / i
i% N años
21 22 23 24 25 26 27 28 29 30
1 18.8570 19.6604 20.4558 21.2434 22.0232 22.7952 23.5596 24.3164 25.0658 25.8077
1 ¼ 18.3697 19.1306 19.8820 20.6242 21.3573 22.0813 22.7963 23.5025 24.2000 24.8889
1 ½ 17.9001 18.6208 19.3309 20.0304 20.7196 21.3986 22.0676 22.7267 23.3761 24.0158
1 ¾ 17.4475 18.1303 18.8012 19.4607 20.1088 20.7457 21.3717 21.9870 22.5916 23.1858
2 17.0112 17.6580 18.2922 18.9139 19.5235 20.1210 20.7069 21.2813 21.8444 22.3965
2 ¼ 16.5904 17.2034 17.8028 18.3890 18.9624 19.5231 20.0715 20.6078 21.1323 21.6453
2 ½ 16.1845 16.7654 17.3321 17.8850 18.4244 18.9506 19.4640 19.9649 20.4535 20.9303
2 ¾ 15.7929 16.3435 16.8793 17.4008 17.9083 18.4023 18.8830 19.3508 19.8062 20.2493
3 15.4150 15.9369 16.4436 16.9355 17.4131 17.8768 18.3270 18.7641 19.1885 19.6004
3 ¼ 15.0502 15.5450 16.0242 16.4883 16.9379 17.3732 17.7949 18.2033 18.5988 18.9819
3 ½ 14.6980 15.1671 15.6204 16.0584 16.4815 16.8904 17.2854 17.6670 18.0358 18.3920
3 ¾ 14.3578 14.8027 15.2315 15.6448 16.0432 16.4272 16.7973 17.1540 17.4978 17.8292
21 22 23 24 25 26 27 28 29 30
4 14.0292 14.4511 14.8568 15.2470 15.6221 15.9828 16.3296 16.6631 16.9837 17.2920
4 ¼ 13.7116 14.1119 14.4958 14.8641 15.2173 15.5562 15.8812 16.1930 16.4921 16.7790
4 ½ 13.4047 13.7844 14.1478 14.4955 14.8282 15.1466 15.4513 15.7429 16.0219 16.2889
4 ¾ 13.1080 13.4683 13.8122 14.1405 14.4540 14.7532 15.0389 15.3116 15.5719 15.8204
5 12.8212 13.1630 13.4886 13.7986 14.0939 14.3752 14.6430 14.8981 15.1411 15.3725
5 ¼ 12.5437 12.8681 13.1763 13.4692 13.7475 14.0118 14.2630 14.5017 14.7285 14.9439
5 ½ 12.2752 12.5832 12.8750 13.1517 13.4139 13.6625 13.8981 14.1214 14.3331 14.5337
5 ¾ 12.0155 12.3078 12.5842 12.8456 13.0927 13.3265 13.5475 13.7565 13.9541 14.1410
6 11.7641 12.0416 12.3034 12.5504 12.7834 13.0032 13.2105 13.4062 13.5907 13.7648
6 ¼ 11.5207 11.7842 12.0322 12.2656 12.4852 12.6920 12.8866 13.0697 13.2421 13.4043
6 ½ 11.2850 11.5352 11.7701 11.9907 12.1979 12.3924 12.5750 12.7465 12.9075 13.0587
6 ¾ 11.0567 11.2943 11.5169 11.7255 11.9208 12.1038 12.2752 12.4358 12.5862 12.7272
21 22 23 24 25 26 27 28 29 30
7 10.8355 11.0612 11.2722 11.4693 11.6536 11.8258 11.9867 12.1371 12.2777 12.4090
7 ¼ 10.6212 10.8356 11.0355 11.2220 11.3958 11.5578 11.7089 11.8498 11.9812 12.1037
7 ½ 10.4135 10.6172 10.8067 10.9830 11.1469 11.2995 11.4414 11.5734 11.6962 11.8104
7 ¾ 10.2121 10.4057 10.5853 10.7520 10.9067 11.0503 11.1836 11.3073 11.4221 11.5286
8 10.0168 10.2007 10.3711 10.5288 10.6748 10.8100 10.9352 11.0511 11.1584 11.2578
8 ¼ 9,82739 10.0022 10.1637 10.3129 10.4507 10.5780 10.6956 10.8043 10.9046 10.9974
8 ½ 9,64363 9,80980 9,96295 10.1041 10.2342 10.3541 10.4646 10.5665 10.6603 10.7468
8 ¾ 9,46531 9,62328 9,76853 9,90210 10.0249 10.1379 10.2417 10.3372 10.4250 10.5058
9 9,29224 9,44243 9,58021 9,70661 9,82258 9,92897 10.0266 10.1161 10.1983 10.2737
9 ¼ 9,12423 9,26703 9,39774 9,51738 9,62689 9,72713 9,81888 9,90287 9,97974 10.0501
9 ½ 8,96108 9,09688 9,22089 9,33415 9,43758 9,53203 9,61830 9,69707 9,76902 9,83472
9 ¾ 8,80262 8,93178 9,04945 9,15668 9,25438 9,34340 9,42451 9,49841 9,56575 9,62711
10 8,64869 8,77154 8,88322 8,98474 9,07704 9,16095 9,23722 9,30657 9,36961 9,42691
3

4. VALOR ACTUAL DE UNA ANUALIDAD: (1 - (1 + i)-n) / i
i% N años
31 32 33 34 35 36 37 38 39 40
1 26.5423 27.2696 27.9897 28.7027 29.4086 30.1075 30.7995 31.4847 32.1630 32.8347
1 ¼ 25.5693 26.2413 26.9050 27.5605 28.2079 28.8473 29.4788 30.1025 30.7185 31.3269
1 ½ 24,6461 25.2671 25.8790 26.4817 27.0756 27.6607 28.2371 28.8051 29.3646 29.9158
1 ¾ 23.7699 24.3439 24.9080 25.4624 26.0073 26.5428 27.0690 27.5863 28.0946 28.5942
2 22.9377 23.4683 23.9886 24.4986 24.9986 25.4888 25.9695 26.4406 26.9026 27.3555
2 ¼ 22.1470 22.6377 23.1175 23.5868 24.0458 24.4947 24.9337 25.3630 25.7829 26.1935
2 ½ 21.3954 21.8492 22.2919 22.7238 23.1452 23.5563 23.9573 24.3486 24.7303 25.1028
2 ¾ 20.6806 21.1003 21.5088 21.9064 22.2933 22.6699 23.0364 23.3931 23.7402 24.0781
3 20.0004 20.3888 20.7658 21.1318 21.4872 21.8323 22.1672 22.4925 22.8082 23.1148
3 ¼ 19.3529 19.7123 20.0603 20.3974 20.7239 21.0401 21.3463 21.6429 21.9302 22.2084
3 ½ 18.7363 19.0689 19.3902 19.7007 20.0007 20.2905 20.5705 20.8411 21.1025 21.3551
3 ¾ 18.1487 18.4565 18.7533 19.0393 19.3150 19.5807 19.8369 20.0837 20.3217 20.5510
31 32 33 34 35 36 37 38 39 40
4 17.5885 17.8736 18.1476 18.4112 18.6646 18.9083 19.1426 19.3679 19.5845 19.7928
4 ¼ 17.0542 17.3182 17.5714 17.8143 18.0473 18.2708 18.4852 18.6908 18.8881 19.0773
4 ½ 16.5444 16.7889 17.0229 17.2468 17.4610 17.6660 17.8622 18.0500 18.2297 18.4016
4 ¾ 16.0577 16.2842 16.5004 16.7068 16.9039 17.0920 17.2716 17.4431 17.6068 17.7630
5 15.5928 15.8027 16.0025 16.1929 16.3742 16.5469 16.7113 16.8679 17.0170 17.1591
5 ¼ 15.1486 15.3431 15.5279 15.7034 15.8703 16.0287 16.1793 16.3224 16.4583 16.5875
5 ½ 14.7239 14.9042 15.0751 15.2370 15.3906 15.5361 15.6740 15.8047 15.9287 16.0461
5 ¾ 14.3178 14.4849 14.6429 14.7923 14.9337 15.0673 15.1937 15.3131 15.4261 15.5330
6 13.9291 14.0840 14.2302 14.3681 14.4982 14.6210 14.7368 14.8460 14.9491 15.0463
6 ¼ 13.5570 13.7007 13.8360 13.9633 14.0831 14.1958 14.3020 14.4018 14.4958 14.5843
6 ½ 13.2006 13.3339 13.4591 13.5766 13.6870 13.7906 13.8879 13.9792 14.0650 14.1455
6 ¾ 12.8592 12.9828 13.0987 13.2072 13.3088 13.4041 13.4933 13.5768 13.6551 13.7284
31 32 33 34 35 36 37 38 39 40
7 12.5318 12.6466 12.7538 12.8540 12.9477 13.0352 13.1170 13.1935 13.2649 13.3317
7 ¼ 12.2179 12.3244 12.4236 12.5162 12.6025 12.6830 12.7581 12.8280 12.8933 12.9541
7 ½ 11.9166 12.0155 12.1074 12.1929 12.2725 12.3465 12.4154 12.4794 12.5390 12.5944
7 ¾ 11.6275 11.7192 11.8044 11.8834 11.9568 12.0249 12.0880 12.1467 12.2011 12.2516
8 11.3498 11.4350 11.5139 11.5869 11.6546 11.7172 11.7752 11.8289 11.8786 11.9246
8 ¼ 11.0830 11.1621 11.2352 11.3028 11.3651 11.4228 11.4760 11.5252 11.5706 11.6125
8 ½ 10.8266 10.9001 10.9678 11.0302 11.0878 11.1408 11.1897 11.2347 11.2763 11.3145
8 ¾ 10.5800 10.6483 10.7111 10.7688 10.8219 10.8707 10.9156 10.9569 10.9948 11.0297
9 10.3428 10.4062 10.4644 10.5178 10.5668 10.6118 10.6530 10.6908 10.7255 10.7574
9 ¼ 10.1145 10.1735 10.2274 10.2768 10.3220 10.3634 10.4013 10.4360 10.4677 10.4968
9 ½ 9,89472 9,94952 9,99956 10.0453 10.0870 10.1251 10.1599 10.1917 10.2207 10.2472
9 ¾ 9,68301 9,73395 9,78037 9,82266 9,86119 9,89630 9,92829 9,95744 9,98400 10.0082
10 9,47901 9,52638 9,56943 9,60857 9,64416 9,67651 9,70592 9,73265 9,75696 9,77905
4

5. VALOR ACTUAL DE UNA ANUALIDAD: (1 - (1 + i)-n) / i
i% N años
41 42 43 44 45 46 47 48 49 50
1 33.4997 34.1581 34.8100 35.4555 36.0945 36.7272 37.3537 37.9740 38.5881 39.1961
1 ¼ 31.9278 32.5213 33.1075 33.6864 34.2582 34.8229 35.3806 35.9315 36.4755 37.0129
1 ½ 30.4590 30.9941 31.5212 32.0406 32.5523 33.0565 33.5532 34.0426 34.5247 34.9997
1 ¾ 29.0852 29.5678 30.0421 30.5082 30.9663 31.4165 31.8589 32.2938 32.7212 33.1412
2 27.7995 28.2348 28.6616 29.0800 29.4902 29.8923 30.2866 30.6731 31.0521 31.4236
2 ¼ 26.5951 26.9879 27.3720 27.7477 28.1151 28.4744 28.8259 29.1695 29.5057 29.8344
2 ½ 25.4661 25.8206 26.1664 26.5038 26.8330 27.1542 27.4675 27.7732 28.0714 28.3623
2 ¾ 24.4069 24.7269 25.0384 25.3415 25.6365 25.9236 26.2030 26.4749 26.7396 26.9972
3 23.4124 23.7014 23.9819 24.2543 24.5187 24.7754 25.0247 25.2667 25.5017 25.7298
3 ¼ 22.4779 22.7389 22.9917 23.2365 23.4736 23.7032 23.9256 24.1411 24.3497 24.5518
3 ½ 21.5991 21.8349 22.0627 22.2828 22.4955 22.7009 22.8994 23.0912 23.2766 23.4556
3 ¾ 20.7720 20.9851 21.1905 21.3884 21.5792 21.7631 21.9403 22.1111 22.2758 22.4345
41 42 43 44 45 46 47 48 49 50
4 19.9931 20.1856 20.3708 20.5488 20.7200 20.8847 21.0429 21.1951 21.3415 21.4822
4 ¼ 19.2588 19.4329 19.5999 19.7601 19.9137 20.0611 20.2025 20.3382 20.4683 20.5931
4 ½ 18.5661 18.7235 18.8742 19.0184 19.1563 19.2884 19.4147 19.5356 19.6513 19.7620
4 ¾ 17.9122 18.0546 18.1905 18.3203 18.4442 18.5625 18.6754 18.7832 18.8861 18.9844
5 17.2944 17.4232 17.5459 17.6628 17.7741 17.8801 17.9810 18.0772 18.1687 18.2559
5 ¼ 16.7102 16.8268 16.9376 17.0428 17.1428 17.2378 17.3281 17.4139 17.4954 17.5728
5 ½ 16.1575 16.2630 16.3630 16.4579 16.5477 16.6329 16.7137 16.7902 16.8628 16.9315
5 ¾ 15.6340 15.7296 15.8199 15.9054 15.9862 16.0626 16.1348 16.2031 16.2678 16.3288
6 15.1380 15.2245 15.3062 15.3832 15.4558 15.5244 15.5890 15.6500 15.7076 15.7619
6 ¼ 14.6676 14.7460 14.8197 14.8892 14.9545 15.0160 15.0739 15.1284 15.1796 15.2279
6 ½ 14.2212 14.2922 14.3588 14.4214 14.4802 14.5354 14.5873 14.6359 14.6816 14.7245
6 ¾ 13.7971 13.8615 13.9218 13.9782 14.0311 14.0807 14.1271 14.1706 14.2113 14.2495
41 42 43 44 45 46 47 48 49 50
7 13.3941 13.4524 13.5070 13.5579 13.6055 13.6500 13.6916 13.7305 13.7668 13.8007
7 ¼ 13.0108 13.0637 13.1130 13.1590 13.2018 13.2418 13.2791 13.3138 13.3462 13.3764
7 ½ 12.6460 12.6939 12.7385 12.7800 12.8186 12.8545 12.8879 12.9190 12.9479 12.9748
7 ¾ 12.2985 12.3420 12.3823 12.4198 12.4546 12.4868 12.5168 12.5446 12.5704 12.5943
8 11.9672 12.0067 12.0432 12.0771 12.1084 12.1374 12.1643 12.1891 12.2122 12.2335
8 ¼ 11.6513 11.6871 11.7202 11.7508 11.7790 11.8051 11.8292 11.8514 11.8720 11.8910
8 ½ 11.3498 11.3823 11.4123 11.4399 11.4653 11.4888 11.5104 11.5303 11.5487 11.5656
8 ¾ 11.0618 11.0913 11.1184 11.1434 11.1663 11.1874 11.2068 11.2247 11.2411 11.2562
9 10.7866 10.8134 10.8380 10.8605 10.8812 10.9002 10.9176 10.9336 10.9482 10.9617
9 ¼ 10.5233 10.5477 10.5700 10.5904 10.6090 10.6261 10.6417 10.6561 10.6692 10.6812
9 ½ 10.2715 10.2936 10.3138 10.3322 10.3490 10.3644 10.3785 10.3913 10.4030 10.4137
9 ¾ 10.0303 10.0503 10.0687 10.0853 10.1005 10.1144 10.1270 10.1385 10.1490 10.1585
10 9,79914 9,81740 9,83400 9,84909 9,86281 9,87528 9,88662 9,89693 9,90630 9,91481
5

6. VALOR ACTUAL DE UNA CANTIDAD: (1 + i)-n
i% N años
1 2 3 4 5 6 7 8 9 10
1 0.990099 0.980296 0.970590 0.960980 0.951466 0.942045 0.932718 0.923483 0.914340 0.905287
1 ¼ 0.987654 0.975461 0.963418 0.951524 0.939777 0.928175 0.916716 0.905398 0.894221 0.883181
1 ½ 0.985222 0.970662 0.956317 0.942184 0.928260 0.914542 0.901027 0.887711 0.874592 0.861667
1 ¾ 0.982801 0.965898 0.949285 0.932959 0.916913 0.901143 0.885644 0.870412 0.855441 0.840729
2 0.980392 0.961169 0.942322 0.923845 0.905731 0.887971 0.870560 0.853490 0.836755 0.820348
2 ¼ 0.977995 0.956474 0.935427 0.914843 0.894712 0.875024 0.855769 0.836938 0.818522 0.800510
2 ½ 0.975610 0.951814 0.928599 0.905951 0.883854 0.862297 0.841265 0.820747 0.800728 0.781198
2 ¾ 0.973236 0.947188 0.921838 0.897166 0.873154 0.849785 0.827041 0.804906 0.783364 0.762398
3 0.970874 0.942596 0.915142 0.888487 0.862609 0.837484 0.813092 0.789409 0.766417 0.744094
3 ¼ 0.968523 0.938037 0.908510 0.879913 0.852216 0.825391 0.799410 0.774247 0.749876 0.726272
3 ½ 0.966184 0.933511 0.901943 0.871442 0.841973 0.813501 0.785991 0.759412 0.733731 0.708919
3 ¾ 0.963855 0.929017 0.895438 0.863073 0.831878 0.801810 0.772829 0.744895 0.717971 0.692020
1 2 3 4 5 6 7 8 9 10
4 0.961538 0.924556 0.888996 0.854804 0.821927 0.790315 0.759918 0.730690 0.702587 0.675564
4 ¼ 0.959233 0.920127 0.882616 0.846634 0.812119 0.779011 0.747253 0.716789 0.687568 0.659537
4 ½ 0.956938 0.915730 0.876297 0.838561 0.802451 0.767896 0.734828 0.703185 0.672904 0.643928
4 ¾ 0.954654 0.911364 0.870037 0.830585 0.792921 0.756965 0.722640 0.689871 0.658588 0.628723
5 0.952381 0.907029 0.863838 0.822702 0.783526 0.746215 0.710681 0.676839 0.644609 0.613913
5 ¼ 0.950119 0.902726 0.857697 0.814914 0.774265 0.735643 0.698949 0.664084 0.630959 0.599486
5 ½ 0.947867 0.898452 0.851614 0.807217 0.765134 0.725246 0.687437 0.651599 0.617629 0.585431
5 ¾ 0.945626 0.894209 0.845588 0.799611 0.756133 0.715019 0.676141 0.639377 0.604612 0.571737
6 0.943396 0.889996 0.839619 0.792094 0.747258 0.704961 0.665057 0.627412 0.591898 0.558395
6 ¼ 0.941176 0.885813 0.833706 0.784665 0.738508 0.695067 0.654180 0.615699 0.579481 0.545394
6 ½ 0.938967 0.881659 0.827849 0.777323 0.729881 0.685334 0.643506 0.604231 0.567353 0.532726
6 ¾ 0.936768 0.877535 0.822046 0.770067 0.721374 0.675760 0.633031 0.593003 0.555506 0.520381
1 2 3 4 5 6 7 8 9 10
7 0.934579 0.873439 0.816298 0.762895 0.712986 0.666342 0.622750 0.582009 0.543934 0.508349
7 ¼ 0.932401 0.869371 0.810603 0.755807 0.704715 0.657077 0.612659 0.571244 0.532628 0.496623
7 ½ 0.930233 0.865333 0.804961 0.748801 0.696559 0.647962 0.602755 0.560702 0.521583 0.485194
7 ¾ 0.928074 0.861322 0.799371 0.741875 0.688515 0.638993 0.593033 0.550379 0.510792 0.474053
8 0.925926 0.857339 0.793832 0.735030 0.680583 0.630170 0.583490 0.540269 0.500249 0.463193
8 ¼ 0.923788 0.853383 0.788345 0.728263 0.672760 0.621488 0.574123 0.530367 0.489947 0.452607
8 ½ 0.921659 0.849455 0.782908 0.721574 0.665045 0.612945 0.564926 0.520669 0.479880 0.442285
8 ¾ 0.919540 0.845554 0.777521 0.714962 0.657436 0.604539 0.555898 0.511171 0.470042 0.432222
9 0.917431 0.841680 0.772183 0.708425 0.649931 0.596267 0.547034 0.501866 0.460428 0.422411
9 ¼ 0.915332 0.837832 0.766895 0.701963 0.642529 0.588127 0.538332 0.492752 0.451032 0.412844
9 ½ 0.913242 0.834011 0.761654 0.695574 0.635228 0.580117 0.529787 0.483824 0.441848 0.403514
9 ¾ 0.911162 0.830216 0.756461 0.689258 0.628026 0.572233 0.521397 0.475077 0.432872 0.394416
10 0.909091 0.826446 0.751315 0.683013 0.620921 0.564474 0.513158 0.466507 0.424098 0.385543
6

7. VALOR ACTUAL DE UNA CANTIDAD: (1 + i)-n
i% N años
11 12 13 14 15 16 17 18 19 20
1 0.896324 0.887449 0.878663 0.869963 0.861349 0.852821 0.844377 0.836017 0.827740 0.819544
1 ¼ 0.872277 0.861509 0.850873 0.840368 0.829993 0.819746 0.809626 0.799631 0.789759 0.780009
1 ½ 0.848933 0.836387 0.824027 0.811849 0.799852 0.788031 0.776385 0.764912 0.753607 0.742470
1 ¾ 0.826269 0.812058 0.798091 0.784365 0.770875 0.757616 0.744586 0.731780 0.719194 0.706825
2 0.804263 0.788493 0.773033 0.757875 0.743015 0.728446 0.714163 0.700159 0.686431 0.672971
2 ¼ 0.782895 0.765667 0.748819 0.732341 0.716226 0.700466 0.685052 0.669978 0.655235 0.640816
2 ½ 0.762145 0.743556 0.725420 0.707727 0.690466 0.673625 0.657195 0.641166 0.625528 0.610271
2 ¾ 0.741993 0.722134 0.702807 0.683997 0.665691 0.647874 0.630535 0.613659 0.597235 0.581251
3 0.722421 0.701380 0.680951 0.661118 0.641862 0.623167 0.605016 0.587395 0.570286 0.553676
3 ¼ 0.703411 0.681270 0.659826 0.639056 0.618941 0.599458 0.580589 0.562314 0.544614 0.527471
3 ½ 0.684946 0.661783 0.639404 0.617782 0.596891 0.576706 0.557204 0.538361 0.520156 0.502566
3 ¾ 0.667008 0.642899 0.619662 0.597264 0.575676 0.554869 0.534813 0.515483 0.496851 0.478892
11 12 13 14 15 16 17 18 19 20
4 0.649581 0.624597 0.600574 0.577475 0.555265 0.533908 0.513373 0.493628 0.474642 0.456387
4 ¼ 0.632650 0.606858 0.582118 0.558387 0.535623 0.513787 0.492841 0.472749 0.453477 0.434989
4 ½ 0.616199 0.589664 0.564272 0.539973 0.516720 0.494469 0.473176 0.452800 0.433302 0.414643
4 ¾ 0.600213 0.572996 0.547013 0.522208 0.498528 0.475922 0.454341 0.433738 0.414070 0.395293
5 0.584679 0.556837 0.530321 0.505068 0.481017 0.458112 0.436297 0.415521 0.395734 0.376889
5 ¼ 0.569583 0.541171 0.514177 0.488529 0.464161 0.441008 0.419010 0.398109 0.378251 0.359383
5 ½ 0.554911 0.525982 0.498561 0.472569 0.447933 0.424581 0.402447 0.381466 0.361579 0.342729
5 ¾ 0.540650 0.511253 0.483454 0.457167 0.432309 0.408803 0.386575 0.365555 0.345679 0.326883
6 0.526788 0.496969 0.468839 0.442301 0.417265 0.393646 0.371364 0.350344 0.330513 0.311805
6 ¼ 0.513312 0.483117 0.454699 0.427952 0.402778 0.379085 0.356786 0.335799 0.316046 0.297455
6 ½ 0.500212 0.469683 0.441017 0.414100 0.388827 0.365095 0.342813 0.321890 0.302244 0.283797
6 ¾ 0.487476 0.456652 0.427777 0.400728 0.375389 0.351653 0.329417 0.308587 0.289075 0.270796
11 12 13 14 15 16 17 18 19 20
7 0.475093 0.444012 0.414964 0.387817 0.362446 0.338735 0.316574 0.295864 0.276508 0.258419
7 ¼ 0.463052 0.431750 0.402564 0.375351 0.349978 0.326320 0.304261 0.283693 0.264516 0.246635
7 ½ 0.451343 0.419854 0.390562 0.363313 0.337966 0.314387 0.292453 0.272049 0.253069 0.235413
7 ¾ 0.439957 0.408312 0.378944 0.351688 0.326393 0.302917 0.281129 0.260909 0.242143 0.224727
8 0.428883 0.397114 0.367698 0.340461 0.315242 0.291890 0.270269 0.250249 0.231712 0.214548
8 ¼ 0.418112 0.386247 0.356810 0.329617 0.304496 0.281289 0.259852 0.240048 0.221753 0.204853
8 ½ 0.407636 0.375702 0.346269 0.319142 0.294140 0.271097 0.249859 0.230285 0.212244 0.195616
8 ¾ 0.397446 0.365468 0.336062 0.309023 0.284159 0.261295 0.240272 0.220939 0.203163 0.186816
9 0.387533 0.355535 0.326179 0.299246 0.274538 0.251870 0.231073 0.211994 0.194490 0.178431
9 ¼ 0.377889 0.345894 0.316608 0.289801 0.265264 0.242805 0.222247 0.203430 0.186206 0.170440
9 ½ 0.368506 0.336535 0.307338 0.280674 0.256323 0.234085 0.213777 0.195230 0.178292 0.162824
9 ¾ 0.359377 0.327450 0.298360 0.271855 0.247703 0.225698 0.205647 0.187378 0.170732 0.155564
10 0.350494 0.318631 0.289664 0.263331 0.239392 0.217629 0.197845 0.179859 0.163508 0.148644
7

8. VALOR ACTUAL DE UNA CANTIDAD: (1 + i)-n
i% N años
21 22 23 24 25 26 27 28 29 30
1 0.811430 0.803396 0.795442 0.787566 0.779768 0.772048 0.764404 0.756836 0.749342 0.741923
1 ¼ 0.770379 0.760868 0.751475 0.742197 0.733034 0.723984 0.715046 0.706219 0.697500 0.688889
1 ½ 0.731498 0.720688 0.710037 0.699544 0.689206 0.679021 0.668986 0.659099 0.649359 0.639762
1 ¾ 0.694668 0.682720 0.670978 0.659438 0.648096 0.636950 0.625995 0.615228 0.604647 0.594248
2 0.659776 0.646839 0.634156 0.621721 0.609531 0.597579 0.585862 0.574375 0.563112 0.552071
2 ¼ 0.626715 0.612925 0.599437 0.586247 0.573346 0.560730 0.548391 0.536324 0.524522 0.512980
2 ½ 0.595386 0.580865 0.566697 0.552875 0.539391 0.526235 0.513400 0.500878 0.488661 0.476743
2 ¾ 0.565694 0.550554 0.535819 0.521478 0.507521 0.493938 0.480718 0.467852 0.455331 0.443144
3 0.537549 0.521893 0.506692 0.491934 0.477606 0.463695 0.450189 0.437077 0.424346 0.411987
3 ¼ 0.510868 0.494787 0.479213 0.464129 0.449519 0.435370 0.421666 0.408393 0.395538 0.383088
3 ½ 0.485571 0.469151 0.453286 0.437957 0.423147 0.408838 0.395012 0.381654 0.368748 0.356278
3 ¾ 0.461583 0.444899 0.428819 0.413319 0.398380 0.383981 0.370102 0.356725 0.343831 0.331403
21 22 23 24 25 26 27 28 29 30
4 0.438834 0.421955 0.405726 0.390121 0.375117 0.360689 0.346817 0.333477 0.320651 0.308319
4 ¼ 0.417256 0.400246 0.383929 0.368277 0.353263 0.338862 0.325047 0.311796 0.299085 0.286892
4 ½ 0.396787 0.379701 0.363350 0.347703 0.332731 0.318402 0.304691 0.291571 0.279015 0.267000
4 ¾ 0.377368 0.360256 0.343920 0.328324 0.313436 0.299223 0.285655 0.272701 0.260335 0.248530
5 0.358942 0.341850 0.325571 0.310068 0.295303 0.281241 0.267848 0.255094 0.242946 0.231377
5 ¼ 0.341457 0.324425 0.308242 0.292866 0.278258 0.264378 0.251190 0.238661 0.226756 0.215445
5 ½ 0.324862 0.307926 0.291873 0.276657 0.262234 0.248563 0.235605 0.223322 0.211679 0.200644
5 ¾ 0.309109 0.292302 0.276408 0.261379 0.247167 0.233728 0.221019 0.209002 0.197637 0.186891
6 0.294155 0.277505 0.261797 0.246979 0.232999 0.219810 0.207368 0.195630 0.184557 0.174110
6 ¼ 0.279958 0.263490 0.247990 0.233402 0.219673 0.206751 0.194589 0.183143 0.172370 0.162230
6 ½ 0.266476 0.250212 0.234941 0.220602 0.207138 0.194496 0.182625 0.171479 0.161013 0.151186
6 ¾ 0.253673 0.237633 0.222607 0.208531 0.195345 0.182993 0.171422 0.160583 0.150429 0.140917
21 22 23 24 25 26 27 28 29 30
7 0.241513 0.225713 0.210947 0.197147 0.184249 0.172195 0.160930 0.150402 0.140563 0.131367
7 ¼ 0.229962 0.214417 0.199923 0.186408 0.173807 0.162058 0.151103 0.140889 0.131365 0.122484
7 ½ 0.218989 0.203711 0.189498 0.176277 0.163979 0.152539 0.141896 0.131997 0.122788 0.114221
7 ¾ 0.208563 0.193562 0.179640 0.166719 0.154728 0.143599 0.133270 0.123685 0.114789 0.106532
8 0.198656 0.183941 0.170315 0.157699 0.146018 0.135202 0.125187 0.115914 0.107328 0.099377
8 ¼ 0.189240 0.174818 0.161495 0.149187 0.137817 0.127314 0.117611 0.108647 0.100367 0.092718
8 ½ 0.180292 0.166167 0.153150 0.141152 0.130094 0.119902 0.110509 0.101851 0.093872 0.086518
8 ¾ 0.171785 0.157963 0.145254 0.133567 0.122820 0.112938 0.103851 0.095495 0.087811 0.080746
9 0.163698 0.150182 0.137781 0.126405 0.115968 0.106393 0.097608 0.089548 0.082155 0.075371
9 ¼ 0.156009 0.142800 0.130709 0.119642 0.109513 0.100240 0.091753 0.083985 0.076874 0.070365
9 ½ 0.148697 0.135797 0.124015 0.113256 0.103430 0.094457 0.086262 0.078778 0.071943 0.065702
9 ¾ 0.141744 0.129152 0.117678 0.107224 0.097698 0.089019 0.081111 0.073905 0.067339 0.061357
10 0.135131 0.122846 0.111678 0.101526 0.092296 0.083905 0.076278 0.069343 0.063039 0.057309
8

9. VALOR ACTUAL DE UNA CANTIDAD: (1 + i)-n
i% N años
31 32 33 34 35 36 37 38 39 40
1 0.734577 0.727304 0.720103 0.712973 0.705914 0.698925 0.692005 0.685153 0.678370 0.671653
1 ¼ 0.680384 0.671984 0.663688 0.655494 0.647402 0.639409 0.631515 0.623719 0.616019 0.608413
1 ½ 0.630308 0.620993 0.611816 0.602774 0.593866 0.585090 0.576443 0.567924 0.559531 0.551262
1 ¾ 0.584027 0.573982 0.564111 0.554408 0.544873 0.535502 0.526292 0.517240 0.508344 0.499601
2 0.541246 0.530633 0.520229 0.510028 0.500028 0.490223 0.480611 0.471187 0.461948 0.452890
2 ¼ 0.501692 0.490652 0.479856 0.469296 0.458970 0.448870 0.438993 0.429333 0.419885 0.410646
2 ½ 0.465115 0.453771 0.442703 0.431905 0.421371 0.411094 0.401067 0.391285 0.381741 0.372431
2 ¾ 0.431284 0.419741 0.408507 0.397574 0.386933 0.376577 0.366499 0.356690 0.347143 0.337852
3 0.399987 0.388337 0.377026 0.366045 0.355383 0.345032 0.334983 0.325226 0.315754 0.306557
3 ¼ 0.371029 0.359350 0.348039 0.337084 0.326473 0.316197 0.306244 0.296604 0.287268 0.278226
3 ½ 0.344230 0.332590 0.321343 0.310476 0.299977 0.289833 0.280032 0.270562 0.261413 0.252572
3 ¾ 0.319425 0.307879 0.296751 0.286025 0.275687 0.265722 0.256118 0.246861 0.237938 0.229338
31 32 33 34 35 36 37 38 39 40
4 0.296460 0.285058 0.274094 0.263552 0.253415 0.243669 0.234297 0.225285 0.216621 0.208289
4 ¼ 0.275196 0.263977 0.253215 0.242892 0.232990 0.223492 0.214381 0.205641 0.197257 0.189216
4 ½ 0.255502 0.244500 0.233971 0.223896 0.214254 0.205028 0.196199 0.187750 0.179665 0.171929
4 ¾ 0.237260 0.226501 0.216231 0.206425 0.197065 0.188129 0.179598 0.171454 0.163679 0.156257
5 0.220359 0.209866 0.199873 0.190355 0.181290 0.172657 0.164436 0.156605 0.149148 0.142046
5 ¼ 0.204699 0.194488 0.184787 0.175569 0.166812 0.158491 0.150585 0.143074 0.135937 0.129156
5 ½ 0.190184 0.180269 0.170871 0.161963 0.153520 0.145516 0.137930 0.130739 0.123924 0.117463
5 ¾ 0.176729 0.167120 0.158033 0.149440 0.141315 0.133631 0.126365 0.119494 0.112997 0.106853
6 0.164255 0.154957 0.146186 0.137912 0.130105 0.122741 0.115793 0.109239 0.103056 0.097222
6 ¼ 0.152687 0.143706 0.135252 0.127296 0.119808 0.112761 0.106128 0.099885 0.094009 0.088479
6 ½ 0.141959 0.133295 0.125159 0.117520 0.110348 0.103613 0.097289 0.091351 0.085776 0.080541
6 ¾ 0.132007 0.123660 0.115840 0.108516 0.101654 0.095226 0.089205 0.083564 0.078280 0.073331
31 32 33 34 35 36 37 38 39 40
7 0.122773 0.114741 0.107235 0.100219 0.093663 0.087535 0.081809 0.076457 0.071455 0.066780
7 ¼ 0.114205 0.106484 0.099286 0.092575 0.086317 0.080482 0.075041 0.069969 0.065239 0.060829
7 ½ 0.106252 0.098839 0.091943 0.085529 0.079562 0.074011 0.068847 0.064044 0.059576 0.055419
7 ¾ 0.098870 0.091759 0.085159 0.079034 0.073349 0.068073 0.063177 0.058633 0.054416 0.050502
8 0.092016 0.085200 0.078889 0.073045 0.067635 0.062625 0.057986 0.053690 0.049713 0.046031
8 ¼ 0.085651 0.079124 0.073094 0.067523 0.062377 0.057623 0.053231 0.049174 0.045427 0.041965
8 ½ 0.079740 0.073493 0.067736 0.062429 0.057539 0.053031 0.048876 0.045047 0.041518 0.038266
8 ¾ 0.074249 0.068275 0.062782 0.057730 0.053085 0.048814 0.044887 0.041275 0.037954 0.034900
9 0.069148 0.063438 0.058200 0.053395 0.048986 0.044941 0.041231 0.037826 0.034703 0.031838
9 ¼ 0.064407 0.058954 0.053963 0.049394 0.045212 0.041384 0.037880 0.034672 0.031737 0.029050
9 ½ 0.060002 0.054796 0.050042 0.045700 0.041736 0.038115 0.034808 0.031788 0.029030 0.026512
9 ¾ 0.055906 0.050940 0.046414 0.042291 0.038534 0.035110 0.031991 0.029149 0.026560 0.024200
10 0.052099 0.047362 0.043057 0.039143 0.035584 0.032349 0.029408 0.026735 0.024304 0.022095
9

10. VALOR ACTUAL DE UNA CANTIDAD: (1 + i)-n
i% N años
41 42 43 44 45 46 47 48 49 50
1 0.665003 0.658419 0.651900 0.645445 0.639055 0.632728 0.626463 0.620260 0.614119 0.608039
1 ¼ 0.600902 0.593484 0.586157 0.578920 0.571773 0.564714 0.557742 0.550856 0.544056 0.537339
1 ½ 0.543116 0.535089 0.527182 0.519391 0.511715 0.504153 0.496702 0.489362 0.482130 0.475005
1 ¾ 0.491008 0.482563 0.474264 0.466107 0.458090 0.450212 0.442469 0.434858 0.427379 0.420029
2 0.444010 0.435304 0.426769 0.418401 0.410197 0.402154 0.394268 0.386538 0.378958 0.371528
2 ¼ 0.401610 0.392772 0.384129 0.375677 0.367410 0.359325 0.351418 0.343685 0.336122 0.328726
2 ½ 0.363347 0.354485 0.345839 0.337404 0.329174 0.321146 0.313313 0.305671 0.298216 0.290942
2 ¾ 0.328810 0.320010 0.311445 0.303109 0.294997 0.287102 0.279418 0.271939 0.264661 0.257578
3 0.297628 0.288959 0.280543 0.272372 0.264439 0.256737 0.249259 0.241999 0.234950 0.228107
3 ¼ 0.269468 0.260986 0.252771 0.244815 0.237109 0.229645 0.222417 0.215416 0.208635 0.202068
3 ½ 0.244031 0.235779 0.227806 0.220102 0.212659 0.205468 0.198520 0.191806 0.185320 0.179053
3 ¾ 0.221049 0.213059 0.205358 0.197935 0.190781 0.183885 0.177239 0.170833 0.164658 0.158707
41 42 43 44 45 46 47 48 49 50
4 0.200278 0.192575 0.185168 0.178046 0.171198 0.164614 0.158283 0.152195 0.146341 0.140713
4 ¼ 0.181502 0.174103 0.167005 0.160197 0.153666 0.147401 0.141392 0.135628 0.130099 0.124795
4 ½ 0.164525 0.157440 0.150661 0.144173 0.137964 0.132023 0.126338 0.120898 0.115692 0.110710
4 ¾ 0.149171 0.142407 0.135949 0.129784 0.123899 0.118281 0.112917 0.107797 0.102909 0.098242
5 0.135282 0.128840 0.122704 0.116861 0.111297 0.105997 0.100949 0.096142 0.091564 0.087204
5 ¼ 0.122714 0.116593 0.110777 0.105251 0.100001 0.095013 0.090274 0.085771 0.081492 0.077427
5 ½ 0.111339 0.105535 0.100033 0.094818 0.089875 0.085190 0.080748 0.076539 0.072549 0.068767
5 ¾ 0.101043 0.095549 0.090353 0.085440 0.080795 0.076402 0.072247 0.068319 0.064604 0.061092
6 0.091719 0.086527 0.081630 0.077009 0.072650 0.068538 0.064658 0.060998 0.057546 0.054288
6 ¼ 0.083275 0.078376 0.073766 0.069427 0.065343 0.061499 0.057882 0.054477 0.051272 0.048256
6 ½ 0.075625 0.071010 0.066676 0.062606 0.058785 0.055197 0.051828 0.048665 0.045695 0.042906
6 ¾ 0.068694 0.064350 0.060281 0.056469 0.052899 0.049554 0.046420 0.043485 0.040736 0.038160
41 42 43 44 45 46 47 48 49 50
7 0.062412 0.058329 0.054513 0.050946 0.047613 0.044499 0.041587 0.038867 0.036324 0.033948
7 ¼ 0.056717 0.052883 0.049308 0.045975 0.042867 0.039969 0.037267 0.034748 0.032399 0.030209
7 ½ 0.051553 0.047956 0.044610 0.041498 0.038603 0.035910 0.033404 0.031074 0.028906 0.026889
7 ¾ 0.046870 0.043499 0.040370 0.037466 0.034771 0.032270 0.029949 0.027795 0.025796 0.023941
8 0.042621 0.039464 0.036541 0.033834 0.031328 0.029007 0.026859 0.024869 0.023027 0.021321
8 ¼ 0.038766 0.035812 0.033083 0.030561 0.028232 0.026081 0.024093 0.022257 0.020560 0.018993
8 ½ 0.035268 0.032505 0.029959 0.027612 0.025448 0.023455 0.021617 0.019924 0.018363 0.016924
8 ¾ 0.032092 0.029510 0.027136 0.024952 0.022945 0.021099 0.019401 0.017840 0.016405 0.015085
9 0.029209 0.026797 0.024584 0.022555 0.020692 0.018984 0.017416 0.015978 0.014659 0.013449
9 ¼ 0.026590 0.024339 0.022278 0.020392 0.018665 0.017085 0.015638 0.014314 0.013102 0.011993
9 ½ 0.024211 0.022111 0.020193 0.018441 0.016841 0.015380 0.014045 0.012827 0.011714 0.010698
9 ¾ 0.022050 0.020091 0.018306 0.016680 0.015198 0.013848 0.012618 0.011497 0.010476 3z95449
10 0.020086 0.018260 0.016600 0.015091 0.013719 0.012472 0.011338 0.010307 3z93704 3z85186
10

11. n
VALOR FUTURO DE UNA ANUALIDAD: ((1 + i) -1) / i
i% N años
1 2 3 4 5 6 7 8 9 10
1 1,00000 2,01000 3,03010 4,06040 5,10101 6,15202 7,21354 8,28567 9,36853 10.4622
1 ¼ 1,00000 2,01250 3,03766 4,07563 5,12657 6,19065 7,26804 8,35889 9,46337 10.5817
1 ½ 1,00000 2,01500 3,04522 4,09090 5,15227 6,22955 7,32299 8,43284 9,55933 10.7027
1 ¾ 1,00000 2,01750 3,05281 4,10623 5,17809 6,26871 7,37841 8,50753 9,65641 10.8254
2 1,00000 2,02000 3,06040 4,12161 5,20404 6,30812 7,43428 8,58297 9,75463 10.9497
2 ¼ 1,00000 2,02250 3,06801 4,13704 5,23012 6,34780 7,49062 8,65916 9,85399 11.0757
2 ½ 1,00000 2,02500 3,07563 4,15252 5,25633 6,38774 7,54743 8,73612 9,95452 11.2034
2 ¾ 1,00000 2,02750 3,08326 4,16805 5,28267 6,42794 7,60471 8,81384 10.0562 11.3328
3 1,00000 2,03000 3,09090 4,18363 5,30914 6,46841 7,66246 8,89234 10.1591 11.4639
3 ¼ 1,00000 2,03250 3,09856 4,19926 5,33574 6,50915 7,72069 8,97162 10.2632 11.5967
3 ½ 1,00000 2,03500 3,10622 4,21494 5,36247 6,55015 7,77941 9,05169 10.3685 11.7314
3 ¾ 1,00000 2,03750 3,11391 4,23068 5,38933 6,59143 7,83861 9,13255 10.4750 11.8678
1 2 3 4 5 6 7 8 9 10
4 1,00000 2,04000 3,12160 4,24646 5,41632 6,63298 7,89829 9,21423 10.5828 12.0061
4 ¼ 1,00000 2,04250 3,12931 4,26230 5,44345 6,67480 7,95848 9,29671 10.6918 12.1462
4 ½ 1,00000 2,04500 3,13702 4,27819 5,47071 6,71689 8,01915 9,38001 10.8021 12.2882
4 ¾ 1,00000 2,04750 3,14476 4,29413 5,49810 6,75926 8,08033 9,46414 10.9137 12.4321
5 1,00000 2,05000 3,15250 4,31013 5,52563 6,80191 8,14201 9,54911 11.0266 12.5779
5 ¼ 1,00000 2,05250 3,16026 4,32617 5,55329 6,84484 8,20420 9,63492 11.1407 12.7256
5 ½ 1,00000 2,05500 3,16803 4,34227 5,58109 6,88805 8,26689 9,72157 11.2563 12.8754
5 ¾ 1,00000 2,05750 3,17581 4,35842 5,60902 6,93154 8,33011 9,80909 11.3731 13.0271
6 1,00000 2,06000 3,18360 4,37462 5,63709 6,97532 8,39384 9,89747 11.4913 13.1808
6 ¼ 1,00000 2,06250 3,19141 4,39087 5,66530 7,01938 8,45809 9,98672 11.6109 13.3366
6 ½ 1,00000 2,06500 3,19923 4,40717 5,69364 7,06373 8,52287 10.0769 11.7319 13.4944
6 ¾ 1,00000 2,06750 3,20706 4,42353 5,72212 7,10836 8,58818 10.1679 11.8542 13.6544
1 2 3 4 5 6 7 8 9 10
7 1,00000 2,07000 3,21490 4,43994 5,75074 7,15329 8,65402 10.2598 11.9780 13.8164
7 ¼ 1,00000 2,07250 3,22276 4,45641 5,77950 7,19851 8,72040 10.3526 12.1032 13.9807
7 ½ 1,00000 2,07500 3,23062 4,47292 5,80839 7,24402 8,78732 10.4464 12.2298 14.1471
7 ¾ 1,00000 2,07750 3.23851 4,48949 5,83743 7,28983 8,85479 10.5410 12.3580 14.3157
8 1,00000 2,08000 3,24640 4,50611 5,86660 7,33593 8,92280 10.6366 12.4876 14.4866
8 ¼ 1,00000 2,08250 3,25431 4,52279 5,89592 7,38233 8,99137 10.7332 12.6186 14.6597
8 ½ 1,00000 2,08500 3,26222 4,53951 5,92537 7,42903 9,06050 10.8306 12.7512 14.8351
8 ¾ 1,00000 2,08750 3,27016 4,55629 5,95497 7,47603 9,13018 10.9291 12.8854 15.0128
9 1,00000 2,09000 3,27810 4,57313 5,98471 7,52333 9,20043 11.0285 13.0210 15.1929
9 ¼ 1,00000 2,09250 3,28606 4,59002 6,01459 7,57094 9,27126 11.1288 13.1583 15.3754
9 ½ 1,00000 2,09500 3,29402 4,60696 6,04462 7,61886 9,34265 11.2302 13.2971 15.5603
9 ¾ 1,00000 2,09750 3,30201 4,62395 6,07479 7,66708 9,41462 11.3325 13.4375 15.7476
10 1,00000 2,10000 3,31000 4,64100 6,10510 7,71561 9,48717 11.4359 13.5795 15.9374
11

12. n
VALOR FUTURO DE UNA ANUALIDAD: ((1 + i) -1) / i
i% N años
11 12 13 14 15 16 17 18 19 20
1 11.5668 12.6825 13.8093 14.9474 16.0969 17.2579 18.4304 19.6147 20.8109 22.0190
1 ¼ 11.7139 12.8604 14.0211 15.1964 16.3863 17.5912 18.8111 20.0462 21.2968 22.5630
1 ½ 11.8633 13.0412 14.2368 15.4504 16.6821 17.9324 19.2014 20.4894 21.7967 23.1237
1 ¾ 12.0148 13.2251 14.4565 15.7095 16.9844 18.2817 19.6016 20.9446 22.3112 23.7016
2 12.1687 13.4121 14.6803 15.9739 17.2934 18.6393 20.0121 21.4123 22.8406 24.2974
2 ¼ 12.3249 13.6022 14.9083 16.2437 17.6092 19.0054 20.4330 21.8928 23.3853 24.9115
2 ½ 12.4835 13.7956 15.1404 16.5190 17.9319 19.3802 20.8647 22.3863 23.9460 25.5447
2 ¾ 12.6444 13.9921 15.3769 16.7998 18.2618 19.7640 21.3075 22.8934 24.5230 26.1974
3 12.8078 14.1920 15.6178 17.0863 18.5989 20.1569 21.7616 23.4144 25.1169 26.8704
3 ¼ 12.9736 14.3953 15.8631 17.3787 18.9435 20.5592 22.2273 23.9497 25.7281 27.5642
3 ½ 13.1420 14.6020 16.1130 17.6770 19.2957 20.9710 22.7050 24.4997 26.3572 28.2797
3 ¾ 13.3129 14.8121 16.3676 17.9814 19.6557 21.3927 23.1950 25.0648 27.0047 29.0174
11 12 13 14 15 16 17 18 19 20
4 13.4864 15.0258 16.6268 18.2919 20.0236 21.8245 23.6975 25.6454 27.6712 29.7781
4 ¼ 13.6624 15.2431 16.8909 18.6088 20.3997 22.2666 24.2130 26.2420 28.3573 30.5625
4 ½ 13.8412 15.4640 17.1599 18.9321 20.7841 22.7193 24.7417 26.8551 29.0636 31.3714
4 ¾ 14.0226 15.6887 17.4339 19.2620 21.1770 23.1829 25.2840 27.4850 29.7906 32.2056
5 14.2068 15.9171 17.7130 19.5986 21.5786 23.6575 25.8404 28.1324 30.5390 33.0660
5 ¼ 14.3937 16.1494 17.9972 19.9421 21.9891 24.1435 26.4110 28.7976 31.3095 33.9532
5 ½ 14.5835 16.3856 18.2868 20.2926 22.4087 24.6411 26.9964 29.4812 32.1027 34.8683
5 ¾ 14.7761 16.6257 18.5817 20.6502 22.8376 25.1507 27.5969 30.1837 32.9193 35.8121
6 14.9716 16.8699 18.8821 21.0151 23.2760 25.6725 28.2129 30.9057 33.7600 36.7856
6 ¼ 15.1701 17.1182 19.1881 21.3874 23.7241 26.2069 28.8448 31.6476 34.6256 37.7897
6 ½ 15.3716 17.3707 19.4998 21.7673 24.1822 26.7540 29.4930 32.4101 35.5167 38.8253
6 ¾ 15.5760 17.6274 19.8173 22.1549 24.6504 27.3143 30.1580 33.1937 36.4343 39.8936
11 12 13 14 15 16 17 18 19 20
7 15.7836 17.8885 20.1406 22.5505 25.1290 27.8881 30.8402 33.9990 37.3790 40.9955
7 ¼ 15.9943 18.1539 20.4700 22.9541 25.6183 28.4756 31.5401 34.8267 38.3517 42.1322
7 ½ 16.2081 18.4237 20.8055 23.3659 26.1184 29.0772 32.2580 35.6774 39.3532 43.3047
7 ¾ 16.4252 18.6981 21.1472 23.7861 26.6296 29.6934 32.9946 36.5517 40.3844 44.5142
8 16.6455 18.9771 21.4953 24.2149 27.1521 30.3243 33.7502 37.4502 41.4463 45.7620
8 ¼ 16.8691 19.2608 21.8498 24.6524 27.6863 30.9704 34.5254 38.3738 42.5396 47.0491
8 ½ 17.0961 19.5492 22.2109 25.0989 28.2323 31.6320 35.3207 39.3230 43.6654 48.3770
8 ¾ 17.3265 19.8425 22.5787 25.5544 28.7904 32.3096 36.1366 40.2986 44.8247 49.7469
9 17.5603 20.1407 22.9534 26.0192 29.3609 33.0034 36.9737 41.3013 46.0185 51.1601
9 ¼ 17.7976 20.4439 23.3350 26.4935 29.9441 33.7139 37.8325 42.3320 47.2477 52.6181
9 ½ 18.0385 20.7522 23.7236 26.9774 30.5402 34.4416 38.7135 43.3913 48.5135 54.1222
9 ¾ 18.2830 21.0656 24.1195 27.4712 31.1496 35.1867 39.6174 44.4801 49.8169 55.6740
10 18.5312 21.3843 24.5227 27.9750 31.7725 35.9497 40.5447 45.5992 51.1591 57.2750
12

13. n
VALOR FUTURO DE UNA ANUALIDAD: ((1 + i) -1) / i
i% N años
21 22 23 24 25 26 27 28 29 30
1 23.2392 24.4716 25.7163 26.9735 28.2432 29.5256 30.8209 32.1291 33.4504 34.7849
1 ¼ 23.8450 25.1431 26.4574 27.7881 29.1354 30.4996 31.8809 33.2794 34.6954 36.1291
1 ½ 24.4705 25.8376 27.2251 28.6335 30.0630 31.5140 32.9867 34.4815 35.9987 37.5387
1 ¾ 25.1164 26.5559 28.0207 29.5110 31.0275 32.5704 34.1404 35.7379 37.3633 39.0172
2 25.7833 27.2990 28.8450 30.4219 32.0303 33.6709 35.3443 37.0512 38.7922 40.5681
2 ¼ 26.4720 28.0676 29.6992 31.3674 33.0732 34.8173 36.6007 38.4242 40.2888 42.1953
2 ½ 27.1833 28.8629 30.5844 32.3490 34.1578 36.0117 37.9120 39.8598 41.8563 43.9027
2 ¾ 27.9178 29.6856 31.5019 33.3682 35.2858 37.2562 39.2808 41.3610 43.4984 45.6946
3 28.6765 30.5368 32.4529 34.4265 36.4593 38.5530 40.7096 42.9309 45.2189 47.5754
3 ¼ 29.4601 31.4175 33.4386 35.5254 37.6799 39.9045 42.2014 44.5730 47.0216 49.5498
3 ½ 30.2695 32.3289 34.4604 36.6665 38.9499 41.3131 43.7591 46.2906 48.9108 51.6227
3 ¾ 31.1055 33.2720 35.5197 37.8517 40.2711 42.7813 45.3856 48.0875 50.8908 53.7992
21 22 23 24 25 26 27 28 29 30
4 31.9692 34.2480 36.6179 39.0826 41.6459 44.3117 47.0842 49.9676 52.9663 56.0849
4 ¼ 32.8614 35.2580 37.7565 40.3611 43.0765 45.9072 48.8583 51.9348 55.1420 58.4855
4 ½ 33.7831 36.3034 38.9370 41.6892 44.5652 47.5706 50.7113 53.9933 57.4230 61.0071
4 ¾ 34.7354 37.3853 40.1611 43.0688 46.1146 49.3050 52.6470 56.1477 59.8147 63.6559
5 35.7193 38.5052 41.4305 44.5020 47.7271 51.1135 54.6691 58.4026 62.3227 66.4388
5 ¼ 36.7358 39.6644 42.7468 45.9910 49.4055 52.9993 56.7818 60.7628 64.9529 69.3629
5 ½ 37.7861 40,8643 44.1118 47.5380 51.1526 54.9660 58.9891 63.2335 67.7114 72.4355
5 ¾ 38.8713 42.1064 45.5275 49.1454 52.9712 57.0171 61.2956 65.8201 70.6047 75.6645
6 39.9927 43.3923 46.9958 50.8156 54.8645 59.1564 63.7058 68.5281 73.6398 79.0582
6 ¼ 41.1515 44.7235 48.5187 52.5511 56.8356 61.3878 66.2245 71.3635 76.8238 82.6253
6 ½ 42.3490 46.1016 50.0982 54.3546 58.8877 63.7154 68.8569 74.3326 80.1642 86.3749
6 ¾ 43.5864 47.5285 51.7366 56.2289 61.0243 66.1435 71.6081 77.4417 83.6690 90.3167
21 22 23 24 25 26 27 28 29 30
7 44.8652 49.0057 53.4361 58.1767 63.2490 68.6765 74.4838 80.6977 87.3465 94.4608
7 ¼ 46.1867 50.5353 55.1991 60.2010 65.5656 71.3191 77.4897 84.1077 91.2055 98.8179
7 ½ 47.5525 52.1190 57.0279 62.3050 67.9779 74.0762 80.6319 87.6793 95.2553 103.399
7 ¾ 48.9641 53.7588 58.9251 64.4918 70.4899 76.9529 83.9167 91.4203 99.5053 108.217
8 50.4229 55.4568 60.8933 66.7648 73.1059 79.9544 87.3508 95.3388 103.966 113.283
8 ¼ 51.9307 57.2150 62.9352 69.1274 75.8304 83.0864 90.9410 99.4436 108.648 118.611
8 ½ 53.4891 59.0356 65.0537 71.5832 78.6678 86.3546 94.6947 103.744 113.562 124.215
8 ¾ 55.0997 60.9210 67.2516 74.1361 81.6230 89.7650 98.6194 108.249 118.720 130.108
9 56.7645 62.8733 69.5319 76.7898 84.7009 93.3240 102.723 112.968 124.135 136.308
9 ¼ 58.4853 64.8951 71.8980 79.5485 87.9067 97.0381 107.014 117.913 129.820 142.828
9 ½ 60.2638 66.9889 74.3529 82.4164 91.2459 100.914 111.501 123.094 135.788 149.688
9 ¾ 62.1022 69.1572 76.9000 85.3978 94.7241 104.960 116.193 128.522 142.053 156.903
10 64.0025 71.4027 79.5430 88.4973 98.3471 109.182 121.100 134.210 148.631 164.494
13

14. n
VALOR FUTURO DE UNA ANUALIDAD: ((1 + i) -1) / i
i% N años
31 32 33 34 35 36 37 38 39 40
1 36.1327 37.4941 38.8690 40.2577 41.6603 43.0769 44.5076 45.9527 47.4123 48.8864
1 ¼ 37.5807 39.0504 40.5386 42.0453 43.5709 45.1155 46.6794 48.2629 49.8662 51.4896
1 ½ 39.1018 40.6883 42.2986 43.9331 45.5921 47.2760 48.9851 50.7199 52.4807 54.2679
1 ¾ 40.7000 42.4122 44.1544 45.9271 47.7308 49.5661 51.4335 53.3336 55.2670 57.2341
2 42.3794 44.2270 46.1116 48.0338 49.9945 51.9944 54.0343 56.1149 58.2372 60.4020
2 ¼ 44.1447 46.1379 48.1760 50.2600 52.3908 54.5696 56.7974 59.0754 61.4046 63.7862
2 ½ 46.0003 48.1503 50.3540 52.6129 54.9282 57.3014 59.7339 62.2273 64.7830 67.4026
2 ¾ 47.9512 50.2699 52.6523 55.1002 57.6155 60.1999 62.8554 65.5839 68.3875 71.2681
3 50.0027 52.5028 55.0778 57.7302 60.4621 63.2759 66.1742 69.1594 72.2342 75.4013
3 ¼ 52.1602 54.8554 57.6382 60.5114 63.4780 66.5411 69.7037 72.9690 76.3405 79.8216
3 ½ 54.4295 57.3345 60.3412 63.4532 66.6740 70.0076 73.4579 77.0289 80.7249 84.5503
3 ¾ 56.8167 59.9473 63.1954 66.5652 70.0614 73.6887 77.4520 81.3565 85.4073 89.6101
31 32 33 34 35 36 37 38 39 40
4 59.3283 62.7015 66.2095 69.8579 73.6522 77.5983 81.7022 85.9703 90.4091 95.0255
4 ¼ 61.9712 65.6049 69.3931 73.3424 77.4594 81.7514 86.2259 90.8905 95.7533 100.823
4 ½ 64.7524 68.6662 72.7562 77.0303 81.4966 86.1640 91.0413 96.1382 101.464 107.030
4 ¾ 67.6796 71.8944 76.3094 80.9341 85.7784 90.8529 96.1684 101.736 107.569 113.678
5 70.7608 75.2988 80.0638 85.0670 90.3203 95.8363 101.628 107.710 114.095 120.800
5 ¼ 74.0044 78.8897 84.0314 89.4430 95.1388 101.134 107.443 114.084 121.073 128.430
5 ½ 77.4194 82.6775 88.2248 94.0771 100.251 106.765 113.637 120.887 128.536 136.606
5 ¾ 81.0152 86.6736 92.6573 98.9851 105.677 112.753 120.236 128.150 136.519 145.369
6 84.8017 90.8898 97.3432 104.184 111.435 119.121 127.268 135.904 145.058 154.762
6 ¼ 88.7893 95.3387 102.297 109.691 117.547 125.893 134.762 144.184 154.196 164.833
6 ½ 92.9892 100.034 107.536 115.526 124.035 133.097 142.748 153.027 163.974 175.632
6 ¾ 97.4130 104.988 113.075 121.708 130.923 140.760 151.262 162.472 174.439 187.213
31 32 33 34 35 36 37 38 39 40
7 102.073 110.218 118.933 128.259 138.237 148.913 160.337 172.561 185.640 199.635
7 ¼ 106.982 115.738 125.130 135.201 146.003 157.589 170.014 183.340 197.632 212.960
7 ½ 112.154 121.566 131.683 142.560 154.252 166.820 180.332 194.857 210.471 227.257
7 ¾ 117.604 127.718 138.616 150.359 163.012 176.645 191.335 207.164 224.219 242.596
8 123.346 134.214 145.951 158.627 172.317 187.102 203.070 220.316 238.941 259.057
8 ¼ 129.397 141.072 153.710 167.391 182.201 198.233 215.587 234.373 254.709 276.722
8 ½ 135.773 148.314 161.920 176.684 192.702 210.081 228.938 249.398 271.597 295.683
8 ¾ 142.493 155.961 170.608 186.536 203.858 222.695 243.181 265.459 289.687 316.035
9 149.575 164.037 179.800 196.982 215.711 236.125 258.376 282.630 309.066 337.882
9 ¼ 157.040 172.566 189.528 208.060 228.305 250.424 274.588 300.987 329.828 361.338
9 ½ 164.908 181.574 199.824 219.807 241.688 265.649 291.886 320.615 352.073 386.520
9 ¾ 173.201 191.088 210.719 232.265 255.910 281.862 310.343 341.602 375.908 413.559
10 181.943 201.138 222.252 245.477 271.024 299.127 330.039 364.043 401.448 442.593
14

15. n
VALOR FUTURO DE UNA ANUALIDAD: ((1 + i) -1) / i
i% N años
41 42 43 44 45 46 47 48 49 50
1 50.3752 51.8790 53.3978 54.9318 56.4811 58.0459 59.6263 61.2226 62.8348 64.4632
1 ¼ 53.1332 54.7973 56.4823 58.1883 59.9157 61.6646 63.4354 65.2284 67.0437 68.8818
1 ½ 56.0819 57.9231 59.7920 61.6889 63.6142 65.5684 67.5519 69.5652 71.6087 73.6828
1 ¾ 59.2357 61.2724 63.3446 65.4532 67.5986 69.7816 72.0027 74.2628 76.5624 78.9022
2 62.6100 64.8622 67.1595 69.5027 71.8927 74.3306 76.8172 79.3535 81.9406 84.5794
2 ¼ 66.2214 68.7113 71.2574 73.8606 76.5225 79.2443 82.0273 84.8729 87.7825 90.7576
2 ½ 70.0876 72.8398 75.6608 78.5523 81.5161 84.5540 87.6679 90.8596 94.1311 97.4843
2 ¾ 74.2280 77.2693 80.3942 83.6050 86.9042 90.2940 93.7771 97.3560 101.033 104.812
3 78.6633 82.0232 85.4839 89.0484 92.7199 96.5015 100.397 104.408 108.541 112.797
3 ¼ 83.4158 87.1268 90.9584 94.9146 98.9993 103.217 107.571 112.067 116.710 121.503
3 ½ 88.5095 92.6074 96.8486 101.238 105.782 110.484 115.351 120.388 125.602 130.998
3 ¾ 93.9705 98.4944 103.188 108.057 113.110 118.351 123.789 129.431 135.285 141.358
41 42 43 44 45 46 47 48 49 50
4 99.8265 104.820 110.012 115.413 121.029 126.871 132.945 139.263 145.834 152.667
4 ¼ 106.108 111.617 117.361 123.349 129.591 136.099 142.883 149.956 157.329 165.015
4 ½ 112.847 118.925 125.276 131.914 138.850 146.098 153.673 161.588 169.859 178.503
4 ¾ 120.078 126.782 133.804 141.160 148.865 156.936 165.390 174.246 183.523 193.240
5 127.840 135.232 142.993 151.143 159.700 168.685 178.119 188.025 198.427 209.348
5 ¼ 136.172 144.321 152.898 161.925 171.426 181.426 191.951 203.028 214.687 226.959
5 ½ 145.119 154.100 163.576 173.573 184.119 195.246 206.984 219.368 232.434 246.217
5 ¾ 154.727 164.624 175.090 186.158 197.862 210.239 223.327 237.169 251.806 267.285
6 165.048 175.951 187.508 199.758 212.744 226.508 241.099 256.565 272.958 290.336
6 ¼ 176.135 188.143 200.902 214.459 228.862 244.166 260.427 277.703 296.060 315.564
6 ½ 188.048 201.271 215.354 230.352 246.325 263.336 281.453 300.747 321.295 343.180
6 ¾ 200.850 215.407 230.947 247.536 265.245 284.149 304.329 325.871 348.868 373.416
41 42 43 44 45 46 47 48 49 50
7 214.610 230.632 247.776 266.121 285.749 306.752 329.224 353.270 378.999 406.529
7 ¼ 229.400 247.032 265.941 286.222 307.973 331.301 356.321 383.154 411.932 442.798
7 ½ 245.301 264.698 285.551 307.967 332.065 357.969 385.817 415.753 447.935 482.530
7 ¾ 262.397 283.733 306.722 331.493 358.184 386.943 417.931 451.321 487.298 526.064
8 280.781 304.244 329.583 356.950 386.506 418.426 452.900 490.132 530.343 573.770
8 ¼ 300.552 326.347 354.271 384.498 417.219 452.640 490.983 532.489 577.419 626.056
8 ½ 321.816 350.170 380.934 414.314 450.530 489.825 532.461 578.720 628.911 683.368
8 ¾ 344.688 375.848 409.735 446.586 486.663 530.246 577.642 629.186 685.240 746.198
9 369.292 403.528 440.846 481.522 525.859 574.186 626.863 684.280 746.866 815.084
9 ¼ 395.761 433.369 474.456 519.343 568.382 621.958 680.489 744.434 814.294 890.616
9 ½ 424.239 465.542 510.769 560.292 614.519 673.899 738.919 810.116 888.077 973.445
9 ¾ 454.881 500.232 550.004 604.630 664.581 730.378 802.590 881.842 968.822 1.064,28
10 487.852 537.637 592.401 652.641 718.905 791.795 871.975 960.172 1.057,19 1.163,91
15

16. VALOR FUTURO DE CANTIDAD UNICA: (1 + i) n
i% N años
1 2 3 4 5 6 7 8 9 10
1 1,01000 1,02010 1,03030 1,04060 1,05101 1,06152 1,07214 1,08286 1,09369 1,10462
1 ¼ 1,01250 1,02516 1,03797 1,05095 1,06408 1,07738 1,09085 1,10449 1,11829 1,13227
1 ½ 1,01500 1,03022 1,04568 1,06136 1,07728 1,09344 1,10984 1,12649 1,14339 1,16054
1 ¾ 1,01750 1,03531 1,05342 1,07186 1,09062 1,10970 1,12912 1,14888 1,16899 1,18944
2 1,02000 1,04040 1,06121 1,08243 1,10408 1,12616 1,14869 1,17166 1,19509 1,21899
2 ¼ 1,02250 1,04551 1,06903 1,09308 1,11768 1,14283 1,16854 1,19483 1,22171 1,24920
2 ½ 1,02500 1,05062 1,07689 1,10381 1,13141 1,15969 1,18869 1,21840 1,24886 1,28008
2 ¾ 1,02750 1,05576 1,08479 1,11462 1,14527 1,17677 1,20913 1,24238 1,27655 1,31165
3 1,03000 1,06090 1,09273 1,12551 1,15927 1,19405 1,22987 1,26677 1,30477 1,34392
3 ¼ 1,03250 1,06606 1,10070 1,13648 1,17341 1,21155 1,25092 1,29158 1,33355 1,37689
3 ½ 1,03500 1,07123 1,10872 1,14752 1,18769 1,22926 1,27228 1,31681 1,36290 1,41060
3 ¾ 1,03750 1,07641 1,11677 1,15865 1,20210 1,24718 1,29395 1,34247 1,39281 1,44504
1 2 3 4 5 6 7 8 9 10
4 1,04000 1,08160 1,12486 1,16986 1,21665 1,26532 1,31593 1,36857 1,42331 1,48024
4 ¼ 1,04250 1,08681 1,13300 1,18115 1,23135 1,28368 1,33824 1,39511 1,45440 1,51621
4 ½ 1,04500 1,09203 1,14117 1,19252 1,24618 1,30226 1,36086 1,42210 1,48610 1,55297
4 ¾ 1,04750 1,09726 1,14938 1,20397 1,26116 1,32107 1,38382 1,44955 1,51840 1,59052
5 1,05000 1,10250 1,15762 1,21551 1,27628 1,34010 1,40710 1,47746 1,55133 1,62889
5 ¼ 1,05250 1,10776 1,16591 1,22712 1,29155 1,35935 1,43072 1,50583 1,58489 1,66810
5 ½ 1,05500 1,11302 1,17424 1,23882 1,30696 1,37884 1,45468 1,53469 1,61909 1,70814
5 ¾ 1,05750 1,11831 1,18261 1,25061 1,32252 1,39856 1,47898 1,56402 1,65395 1,74906
6 1,06000 1,12360 1,19102 1,26248 1,33823 1,41852 1,50363 1,59385 1,68948 1,79085
6 ¼ 1,06250 1,12891 1,19946 1,27443 1,35408 1,43871 1,52863 1,62417 1,72568 1,83354
6 ½ 1,06500 1,13423 1,20795 1,28647 1,37009 1,45914 1,55399 1,65500 1,76257 1,87714
6 ¾ 1,06750 1,13956 1,21648 1,29859 1,38624 1,47981 1,57970 1,68633 1,80016 1,92167
1 2 3 4 5 6 7 8 9 10
7 1,07000 1,14490 1,22504 1,31080 1,40255 1,50073 1,60578 1,71819 1,83846 1,96715
7 ¼ 1,07250 1,15026 1,23365 1,32309 1,41901 1,52189 1,63223 1,75057 1,87748 2,01360
7 ½ 1,07500 1,15562 1,24230 1,33547 1,43563 1,54330 1,65905 1,78348 1,91724 2,06103
7 ¾ 1,07750 1,16101 1,25098 1,34794 1,45240 1,56496 1,68625 1,81693 1,95774 2,10947
8 1,08000 1,16640 1,25971 1,36049 1,46933 1,58687 1,71382 1,85093 1,99900 2,15892
8 ¼ 1,08250 1,17181 1,26848 1,37313 1,48641 1,60904 1,74179 1,88549 2,04104 2,20942
8 ½ 1,08500 1,17722 1,27729 1,38586 1,50366 1,63147 1,77014 1,92060 2,08386 2,26098
8 ¾ 1,08750 1,18266 1,28614 1,39868 1,52106 1,65415 1,79889 1,95629 2,12747 2,31362
9 1,09000 1,18810 1,29503 1,41158 1,53862 1,67710 1,82804 1,99256 2,17189 2,36736
9 ¼ 1,09250 1,19356 1,30396 1,42458 1,55635 1,70031 1,85759 2,02942 2,21714 2,42222
9 ½ 1,09500 1,19903 1,31293 1,43766 1,57424 1,72379 1,88755 2,06687 2,26322 2,47823
9 ¾ 1,09750 1,20451 1,32195 1,45084 1,59229 1,74754 1,91793 2,10492 2,31015 2,53539
10 1,10000 1,21000 1,33100 1,46410 1,61051 1,77156 1,94872 2,14359 2,35795 2,59374
16

17. VALOR FUTURO DE CANTIDAD UNICA: (1 + i) n
i% N años
11 12 13 14 15 16 17 18 19 20
1 1,11567 1,12683 1,13809 1,14947 1,16097 1,17258 1,18430 1,19615 1,20811 1,22019
1 ¼ 1,14642 1,16075 1,17526 1,18995 1,20483 1,21989 1,23514 1,25058 1,26621 1,28204
1 ½ 1,17795 1,19562 1,21355 1,23176 1,25023 1,26899 1,28802 1,30734 1,32695 1,34686
1 ¾ 1,21026 1,23144 1,25299 1,27492 1,29723 1,31993 1,34303 1,36653 1,39045 1,41478
2 1,24337 1,26824 1,29361 1,31948 1,34587 1,37279 1,40024 1,42825 1,45681 1,48595
2 ¼ 1,27731 1,30605 1,33544 1,36548 1,39621 1,42762 1,45974 1,49259 1,52617 1,56051
2 ½ 1,31209 1,34489 1,37851 1,41297 1,44830 1,48451 1,52162 1,55966 1,59865 1,63862
2 ¾ 1,34772 1,38478 1,42287 1,46199 1,50220 1,54351 1,58596 1,62957 1,67438 1,72043
3 1,38423 1,42576 1,46853 1,51259 1,55797 1,60471 1,65285 1,70243 1,75351 1,80611
3 ¼ 1,42164 1,46785 1,51555 1,56481 1,61566 1,66817 1,72239 1,77837 1,83616 1,89584
3 ½ 1,45997 1,51107 1,56396 1,61869 1,67535 1,73399 1,79468 1,85749 1,92250 1,98979
3 ¾ 1,49923 1,55545 1,61378 1,67430 1,73709 1,80223 1,86981 1,93993 2,01268 2,08815
11 12 13 14 15 16 17 18 19 20
4 1,53945 1,60103 1,66507 1,73168 1,80094 1,87298 1,94790 2,02582 2,10685 2,19112
4 ¼ 1,58065 1,64783 1,71786 1,79087 1,86699 1,94633 2,02905 2,11529 2,20519 2,29891
4 ½ 1,62285 1,69588 1,77220 1,85194 1,93528 2,02237 2,11338 2,20848 2,30786 2,41171
4 ¾ 1,66607 1,74521 1,82811 1,91495 2,00591 2,10119 2,20099 2,30554 2,41505 2,52977
5 1,71034 1,79586 1,88565 1,97993 2,07893 2,18287 2,29202 2,40662 2,52695 2,65330
5 ¼ 1,75567 1,84784 1,94486 2,04696 2,15443 2,26753 2,38658 2,51187 2,64375 2,78254
5 ½ 1,80209 1,90121 2,00577 2,11609 2,23248 2,35526 2,48480 2,62147 2,76565 2,91776
5 ¾ 1,84963 1,95598 2,06845 2,18739 2,31316 2,44617 2,58682 2,73556 2,89286 3,05920
6 1,89830 2,01220 2,13293 2,26090 2,39656 2,54035 2,69277 2,85434 3,02560 3,20714
6 ¼ 1,94813 2,06989 2,19926 2,33671 2,48276 2,63793 2,80280 2,97797 3,16410 3,36185
6 ½ 1,99915 2,12910 2,26749 2,41487 2,57184 2,73901 2,91705 3,10665 3,30859 3,52365
6 ¾ 2,05138 2,18985 2,33767 2,49546 2,66390 2,84372 3,03567 3,24057 3,45931 3,69282
11 12 13 14 15 16 17 18 19 20
7 2,10485 2,25219 2,40985 2,57853 2,75903 2,95216 3,15882 3,37993 3,61653 3,86968
7 ¼ 2,15959 2,31615 2,48408 2,66417 2,85732 3,06448 3,28665 3,52494 3,78050 4,05458
7 ½ 2,21561 2,38178 2,56041 2,75244 2,95888 3,18079 3,41935 3,67580 3,95149 4,24785
7 ¾ 2,27295 2,44910 2,63891 2,84343 3,06379 3,30124 3,55708 3,83275 4,12979 4,44985
8 2,33164 2,51817 2,71962 2,93719 3,17217 3,42594 3,70002 3,99602 4,31570 4,66096
8 ¼ 2,39170 2,58902 2,80261 3,03383 3,28412 3,55506 3,84835 4,16584 4,50952 4,88155
8 ½ 2,45317 2,66169 2,88793 3,13340 3,39974 3,68872 4,00226 4,34245 4,71156 5,11205
8 ¾ 2,51607 2,73622 2,97564 3,23601 3,51916 3,82709 4,16196 4,52613 4,92216 5,35285
9 2,58043 2,81266 3,06580 3,34173 3,64248 3,97031 4,32763 4,71712 5,14166 5,60441
9 ¼ 2,64628 2,89106 3,15848 3,45064 3,76983 4,11854 4,49950 4,91571 5,37041 5,86717
9 ½ 2,71366 2,97146 3,25375 3,56285 3,90132 4,27195 4,67778 5,12217 5,60878 6,14161
9 ¾ 2,78259 3,05390 3,35165 3,67844 4,03709 4,43070 4,86269 5,33681 5,85715 6,42822
10 2,85312 3,13843 3,45227 3,79750 4,17725 4,59497 5,05447 5,55992 6,11591 6,72750
17

18. VALOR FUTURO DE CANTIDAD UNICA: (1 + i) n
i% N años
21 22 23 24 25 26 27 28 29 30
1 1,23239 1,24472 1,25716 1,26973 1,28243 1,29526 1,30821 1,32129 1,33450 1,34785
1 ¼ 1,29806 1,31429 1,33072 1,34735 1,36419 1,38125 1,39851 1,41599 1,43369 1,45161
1 ½ 1,36706 1,38756 1,40838 1,42950 1,45095 1,47271 1,49480 1,51722 1,53998 1,56308
1 ¾ 1,43954 1,46473 1,49036 1,51644 1,54298 1,56998 1,59746 1,62541 1,65386 1,68280
2 1,51567 1,54598 1,57690 1,60844 1,64061 1,67342 1,70689 1,74102 1,77584 1,81136
2 ¼ 1,59562 1,63152 1,66823 1,70577 1,74415 1,78339 1,82352 1,86454 1,90650 1,94939
2 ½ 1,67958 1,72157 1,76461 1,80873 1,85394 1,90029 1,94780 1,99650 2,04641 2,09757
2 ¾ 1,76774 1,81635 1,86630 1,91763 1,97036 2,02455 2,08022 2,13743 2,19621 2,25660
3 1,86029 1,91610 1,97359 2,03279 2,09378 2,15659 2,22129 2,28793 2,35657 2,42726
3 ¼ 1,95745 2,02107 2,08675 2,15457 2,22460 2,29690 2,37155 2,44862 2,52820 2,61037
3 ½ 2,05943 2,13151 2,20611 2,28333 2,36324 2,44596 2,53157 2,62017 2,71188 2,80679
3 ¾ 2,16646 2,24770 2,33199 2,41944 2,51017 2,60430 2,70196 2,80328 2,90841 3,01747
21 22 23 24 25 26 27 28 29 30
4 2,27877 2,36992 2,46472 2,56330 2,66584 2,77247 2,88337 2,99870 3,11865 3,24340
4 ¼ 2,39661 2,49847 2,60465 2,71535 2,83075 2,95106 3,07648 3,20723 3,34353 3,48564
4 ½ 2,52024 2,63365 2,75217 2,87601 3,00543 3,14068 3,28201 3,42970 3,58404 3,74532
4 ¾ 2,64993 2,77580 2,90765 3,04577 3,19044 3,34199 3,50073 3,66702 3,84120 4,02366
5 2,78596 2,92526 3,07152 3,22510 3,38635 3,55567 3,73346 3,92013 4,11614 4,32194
5 ¼ 2,92863 3,08238 3,24421 3,41453 3,59379 3,78246 3,98104 4,19005 4,41002 4,64155
5 ½ 3,07823 3,24754 3,42615 3,61459 3,81339 4,02313 4,24440 4,47784 4,72412 4,98395
5 ¾ 3,23510 3,42112 3,61783 3,82586 4,04585 4,27848 4,52450 4,78465 5,05977 5,35071
6 3,39956 3,60354 3,81975 4,04893 4,29187 4,54938 4,82235 5,11169 5,41839 5,74349
6 ¼ 3,57197 3,79522 4,03242 4,28444 4,55222 4,83674 5,13903 5,46022 5,80149 6,16408
6 ½ 3,75268 3,99661 4,25639 4,53305 4,82770 5,14150 5,47570 5,83162 6,21067 6,61437
6 ¾ 3,94208 4,20817 4,49222 4,79545 5,11914 5,46468 5,83355 6,22731 6,64766 7,09637
21 22 23 24 25 26 27 28 29 30
7 4,14056 4,43040 4,74053 5,07237 5,42743 5,80735 6,21387 6,64884 7,11426 7,61226
7 ¼ 4,34854 4,66381 5,00193 5,36457 5,75351 6,17063 6,61801 7,09781 7,61240 8,16430
7 ½ 4,56644 4,90892 5,27709 5,67287 6,09834 6,55572 7,04739 7,57595 8,14414 8,75496
7 ¾ 4,79472 5,16631 5,56669 5,99811 6,46297 6,96385 7,50355 8,08507 8,71166 9,38682
8 5,03383 5,43654 5,87146 6,34118 6,84848 7,39635 7,98806 8,62711 9,31727 10.0627
8 ¼ 5,28428 5,72024 6,19215 6,70301 7,25601 7,85463 8,50263 9,20410 9,96344 10.7854
8 ½ 5,54657 6,01803 6,52956 7,08457 7,68676 8,34014 9,04905 9,81822 10.6528 11.5583
8 ¾ 5,82123 6,33058 6,88451 7,48691 8,14201 8,85444 9,62920 10.4718 11.3880 12.3845
9 6,10881 6,65860 7,25787 7,91108 8,62308 9,39916 10.2451 11.1671 12.1722 13.2677
9 ¼ 6,40989 7,00280 7,65056 8,35824 9,13137 9,97603 10.8988 11.9069 13.0083 14.2116
9 ½ 6,72507 7,36395 8,06352 8,82956 9,66836 10.5869 11.5926 12.6939 13.8998 15.2203
9 ¾ 7,05497 7,74283 8,49775 9,32629 10.2356 11.2336 12.3288 13.5309 14.8502 16.2981
10 7,40025 8,14027 8,95430 9,84973 10.8347 11.9182 13.1100 14.4210 15.8631 17.4494
18

19. VALOR FUTURO DE CANTIDAD UNICA: (1 + i) n
i% N años
31 32 33 34 35 36 37 38 39 40
1 1,36133 1,37494 1,38869 1,40258 1,41660 1,43077 1,44508 1,45953 1,47412 1,48886
1 ¼ 1,46976 1,48813 1,50673 1,52557 1,54464 1,56394 1,58349 1,60329 1,62333 1,64362
1 ½ 1,58653 1,61032 1,63448 1,65900 1,68388 1,70914 1,73478 1,76080 1,78721 1,81402
1 ¾ 1,71225 1,74221 1,77270 1,80372 1,83529 1,86741 1,90009 1,93334 1,96717 2,00160
2 1,84759 1,88454 1,92223 1,96068 1,99989 2,03989 2,08069 2,12230 2,16474 2,20804
2 ¼ 1,99325 2,03810 2,08396 2,13085 2,17879 2,22782 2,27794 2,32920 2,38160 2,43519
2 ½ 2,15001 2,20376 2,25885 2,31532 2,37321 2,43254 2,49335 2,55568 2,61957 2,68506
2 ¾ 2,31866 2,38242 2,44794 2,51526 2,58443 2,65550 2,72852 2,80356 2,88066 2,95987
3 2,50008 2,57508 2,65234 2,73191 2,81386 2,89828 2,98523 3,07478 3,16703 3,26204
3 ¼ 2,69521 2,78280 2,87324 2,96662 3,06304 3,16258 3,26537 3,37149 3,48107 3,59420
3 ½ 2,90503 3,00671 3,11194 3,22086 3,33359 3,45027 3,57103 3,69601 3,82537 3,95926
3 ¾ 3,13063 3,24803 3,36983 3,49619 3,62730 3,76333 3,90445 4,05087 4,20277 4,36038
31 32 33 34 35 36 37 38 39 40
4 3,37313 3,50806 3,64838 3,79432 3,94609 4,10393 4,26809 4,43881 4,61637 4,80102
4 ¼ 3,63377 3,78821 3,94921 4,11705 4,29202 4,47444 4,66460 4,86284 5,06952 5,28497
4 ½ 3,91386 4,08998 4,27403 4,46636 4,66735 4,87738 5,09686 5,32622 5,56590 5,81636
4 ¾ 4,21478 4,41498 4,62469 4,84437 5,07447 5,31551 5,56800 5,83248 6,10952 6,39972
5 4,53804 4,76494 5,00319 5,25335 5,51602 5,79182 6,08141 6,38548 6,70475 7,03999
5 ¼ 4,88523 5,14171 5,41165 5,69576 5,99479 6,30951 6,64076 6,98940 7,35634 7,74255
5 ½ 5,25807 5,54726 5,85236 6,17424 6,51383 6,87209 7,25005 7,64880 8,06949 8,51331
5 ¾ 5,65837 5,98373 6,32780 6,69164 7,07641 7,48331 7,91360 8,36863 8,84982 9,35869
6 6,08810 6,45339 6,84059 7,25103 7,68609 8,14725 8,63609 9,15425 9,70351 10.2857
6 ¼ 6,54933 6,95867 7,39358 7,85568 8,34666 8,86833 9,42260 10.0115 10.6372 11.3021
6 ½ 7,04430 7,50218 7,98982 8,50916 9,06225 9,65130 10.2786 10.9467 11.6583 12.4161
6 ¾ 7,57538 8,08672 8,63257 9,21527 9,83730 10.5013 11.2102 11.9668 12.7746 13.6369
31 32 33 34 35 36 37 38 39 40
7 8,14511 8,71527 9,32534 9,97811 10.6766 11.4239 12.2236 13.0793 13.9948 14.9745
7 ¼ 8,75621 9,39104 10.0719 10.8021 11.5853 12.4252 13.3260 14.2921 15.3283 16.4396
7 ½ 9,41158 10.1174 10.8763 11.6920 12.5689 13.5115 14.5249 15.6143 16.7853 18.0442
7 ¾ 10.1143 10.8982 11.7428 12.6528 13.6334 14.6900 15.8285 17.0552 18.3770 19.8012
8 10.8677 11.7371 12.6760 13.6901 14.7853 15.9682 17.2456 18.6253 20.1153 21.7245
8 ¼ 11.6752 12.6384 13.6811 14.8098 16.0316 17.3542 18.7859 20.3358 22.0135 23.8296
8 ½ 12.5407 13.6067 14.7632 16.0181 17.3796 18.8569 20.4597 22.1988 24.0857 26.1330
8 ¾ 13.4681 14.6466 15.9282 17.3219 18.8375 20.4858 22.2783 24.2277 26.3476 28.6530
9 14.4618 15.7633 17.1820 18.7284 20.4140 22.2512 24.2538 26.4367 28.8160 31.4094
9 ¼ 15.5262 16.9624 18.5314 20.2455 22.1182 24.1642 26.3994 28.8413 31.5091 34.4237
9 ½ 16.6662 18.2495 19.9832 21.8816 23.9604 26.2366 28.7291 31.4584 34.4469 37.7194
9 ¾ 17.8871 19.6311 21.5451 23.6458 25.9513 28.4815 31.2585 34.3062 37.6510 41.3220
10 19.1943 21.1138 23.2252 25.5477 28.1024 30.9127 34.0039 37.4043 41.1448 45.2593
19

20. VALOR FUTURO DE CANTIDAD UNICA: (1 + i) n
i% N años
41 42 43 44 45 46 47 48 49 50
1 1,50375 1,51879 1,53398 1,54932 1,56481 1,58046 1,59626 1,61223 1,62835 1,64463
1 ¼ 1,66416 1,68497 1,70603 1,72735 1,74895 1,77081 1,79294 1,81535 1,83805 1,86102
1 ½ 1,84123 1,86885 1,89688 1,92533 1,95421 1,98353 2,01328 2,04348 2,07413 2,10524
1 ¾ 2,03663 2,07227 2,10853 2,14543 2,18298 2,22118 2,26005 2,29960 2,33984 2,38079
2 2,25220 2,29724 2,34319 2,39005 2,43785 2,48661 2,53634 2,58707 2,63881 2,69159
2 ¼ 2,48998 2,54601 2,60329 2,66186 2,72176 2,78300 2,84561 2,90964 2,97511 3,04205
2 ½ 2,75219 2,82100 2,89152 2,96381 3,03790 3,11385 3,19170 3,27149 3,35328 3,43711
2 ¾ 3,04127 3,12491 3,21084 3,29914 3,38986 3,48309 3,57887 3,67729 3,77842 3,88232
3 3,35990 3,46070 3,56452 3,67145 3,78160 3,89504 4,01190 4,13225 4,25622 4,38391
3 ¼ 3,71101 3,83162 3,95615 4,08472 4,21748 4,35454 4,49607 4,64219 4,79306 4,94884
3 ½ 4,09783 4,24126 4,38970 4,54334 4,70236 4,86694 5,03728 5,21359 5,39606 5,58493
3 ¾ 4,52389 4,69354 4,86955 5,05215 5,24161 5,43817 5,64210 5,85368 6,07319 6,30094
41 42 43 44 45 46 47 48 49 50
4 4,99306 5,19278 5,40050 5,61652 5,84118 6,07482 6,31782 6,57053 6,83335 7,10668
4 ¼ 5,50958 5,74374 5,98785 6,24233 6,50763 6,78420 7,07253 7,37312 7,68647 8,01315
4 ½ 6,07810 6,35162 6,63744 6,93612 7,24825 7,57442 7,91527 8,27146 8,64367 9,03264
4 ¾ 6,70371 7,02214 7,35569 7,70508 8,07108 8,45445 8,85604 9,27670 9,71734 10.1789
5 7,39199 7,76159 8,14967 8,55715 8,98501 9,43426 9,90597 10.4013 10.9213 11.4674
5 ¼ 8,14904 8,57686 9,02715 9,50107 9,99988 10.5249 11.0774 11.6590 12.2711 12.9153
5 ½ 8,98154 9,47553 9,99668 10.5465 11.1266 11.7385 12.3841 13.0653 13.7838 14.5420
5 ¾ 9,89681 10.4659 11.0677 11.7041 12.3770 13.0887 13.8413 14.6372 15.4788 16.3689
6 10.9029 11.5570 12.2505 12.9855 13.7646 14.5905 15.4659 16.3939 17.3775 18.4202
6 ¼ 12.0084 12.7590 13.5564 14.4037 15.3039 16.2604 17.2767 18.3565 19.5037 20.7227
6 ½ 13.2231 14.0826 14.9980 15.9729 17.0111 18.1168 19.2944 20.5485 21.8842 23.3067
6 ¾ 14.5574 15.5400 16.5890 17.7087 18.9040 20.1801 21.5422 22.9963 24.5486 26.2056
41 42 43 44 45 46 47 48 49 50
7 16.0227 17.1443 18.3444 19.6285 21.0025 22.4726 24.0457 25.7289 27.5299 29.4570
7 ¼ 17.6315 18.9098 20.2807 21.7511 23.3281 25.0193 26.8332 28.7787 30.8651 33.1028
7 ½ 19.3976 20.8524 22.4163 24.0975 25.9048 27.8477 29.9363 32.1815 34.5951 37.1897
7 ¾ 21.3358 22.9893 24.7710 26.6907 28.7592 30.9881 33.3897 35.9774 38.7656 41.7699
8 23.4625 25.3395 27.3666 29.5560 31.9204 34.4741 37.2320 40.2106 43.4274 46.9016
8 ¼ 25.7955 27.9236 30.2273 32.7211 35.4206 38.3428 41.5061 44.9303 48.6371 52.6496
8 ½ 28.3543 30.7644 33.3794 36.2167 39.2951 42.6352 46.2592 50.1912 54.4574 59.0863
8 ¾ 31.1602 33.8867 36.8518 40.0763 43.5830 47.3965 51.5437 56.0538 60.9585 66.2923
9 34.2363 37.3175 40.6761 44.3370 48.3273 52.6767 57.4176 62.5852 68.2179 74.3575
9 ¼ 37.6079 41.0866 44.8872 49.0392 53.5754 58.5311 63.9452 69.8601 76.3222 83.3820
9 ½ 41.3027 45.2265 49.5230 54.2277 59.3793 65.0204 71.1973 77.9611 85.3674 93.4773
9 ¾ 45.3509 49.7726 54.6254 59.9514 65.7967 72.2118 79.2525 86.9796 95.4601 104.767
10 49.7852 54.7637 60.2401 66.2641 72.8905 80.1795 88.1975 97.0172 106.719 117.391
20