Discrete Compounding Table 1m5d3r

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APPENDIX

B

End-of-Period Compound Interest Tables Tables Included in Appendix .25% 3% 9% 15% 25% 70%

.50% 4% 10% 16% 30% 80%

.75% 5% 11% 17% 35% 90%

1% 6% 12% 18% 40% 100%

1.5% 7% 13% 19% 50%

2% 8% 14% 20% 60%

Limits of the Factors Factor

(F/P,i,N ) (P/F,i, N) (A/P,i, N ) (P/A,i, N ) (A/F,i, N) (F/A,i, N) (P/G,i, N) (A/G, i, N )

When N = ∞

When i = 0

∞ 0 i 1/i 0 ∞ 1/i2 1/i

1 1 1/N N 1/N N N(N − 1)/2 (N − 1)/2

551

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END-OF-PERIOD COMPOUND INTEREST TABLES

0.25%

End-of-Period Compound Interest Factors Single Payment

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞

Compound Amount Factor F/P 1.003 1.005 1.008 1.010 1.013 1.015 1.018 1.020 1.023 1.025 1.028 1.030 1.033 1.036 1.038 1.041 1.043 1.046 1.049 1.051 1.054 1.056 1.059 1.062 1.064 1.067 1.070 1.072 1.075 1.078 1.080 1.083 1.086 1.089 1.091 1.094 1.105 1.127 1.133 1.162 1.191 1.197 1.221 1.252 1.284 1.349 1.821 2.457 3.315 ∞

Present Worth Factor P/F .9975 .9950 .9925 .9901 .9876 .9851 .9827 .9802 .9778 .9753 .9729 .9705 .9681 .9656 .9632 .9608 .9584 .9561 .9537 .9513 .9489 .9466 .9442 .9418 .9395 .9371 .9348 .9325 .9301 .9278 .9255 .9232 .9209 .9186 .9163 .9140 .9050 .8871 .8826 .8609 .8396 .8355 .8189 .7987 .7790 .7411 .5492 .4070 .3016 0

Uniform Payment Series

0.25% Arithmetic Gradient

Capital Recovery Factor A/P

Present Worth Factor P/A

Sinking Fund Factor A/F

Compound Amount Factor F/A

Present Worth Factor P/G

Uniform Payment Factor A/G

N

1.0025 .5019 .3350 .2516 .2015 .1681 .1443 .1264 .1125 .1014 .0923 .0847 .0783 .0728 .0680 .0638 .0602 .0569 .0540 .0513 .0489 .0468 .0448 .0430 .0413 .0398 .0383 .0370 .0358 .0346 .0336 .0326 .0316 .0307 .0299 .0291 .0263 .0221 .0213 .0180 .0156 .0152 .0138 .0124 .0113 .00966 .00555 .00422 .00358 .0025

.998 1.993 2.985 3.975 4.963 5.948 6.931 7.911 8.889 9.864 10.837 11.807 12.775 13.741 14.704 15.665 16.623 17.580 18.533 19.484 20.433 21.380 22.324 23.266 24.205 25.143 26.077 27.010 27.940 28.868 29.793 30.717 31.638 32.556 33.472 34.386 38.020 45.179 46.946 55.652 64.144 65.817 72.426 80.504 88.382 103.6 180.3 237.2 279.3 400

1.0000 .4994 .3325 .2491 .1990 .1656 .1418 .1239 .1100 .0989 .0898 .0822 .0758 .0703 .0655 .0613 .0577 .0544 .0515 .0488 .0464 .0443 .0423 .0405 .0388 .0373 .0358 .0345 .0333 .0321 .0311 .0301 .0291 .0282 .0274 .0266 .0238 .0196 .0188 .0155 .0131 .0127 .0113 .00992 .00881 .00716 .00305 .00172 .00108 0

1.000 2.002 3.008 4.015 5.025 6.038 7.053 8.070 9.091 10.113 11.139 12.166 13.197 14.230 15.265 16.304 17.344 18.388 19.434 20.482 21.533 22.587 23.644 24.703 25.765 26.829 27.896 28.966 30.038 31.113 32.191 33.272 34.355 35.441 36.529 37.621 42.013 50.931 53.189 64.647 76.394 78.779 88.439 100.8 113.4 139.7 328.3 582.7 926.1 ∞

0 .995 2.980 5.950 9.901 14.826 20.722 27.584 35.406 44.184 53.913 64.589 76.205 88.759 102.244 116.657 131.992 148.245 165.411 183.485 202.463 222.341 243.113 264.775 287.323 310.752 335.057 360.233 386.278 413.185 440.950 469.570 499.039 529.353 560.508 592.499 728.740 1040.055 1125.777 1600 2148 2266 2764 3447 4191 5852 19399 36264 53821 160000

0 .499 .998 1.497 1.995 2.493 2.990 3.487 3.983 4.479 4.975 5.470 5.965 6.459 6.953 7.447 7.940 8.433 8.925 9.417 9.908 10.400 10.890 11.380 11.870 12.360 12.849 13.337 13.825 14.313 14.800 15.287 15.774 16.260 16.745 17.231 19.167 23.021 23.980 28.751 33.481 34.422 38.169 42.816 47.422 56.508 107.586 152.890 192.670 400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞

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END-OF-PERIOD COMPOUND INTEREST TABLES 0.50%


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞


553 0.50%

Arithmetic Gradient

Compound Amount Factor F/P

Present Worth Factor P/F






1.005 1.010 1.015 1.020 1.025 1.030 1.036 1.041 1.046 1.051 1.056 1.062 1.067 1.072 1.078 1.083 1.088 1.094 1.099 1.105 1.110 1.116 1.122 1.127 1.133 1.138 1.144 1.150 1.156 1.161 1.167 1.173 1.179 1.185 1.191 1.197 1.221 1.270 1.283 1.349 1.418 1.432 1.490 1.567 1.647 1.819 3.310 6.023 10.957 ∞

.9950 .9901 .9851 .9802 .9754 .9705 .9657 .9609 .9561 .9513 .9466 .9419 .9372 .9326 .9279 .9233 .9187 .9141 .9096 .9051 .9006 .8961 .8916 .8872 .8828 .8784 .8740 .8697 .8653 .8610 .8567 .8525 .8482 .8440 .8398 .8356 .8191 .7871 .7793 .7414 .7053 .6983 .6710 .6383 .6073 .5496 .3021 .1660 .0913 0

1.0050 .5038 .3367 .2531 .2030 .1696 .1457 .1278 .1139 .1028 .0937 .0861 .0796 .0741 .0694 .0652 .0615 .0582 .0553 .0527 .0503 .0481 .0461 .0443 .0427 .0411 .0397 .0384 .0371 .0360 .0349 .0339 .0329 .0321 .0312 .0304 .0276 .0235 .0227 .0193 .0170 .0166 .0152 .0138 .0127 .0111 .00716 .00600 .00550 .005

.995 1.985 2.970 3.950 4.926 5.896 6.862 7.823 8.779 9.730 10.677 11.619 12.556 13.489 14.417 15.340 16.259 17.173 18.082 18.987 19.888 20.784 21.676 22.563 23.446 24.324 25.198 26.068 26.933 27.794 28.651 29.503 30.352 31.196 32.035 32.871 36.172 42.580 44.143 51.726 58.939 60.340 65.802 72.331 78.543 90.073 139.6 166.8 181.7 200

1.0000 .4988 .3317 .2481 .1980 .1646 .1407 .1228 .1089 .0978 .0887 .0811 .0746 .0691 .0644 .0602 .0565 .0532 .0503 .0477 .0453 .0431 .0411 .0393 .0377 .0361 .0347 .0334 .0321 .0310 .0299 .0289 .0279 .0271 .0262 .0254 .0226 .0185 .0177 .0143 .0120 .0116 .0102 .00883 .00773 .00610 .00216 .00100 .00050 0

1.000 2.005 3.015 4.030 5.050 6.076 7.106 8.141 9.182 10.228 11.279 12.336 13.397 14.464 15.537 16.614 17.697 18.786 19.880 20.979 22.084 23.194 24.310 25.432 26.559 27.692 28.830 29.975 31.124 32.280 33.441 34.609 35.782 36.961 38.145 39.336 44.159 54.098 56.645 69.770 83.566 86.409 98.068 113.3 129.3 163.9 462.0 1004.5 1991.5 ∞

0 .990 2.960 5.901 9.803 14.655 20.449 27.176 34.824 43.386 52.853 63.214 74.460 86.583 99.574 113.424 128.123 143.663 160.036 177.232 195.243 214.061 233.677 254.082 275.269 297.228 319.952 343.433 367.663 392.632 418.335 444.762 471.906 499.758 528.312 557.560 681.335 959.919 1035.697 1449 1914 2012 2425 2976 3563 4824 13416 21403 27588 40000

Uniform Payment Factor A/G 0 .499 .997 1.494 1.990 2.485 2.980 3.474 3.967 4.459 4.950 5.441 5.930 6.419 6.907 7.394 7.880 8.366 8.850 9.334 9.817 10.299 10.781 11.261 11.741 12.220 12.698 13.175 13.651 14.126 14.601 15.075 15.548 16.020 16.492 16.962 18.836 22.544 23.462 28.006 32.468 33.350 36.847 41.145 45.361 53.551 96.113 128.324 151.795 200

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞

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0.75%


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞










1.008 1.015 1.023 1.030 1.038 1.046 1.054 1.062 1.070 1.078 1.086 1.094 1.102 1.110 1.119 1.127 1.135 1.144 1.153 1.161 1.170 1.179 1.188 1.196 1.205 1.214 1.224 1.233 1.242 1.251 1.261 1.270 1.280 1.289 1.299 1.309 1.348 1.431 1.453 1.566 1.687 1.713 1.818 1.959 2.111 2.451 6.009 14.73 36.11 ∞

.9926 .9852 .9778 .9706 .9633 .9562 .9490 .9420 .9350 .9280 .9211 .9142 .9074 .9007 .8940 .8873 .8807 .8742 .8676 .8612 .8548 .8484 .8421 .8358 .8296 .8234 .8173 .8112 .8052 .7992 .7932 .7873 .7815 .7757 .7699 .7641 .7416 .6986 .6883 .6387 .5927 .5839 .5500 .5104 .4737 .4079 .1664 .06789 .02769

1.0075 .5056 .3383 .2547 .2045 .1711 .1472 .1293 .1153 .1042 .0951 .0875 .0810 .0755 .0707 .0666 .0629 .0596 .0567 .0540 .0516 .0495 .0475 .0457 .0440 .0425 .0411 .0397 .0385 .0373 .0363 .0353 .0343 .0334 .0326 .0318 .0290 .0249 .0241 .0208 .0184 .0180 .0167 .0153 .0143 .0127 .00900 .00805 .00771 .0075

.993 1.978 2.956 3.926 4.889 5.846 6.795 7.737 8.672 9.600 10.521 11.435 12.342 13.243 14.137 15.024 15.905 16.779 17.647 18.508 19.363 20.211 21.053 21.889 22.719 23.542 24.359 25.171 25.976 26.775 27.568 28.356 29.137 29.913 30.683 31.447 34.447 40.185 41.566 48.173 54.305 55.477 59.994 65.275 70.175 78.942 111.145 124.282 129.641 133.333

1.0000 .4981 .3308 .2472 .1970 .1636 .1397 .1218 .1078 .0967 .0876 .0800 .0735 .0680 .0632 .0591 .0554 .0521 .0492 .0465 .0441 .0420 .0400 .0382 .0365 .0350 .0336 .0322 .0310 .0298 .0288 .0278 .0268 .0259 .0251 .0243 .0215 .0174 .0166 .0133 .0109 .0105 .00917 .00782 .00675 .00517 .001497 .000546 .000214 0

1.000 2.008 3.023 4.045 5.076 6.114 7.159 8.213 9.275 10.344 11.422 12.508 13.601 14.703 15.814 16.932 18.059 19.195 20.339 21.491 22.652 23.822 25.001 26.188 27.385 28.590 29.805 31.028 32.261 33.503 34.754 36.015 37.285 38.565 39.854 41.153 46.446 57.521 60.394 75.424 91.620 95.007 109.1 127.9 148.1 193.5 668 1831 4681 ∞

0

0

.985 2.941 5.852 9.706 14.487 20.181 26.775 34.254 42.606 51.817 61.874 72.763 84.472 96.988 110.297 124.389 139.249 154.867 171.230 188.325 206.142 224.668 243.892 263.803 284.389 305.639 327.542 350.087 373.263 397.060 421.468 446.475 472.071 498.247 524.992 637.469 886.840 953.849 1314 1709 1791 2132 2578 3041 3999 9494 13312 15513 17778

Uniform Payment Factor A/G 0 .498 .995 1.491 1.985 2.478 2.970 3.461 3.950 4.438 4.925 5.411 5.895 6.379 6.861 7.341 7.821 8.299 8.776 9.252 9.726 10.199 10.671 11.142 11.612 12.080 12.547 13.013 13.477 13.941 14.403 14.864 15.323 15.782 16.239 16.695 18.506 22.069 22.948 27.266 31.463 32.288 35.539 39.495 43.331 50.652 85.421 107.114 119.662 133.333

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞

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END-OF-PERIOD COMPOUND INTEREST TABLES 1%


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞


1% Arithmetic Gradient








1.010 1.020 1.030 1.041 1.051 1.062 1.072 1.083 1.094 1.105 1.116 1.127 1.138 1.149 1.161 1.173 1.184 1.196 1.208 1.220 1.232 1.245 1.257 1.270 1.282 1.295 1.308 1.321 1.335 1.348 1.361 1.375 1.389 1.403 1.417 1.431 1.489 1.612 1.645 1.817 2.007 2.047 2.217 2.449 2.705 3.300 10.89 35.95 118.65 ∞

.9901 .9803 .9706 .9610 .9515 .9420 .9327 .9235 .9143 .9053 .8963 .8874 .8787 .8700 .8613 .8528 .8444 .8360 .8277 .8195 .8114 .8034 .7954 .7876 .7798 .7720 .7644 .7568 .7493 .7419 .7346 .7273 .7201 .7130 .7059 .6989 .6717 .6203 .6080 .5504 .4983 .4885 .4511 .4084 .3697 .3030 .09181 .02782 .00843

1.0100 .5075 .3400 .2563 .2060 .1725 .1486 .1307 .1167 .1056 .0965 .0888 .0824 .0769 .0721 .0679 .0643 .0610 .0581 .0554 .0530 .0509 .0489 .0471 .0454 .0439 .0424 .0411 .0399 .0387 .0377 .0367 .0357 .0348 .0340 .0332 .0305 .0263 .0255 .0222 .0199 .0196 .0182 .0169 .0159 .0143 .0110 .0103 .0101 .01

.990 1.970 2.941 3.902 4.853 5.795 6.728 7.652 8.566 9.471 10.368 11.255 12.134 13.004 13.865 14.718 15.562 16.398 17.226 18.046 18.857 19.660 20.456 21.243 22.023 22.795 23.560 24.316 25.066 25.808 26.542 27.270 27.990 28.703 29.409 30.108 32.835 37.974 39.196 44.955 50.169 51.150 54.888 59.161 63.029 69.701 90.819 97.218 99.157 100

1.0000 .4975 .3300 .2463 .1960 .1625 .1386 .1207 .1067 .0956 .0865 .0788 .0724 .0669 .0621 .0579 .0543 .0510 .0481 .0454 .0430 .0409 .0389 .0371 .0354 .0339 .0324 .0311 .0299 .0287 .0277 .0267 .0257 .0248 .0240 .0232 .0205 .0163 .0155 .0122 .00993 .00955 .00822 .00690 .00587 .00435 .00101 .000286 .000085 0

1.000 2.010 3.030 4.060 5.101 6.152 7.214 8.286 9.369 10.462 11.567 12.683 13.809 14.947 16.097 17.258 18.430 19.615 20.811 22.019 23.239 24.472 25.716 26.973 28.243 29.526 30.821 32.129 33.450 34.785 36.133 37.494 38.869 40.258 41.660 43.077 48.886 61.223 64.463 81.670 100.7 104.7 121.7 144.9 170.5 230.0 989 3495 11765 ∞

0

0

555

.980 2.921 5.804 9.610 14.321 19.917 26.381 33.696 41.843 50.807 60.569 71.113 82.422 94.481 107.273 120.783 134.996 149.895 165.466 181.695 198.566 216.066 234.180 252.894 272.196 292.070 312.505 333.486 355.002 377.039 399.586 422.629 446.157 470.158 494.621 596.856 820.146 879.418 1192.806 1528.647 1597.867 1879.877 2240.567 2605.776 3334.115 6878.602 8720.432 9511.158 10000


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞

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1.5%


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞











N

1.015 1.030 1.046 1.061 1.077 1.093 1.110 1.126 1.143 1.161 1.178 1.196 1.214 1.232 1.250 1.269 1.288 1.307 1.327 1.347 1.367 1.388 1.408 1.430 1.451 1.473 1.495 1.517 1.540 1.563 1.587 1.610 1.634 1.659 1.684 1.709 1.814 2.043 2.105 2.443 2.835 2.921 3.291 3.819 4.432 5.969 35.63 212.70 1269.70 ∞

.9852 .9707 .9563 .9422 .9283 .9145 .9010 .8877 .8746 .8617 .8489 .8364 .8240 .8118 .7999 .7880 .7764 .7649 .7536 .7425 .7315 .7207 .7100 .6995 .6892 .6790 .6690 .6591 .6494 .6398 .6303 .6210 .6118 .6028 .5939 .5851 .5513 .4894 .4750 .4093 .3527 .3423 .3039 .2619 .2256 .1675 .02806 .00470 .00079

1.0150 .5113 .3434 .2594 .2091 .1755 .1516 .1336 .1196 .1084 .0993 .0917 .0852 .0797 .0749 .0708 .0671 .0638 .0609 .0582 .0559 .0537 .0517 .0499 .0483 .0467 .0453 .0440 .0428 .0416 .0406 .0396 .0386 .0378 .0369 .0362 .0334 .0294 .0286 .0254 .0232 .0228 .0215 .0203 .0194 .0180 .0154 .0151 .0150 .015

.985 1.956 2.912 3.854 4.783 5.697 6.598 7.486 8.361 9.222 10.071 10.908 11.732 12.543 13.343 14.131 14.908 15.673 16.426 17.169 17.900 18.621 19.331 20.030 20.720 21.399 22.068 22.727 23.376 24.016 24.646 25.267 25.879 26.482 27.076 27.661 29.916 34.043 35.000 39.380 43.155 43.845 46.407 49.210 51.625 55.498 64.796 66.353 66.614 66.667

1.0000 .4963 .3284 .2444 .1941 .1605 .1366 .1186 .1046 .0934 .0843 .0767 .0702 .0647 .0599 .0558 .0521 .0488 .0459 .0432 .0409 .0387 .0367 .0349 .0333 .0317 .0303 .0290 .0278 .0266 .0256 .0246 .0236 .0228 .0219 .0212 .0184 .0144 .0136 .0104 .00817 .00781 .00655 .00532 .00437 .00302 .000433 .000071 .000012 0

1.000 2.015 3.045 4.091 5.152 6.230 7.323 8.433 9.559 10.703 11.863 13.041 14.237 15.450 16.682 17.932 19.201 20.489 21.797 23.124 24.471 25.838 27.225 28.634 30.063 31.514 32.987 34.481 35.999 37.539 39.102 40.688 42.299 43.933 45.592 47.276 54.268 69.565 73.683 96.215 122.4 128.1 152.7 187.9 228.8 331.3 2309 14114 84580 ∞

0 .971 2.883 5.710 9.423 13.996 19.402 25.616 32.612 40.367 48.857 58.057 67.945 78.499 89.697 101.518 113.940 126.943 140.508 154.615 169.245 184.380 200.001 216.090 232.631 249.607 267.000 284.796 302.978 321.531 340.440 359.691 379.269 399.161 419.352 439.830 524.357 703.546 749.964 988.167 1231.166 1279.794 1473.074 1709.544 1937.451 2359.711 3870.691 4310.716 4415.741 4444.444

0 .496 .990 1.481 1.970 2.457 2.940 3.422 3.901 4.377 4.851 5.323 5.792 6.258 6.722 7.184 7.643 8.100 8.554 9.006 9.455 9.902 10.346 10.788 11.228 11.665 12.099 12.531 12.961 13.388 13.813 14.236 14.656 15.073 15.488 15.901 17.528 20.667 21.428 25.093 28.529 29.189 31.742 34.740 37.530 42.519 59.737 64.966 66.288 66.667

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞

0

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞


557 2%

Arithmetic Gradient








1.020 1.040 1.061 1.082 1.104 1.126 1.149 1.172 1.195 1.219 1.243 1.268 1.294 1.319 1.346 1.373 1.400 1.428 1.457 1.486 1.516 1.546 1.577 1.608 1.641 1.673 1.707 1.741 1.776 1.811 1.848 1.885 1.922 1.961 2.000 2.040 2.208 2.587 2.692 3.281 4.000 4.161 4.875 5.943 7.245 10.765 115.889 1248 13430 ∞

.9804 .9612 .9423 .9238 .9057 .8880 .8706 .8535 .8368 .8203 .8043 .7885 .7730 .7579 .7430 .7284 .7142 .7002 .6864 .6730 .6598 .6468 .6342 .6217 .6095 .5976 .5859 .5744 .5631 .5521 .5412 .5306 .5202 .5100 .5000 .4902 .4529 .3865 .3715 .3048 .2500 .2403 .2051 .1683 .1380 .0929 .00863 .00080 .00007 0

1.0200 .5150 .3468 .2626 .2122 .1785 .1545 .1365 .1225 .1113 .1022 .0946 .0881 .0826 .0778 .0737 .0700 .0667 .0638 .0612 .0588 .0566 .0547 .0529 .0512 .0497 .0483 .0470 .0458 .0446 .0436 .0426 .0417 .0408 .0400 .0392 .0366 .0326 .0318 .0288 .0267 .0263 .0252 .0240 .0232 .0220 .0202 .0200 .0200 .02

.980 1.942 2.884 3.808 4.713 5.601 6.472 7.325 8.162 8.983 9.787 10.575 11.348 12.106 12.849 13.578 14.292 14.992 15.678 16.351 17.011 17.658 18.292 18.914 19.523 20.121 20.707 21.281 21.844 22.396 22.938 23.468 23.989 24.499 24.999 25.489 27.355 30.673 31.424 34.761 37.499 37.984 39.745 41.587 43.098 45.355 49.569 49.960 49.996 50.

1.0000 .4950 .3268 .2426 .1922 .1585 .1345 .1165 .1025 .0913 .0822 .0746 .0681 .0626 .0578 .0537 .0500 .0467 .0438 .0412 .0388 .0366 .0347 .0329 .0312 .0297 .0283 .0270 .0258 .0246 .0236 .0226 .0217 .0208 .0200 .0192 .0166 .0126 .0118 .00877 .00667 .00633 .00516 .00405 .00320 .00205 .00017 .0000160 .0000015 0

1.000 2.020 3.060 4.122 5.204 6.308 7.434 8.583 9.755 10.950 12.169 13.412 14.680 15.974 17.293 18.639 20.012 21.412 22.841 24.297 25.783 27.299 28.845 30.422 32.030 33.671 35.344 37.051 38.792 40.568 42.379 44.227 46.112 48.034 49.994 51.994 60.402 79.354 84.579 114.1 150.0 158.1 193.8 247.2 312.2 488.3 5744 62328 671460 ∞

0 .961 2.846 5.617 9.240 13.680 18.903 24.878 31.572 38.955 46.998 55.671 64.948 74.800 85.202 96.129 107.555 119.458 131.814 144.600 157.796 171.379 185.331 199.630 214.259 229.199 244.431 259.939 275.706 291.716 307.954 324.403 341.051 357.882 374.883 392.040 461.993 605.966 642.361 823.698 999.834 1034.056 1166.787 1322.170 1464.753 1710.416 2374.880 2483.568 2498.027 2500


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40 48 50 60 70 72 80 90 100 120 240 360 480 ∞

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞










1.030 1.061 1.093 1.126 1.159 1.194 1.230 1.267 1.305 1.344 1.384 1.426 1.469 1.513 1.558 1.605 1.653 1.702 1.754 1.806 1.860 1.916 1.974 2.033 2.094 2.157 2.221 2.288 2.357 2.427 2.500 2.575 2.652 2.732 2.814 3.262 3.782 4.384 5.082 5.892 6.830 7.918 9.179 10.641 12.336 14.300 16.578 19.219 ∞

.9709 .9426 .9151 .8885 .8626 .8375 .8131 .7894 .7664 .7441 .7224 .7014 .6810 .6611 .6419 .6232 .6050 .5874 .5703 .5537 .5375 .5219 .5067 .4919 .4776 .4637 .4502 .4371 .4243 .4120 .4000 .3883 .3770 .3660 .3554 .3066 .2644 .2281 .1968 .1697 .1464 .1263 .1089 .0940 .0811 .0699 .0603 .0520

1.0300 .5226 .3535 .2690 .2184 .1846 .1605 .1425 .1284 .1172 .1081 .1005 .0940 .0885 .0838 .0796 .0760 .0727 .0698 .0672 .0649 .0627 .0608 .0590 .0574 .0559 .0546 .0533 .0521 .0510 .0500 .0490 .0482 .0473 .0465 .0433 .0408 .0389 .0373 .0361 .0351 .0343 .0337 .0331 .0326 .0323 .0319 .0316 .03

.971 1.913 2.829 3.717 4.580 5.417 6.230 7.020 7.786 8.530 9.253 9.954 10.635 11.296 11.938 12.561 13.166 13.754 14.324 14.877 15.415 15.937 16.444 16.936 17.413 17.877 18.327 18.764 19.188 19.600 20.000 20.389 20.766 21.132 21.487 23.115 24.519 25.730 26.774 27.676 28.453 29.123 29.702 30.201 30.631 31.002 31.323 31.599 33.333

1.0000 .4926 .3235 .2390 .1884 .1546 .1305 .1125 .0984 .0872 .0781 .0705 .0640 .0585 .0538 .0496 .0460 .0427 .0398 .0372 .0349 .0327 .0308 .0290 .0274 .0259 .0246 .0233 .0221 .0210 .0200 .0190 .0182 .0173 .0165 .0133 .0108 .00887 .00735 .00613 .00515 .00434 .00367 .00311 .00265 .00226 .00193 .00165 0

1.000 2.030 3.091 4.184 5.309 6.468 7.662 8.892 10.159 11.464 12.808 14.192 15.618 17.086 18.599 20.157 21.762 23.414 25.117 26.870 28.676 30.537 32.453 34.426 36.459 38.553 40.710 42.931 45.219 47.575 50.003 52.503 55.078 57.730 60.462 75.401 92.720 112.8 136.1 163.1 194.3 230.6 272.6 321.4 377.9 443.3 519.3 607.3 ∞

0

0

.943 2.773 5.438 8.889 13.076 17.955 23.481 29.612 36.309 43.533 51.248 59.420 68.014 77.000 86.348 96.028 106.014 116.279 126.799 137.550 148.509 159.657 170.971 182.434 194.026 205.731 217.532 229.414 241.361 253.361 265.399 277.464 289.544 301.627 361.750 420.632 477.480 531.741 583.053 631.201 676.087 717.698 756.087 791.353 823.630 853.074 879.854 1111.111

Uniform Payment Factor A/G 0 .493 .980 1.463 1.941 2.414 2.882 3.345 3.803 4.256 4.705 5.148 5.587 6.021 6.450 6.874 7.294 7.708 8.118 8.523 8.923 9.319 9.709 10.095 10.477 10.853 11.226 11.593 11.956 12.314 12.668 13.017 13.362 13.702 14.037 15.650 17.156 18.558 19.860 21.067 22.184 23.215 24.163 25.035 25.835 26.567 27.235 27.844 33.333

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞


559 4%

Arithmetic Gradient







1.040 1.082 1.125 1.170 1.217 1.265 1.316 1.369 1.423 1.480 1.539 1.601 1.665 1.732 1.801 1.873 1.948 2.026 2.107 2.191 2.279 2.370 2.465 2.563 2.666 2.772 2.883 2.999 3.119 3.243 3.373 3.508 3.648 3.794 3.946 4.801 5.841 7.107 8.646 10.520 12.799 15.572 18.945 23.050 28.044 34.119 41.511 50.505 ∞

.9615 .9246 .8890 .8548 .8219 .7903 .7599 .7307 .7026 .6756 .6496 .6246 .6006 .5775 .5553 .5339 .5134 .4936 .4746 .4564 .4388 .4220 .4057 .3901 .3751 .3607 .3468 .3335 .3207 .3083 .2965 .2851 .2741 .2636 .2534 .2083 .1712 .1407 .1157 .0951 .0781 .0642 .0528 .0434 .0357 .0293 .0241 .0198 0

1.0400 .5302 .3603 .2755 .2246 .1908 .1666 .1485 .1345 .1233 .1141 .1066 .1001 .0947 .0899 .0858 .0822 .0790 .0761 .0736 .0713 .0692 .0673 .0656 .0640 .0626 .0612 .0600 .0589 .0578 .0569 .0559 .0551 .0543 .0536 .0505 .0483 .0466 .0452 .0442 .0434 .0427 .0422 .0418 .0415 .0412 .0410 .0408 .04

.962 1.886 2.775 3.630 4.452 5.242 6.002 6.733 7.435 8.111 8.760 9.385 9.986 10.563 11.118 11.652 12.166 12.659 13.134 13.590 14.029 14.451 14.857 15.247 15.622 15.983 16.330 16.663 16.984 17.292 17.588 17.874 18.148 18.411 18.665 19.793 20.720 21.482 22.109 22.623 23.047 23.395 23.680 23.915 24.109 24.267 24.398 24.505 25

1.0000 .4902 .3203 .2355 .1846 .1508 .1266 .1085 .0945 .0833 .0741 .0666 .0601 .0547 .0499 .0458 .0422 .0390 .0361 .0336 .0313 .0292 .0273 .0256 .0240 .0226 .0212 .0200 .0189 .0178 .0169 .0159 .0151 .0143 .0136 .0105 .00826 .00655 .00523 .00420 .00339 .00275 .00223 .00181 .00148 .00121 .000987 .000808 0

1.000 2.040 3.122 4.246 5.416 6.633 7.898 9.214 10.583 12.006 13.486 15.026 16.627 18.292 20.024 21.825 23.698 25.645 27.671 29.778 31.969 34.248 36.618 39.083 41.646 44.312 47.084 49.968 52.966 56.085 59.328 62.701 66.210 69.858 73.652 95.026 121.0 152.7 191.2 238.0 295.0 364.3 448.6 551.2 676.1 828.0 1013 1238 ∞

Present Worth Factor P/G 0 .925 2.703 5.267 8.555 12.506 17.066 22.181 27.801 33.881 40.377 47.248 54.455 61.962 69.735 77.744 85.958 94.350 102.893 111.565 120.341 129.202 138.128 147.101 156.104 165.121 174.138 183.142 192.121 201.062 209.956 218.792 227.563 236.261 244.877 286.530 325.403 361.164 393.689 422.997 449.201 472.479 493.041 511.116 526.938 540.737 552.731 563.125 625


N

0 .490 .974 1.451 1.922 2.386 2.843 3.294 3.739 4.177 4.609 5.034 5.453 5.866 6.272 6.672 7.066 7.453 7.834 8.209 8.578 8.941 9.297 9.648 9.993 10.331 10.664 10.991 11.312 11.627 11.937 12.241 12.540 12.832 13.120 14.477 15.705 16.812 17.807 18.697 19.491 20.196 20.821 21.372 21.857 22.283 22.655 22.980 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞


Arithmetic Gradient







1.050 1.103 1.158 1.216 1.276 1.340 1.407 1.477 1.551 1.629 1.710 1.796 1.886 1.980 2.079 2.183 2.292 2.407 2.527 2.653 2.786 2.925 3.072 3.225 3.386 3.556 3.733 3.920 4.116 4.322 4.538 4.765 5.003 5.253 5.516 7.040 8.985 11.467 14.636 18.679 23.840 30.426 38.833 49.561 63.254 80.730 103.0 131.5 ∞

.9524 .9070 .8638 .8227 .7835 .7462 .7107 .6768 .6446 .6139 .5847 .5568 .5303 .5051 .4810 .4581 .4363 .4155 .3957 .3769 .3589 .3418 .3256 .3101 .2953 .2812 .2678 .2551 .2429 .2314 .2204 .2099 .1999 .1904 .1813 .1420 .1113 .0872 .0683 .0535 .0419 .0329 .0258 .0202 .0158 .0124 .00971 .00760

1.0500 .5378 .3672 .2820 .2310 .1970 .1728 .1547 .1407 .1295 .1204 .1128 .1065 .1010 .0963 .0923 .0887 .0855 .0827 .0802 .0780 .0760 .0741 .0725 .0710 .0696 .0683 .0671 .0660 .0651 .0641 .0633 .0625 .0618 .0611 .0583 .0563 .0548 .0537 .0528 .0522 .0517 .0513 .0510 .0508 .0506 .0505 .0504 .05

.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 12.821 13.163 13.489 13.799 14.094 14.375 14.643 14.898 15.141 15.372 15.593 15.803 16.003 16.193 16.374 17.159 17.774 18.256 18.633 18.929 19.161 19.343 19.485 19.596 19.684 19.752 19.806 19.848 20

1.0000 .4878 .3172 .2320 .1810 .1470 .1228 .1047 .0907 .0795 .0704 .0628 .0565 .0510 .0463 .0423 .0387 .0355 .0327 .0302 .0280 .0260 .0241 .0225 .0210 .0196 .0183 .0171 .0160 .0151 .0141 .0133 .0125 .0118 .0111 .00828 .00626 .00478 .00367 .00283 .00219 .00170 .00132 .00103 .000803 .000627 .000490 .000383 0

1.000 2.050 3.153 4.310 5.526 6.802 8.142 9.549 11.027 12.578 14.207 15.917 17.713 19.599 21.579 23.657 25.840 28.132 30.539 33.066 35.719 38.505 41.430 44.502 47.727 51.113 54.669 58.403 62.323 66.439 70.761 75.299 80.064 85.067 90.320 120.8 159.7 209.3 272.7 353.6 456.8 588.5 756.7 971.2 1245 1595 2041 2610 ∞

0

5%


Uniform Payment Factor A/G 0 .488 .967 1.439 1.903 2.358 2.805 3.245 3.676 4.099 4.514 4.922 5.322 5.713 6.097 6.474 6.842 7.203 7.557 7.903 8.242 8.573 8.897 9.214 9.524 9.827 10.122 10.411 10.694 10.969 11.238 11.501 11.757 12.006 12.250 13.377 14.364 15.223 15.966 16.606 17.154 17.621 18.018 18.353 18.635 18.871 19.069 19.234 20

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞









1.060 1.124 1.191 1.262 1.338 1.419 1.504 1.594 1.689 1.791 1.898 2.012 2.133 2.261 2.397 2.540 2.693 2.854 3.026 3.207 3.400 3.604 3.820 4.049 4.292 4.549 4.822 5.112 5.418 5.743 6.088 6.453 6.841 7.251 7.686 10.286 13.765 18.420 24.650 32.988 44.145 59.076 79.057 105.8 141.6 189.5 253.5 339.3 ∞

.9434 .8900 .8396 .7921 .7473 .7050 .6651 .6274 .5919 .5584 .5268 .4970 .4688 .4423 .4173 .3936 .3714 .3503 .3305 .3118 .2942 .2775 .2618 .2470 .2330 .2198 .2074 .1956 .1846 .1741 .1643 .1550 .1462 .1379 .1301 .0972 .0727 .0543 .0406 .0303 .0227 .0169 .0126 .00945 .00706 .00528 .00394 .00295

1.0600 .5454 .3741 .2886 .2374 .2034 .1791 .1610 .1470 .1359 .1268 .1193 .1130 .1076 .1030 .0990 .0954 .0924 .0896 .0872 .0850 .0830 .0813 .0797 .0782 .0769 .0757 .0746 .0736 .0726 .0718 .0710 .0703 .0696 .0690 .0665 .0647 .0634 .0625 .0619 .0614 .0610 .0608 .0606 .0604 .0603 .0602 .0602 .06

.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9.712 10.106 10.477 10.828 11.158 11.470 11.764 12.042 12.303 12.550 12.783 13.003 13.211 13.406 13.591 13.765 13.929 14.084 14.230 14.368 14.498 15.046 15.456 15.762 15.991 16.161 16.289 16.385 16.456 16.509 16.549 16.579 16.601 16.618 16.667

1.0000 .4854 .3141 .2286 .1774 .1434 .1191 .1010 .0870 .0759 .0668 .0593 .0530 .0476 .0430 .0390 .0354 .0324 .0296 .0272 .0250 .0230 .0213 .0197 .0182 .0169 .0157 .0146 .0136 .0126 .0118 .0110 .0103 .00960 .00897 .00646 .00470 .00344 .00254 .00188 .00139 .00103 .000769 .000573 .000427 .000318 .000238 .000177 0

1.000 2.060 3.184 4.375 5.637 6.975 8.394 9.897 11.491 13.181 14.972 16.870 18.882 21.015 23.276 25.673 28.213 30.906 33.760 36.786 39.993 43.392 46.996 50.816 54.865 59.156 63.706 68.528 73.640 79.058 84.802 90.890 97.343 104.2 111.4 154.8 212.7 290.3 394.2 533.1 719.1 967.9 1301 1747 2343 3141 4209 5638 ∞

0

561

Present Worth Factor P/G 0 .890 2.569 4.946 7.935 11.459 15.450 19.842 24.577 29.602 34.870 40.337 45.963 51.713 57.555 63.459 69.401 75.357 81.306 87.230 93.114 98.941 104.701 110.381 115.973 121.468 126.860 132.142 137.310 142.359 147.286 152.090 156.768 161.319 165.743 185.957 203.110 217.457 229.322 239.043 246.945 253.327 258.453 262.549 265.810 268.395 270.437 272.047 277.778


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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7%



Arithmetic Gradient

N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

1.070 1.145 1.225 1.311 1.403 1.501 1.606 1.718 1.838 1.967 2.105 2.252 2.410 2.579 2.759 2.952 3.159 3.380 3.617 3.870 4.141 4.430 4.741 5.072 5.427 5.807 6.214 6.649 7.114 7.612 8.145 8.715 9.325 9.978 10.677 14.974 21.002 29.457 41.315 57.946 81.273 114.0 159.9 224.2 314.5 441.1 618.7 867.7 ∞

.9346 .8734 .8163 .7629 .7130 .6663 .6227 .5820 .5439 .5083 .4751 .4440 .4150 .3878 .3624 .3387 .3166 .2959 .2765 .2584 .2415 .2257 .2109 .1971 .1842 .1722 .1609 .1504 .1406 .1314 .1228 .1147 .1072 .1002 .0937 .0668 .0476 .0339 .0242 .0173 .0123 .00877 .00625 .00446 .00318 .00227 .00162 .00115

1.0700 .5531 .3811 .2952 .2439 .2098 .1856 .1675 .1535 .1424 .1334 .1259 .1197 .1143 .1098 .1059 .1024 .0994 .0968 .0944 .0923 .0904 .0887 .0872 .0858 .0846 .0834 .0824 .0814 .0806 .0798 .0791 .0784 .0778 .0772 .0750 .0735 .0725 .0717 .0712 .0709 .0706 .0704 .0703 .0702 .0702 .0701 .0701 .07

.935 1.808 2.624 3.387 4.100 4.767 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8.745 9.108 9.447 9.763 10.059 10.336 10.594 10.836 11.061 11.272 11.469 11.654 11.826 11.987 12.137 12.278 12.409 12.532 12.647 12.754 12.854 12.948 13.332 13.606 13.801 13.940 14.039 14.110 14.160 14.196 14.222 14.240 14.253 14.263 14.269 14.286

1.0000 .4831 .3111 .2252 .1739 .1398 .1156 .0975 .0835 .0724 .0634 .0559 .0497 .0443 .0398 .0359 .0324 .0294 .0268 .0244 .0223 .0204 .0187 .0172 .0158 .0146 .0134 .0124 .0114 .0106 .00980 .00907 .00841 .00780 .00723 .00501 .00350 .00246 .00174 .00123 .000872 .000620 .000441 .000314 .000223 .000159 .000113 .0000808 0

1.000 2.070 3.215 4.440 5.751 7.153 8.654 10.260 11.978 13.816 15.784 17.888 20.141 22.550 25.129 27.888 30.840 33.999 37.379 40.995 44.865 49.006 53.436 58.177 63.249 68.676 74.484 80.698 87.347 94.461 102.1 110.2 118.9 128.3 138.2 199.6 285.7 406.5 575.9 813.5 1147 1614 2270 3189 4479 6287 8824 12382 ∞

0

7%



N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞


563 8%

Arithmetic Gradient









N

1.080 1.166 1.260 1.360 1.469 1.587 1.714 1.851 1.999 2.159 2.332 2.518 2.720 2.937 3.172 3.426 3.700 3.996 4.316 4.661 5.034 5.437 5.871 6.341 6.848 7.396 7.988 8.627 9.317 10.063 10.868 11.737 12.676 13.690 14.785 21.725 31.920 46.902 68.914 101.3 148.8 218.6 321.2 472.0 693.5 1019 1497 2200 ∞

.9259 .8573 .7938 .7350 .6806 .6302 .5835 .5403 .5002 .4632 .4289 .3971 .3677 .3405 .3152 .2919 .2703 .2502 .2317 .2145 .1987 .1839 .1703 .1577 .1460 .1352 .1252 .1159 .1073 .0994 .0920 .0852 .0789 .0730 .0676 .0460 .0313 .0213 .0145 .00988 .00672 .00457 .00311 .00212 .00144 .000981 .000668 .000455

1.0800 .5608 .3880 .3019 .2505 .2163 .1921 .1740 .1601 .1490 .1401 .1327 .1265 .1213 .1168 .1130 .1096 .1067 .1041 .1019 .0998 .0980 .0964 .0950 .0937 .0925 .0914 .0905 .0896 .0888 .0881 .0875 .0869 .0863 .0858 .0839 .0826 .0817 .0812 .0808 .0805 .0804 .0802 .0802 .0801 .0801 .0801 .0800 .08

.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 8.244 8.559 8.851 9.122 9.372 9.604 9.818 10.017 10.201 10.371 10.529 10.675 10.810 10.935 11.051 11.158 11.258 11.350 11.435 11.514 11.587 11.655 11.925 12.108 12.233 12.319 12.377 12.416 12.443 12.461 12.474 12.482 12.488 12.492 12.494 12.5

1.0000 .4808 .3080 .2219 .1705 .1363 .1121 .0940 .0801 .0690 .0601 .0527 .0465 .0413 .0368 .0330 .0296 .0267 .0241 .0219 .0198 .0180 .0164 .0150 .0137 .0125 .0114 .0105 .00962 .00883 .00811 .00745 .00685 .00630 .00580 .00386 .00259 .00174 .00118 .000798 .000541 .000368 .000250 .000170 .000116 .0000786 .0000535 .0000364 0

1.000 2.080 3.246 4.506 5.867 7.336 8.923 10.637 12.488 14.487 16.645 18.977 21.495 24.215 27.152 30.324 33.750 37.450 41.446 45.762 50.423 55.457 60.893 66.765 73.106 79.954 87.351 95.339 104.0 113.3 123.3 134.2 146.0 158.6 172.3 259.1 386.5 573.8 848.9 1253 1847 2720 4003 5887 8656 12724 18702 27485 ∞

0 .857 2.445 4.650 7.372 10.523 14.024 17.806 21.808 25.977 30.266 34.634 39.046 43.472 47.886 52.264 56.588 60.843 65.013 69.090 73.063 76.926 80.673 84.300 87.804 91.184 94.439 97.569 100.574 103.456 106.216 108.857 111.382 113.792 116.092 126.042 133.733 139.593 144.006 147.300 149.739 151.533 152.845 153.800 154.492 154.993 155.352 155.611 156.25

0 .481 .949 1.404 1.846 2.276 2.694 3.099 3.491 3.871 4.240 4.596 4.940 5.273 5.594 5.905 6.204 6.492 6.770 7.037 7.294 7.541 7.779 8.007 8.225 8.435 8.636 8.829 9.013 9.190 9.358 9.520 9.674 9.821 9.961 10.570 11.045 11.411 11.690 11.902 12.060 12.178 12.266 12.330 12.377 12.412 12.437 12.455 12.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

0

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9%


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞









1.090 1.188 1.295 1.412 1.539 1.677 1.828 1.993 2.172 2.367 2.580 2.813 3.066 3.342 3.642 3.970 4.328 4.717 5.142 5.604 6.109 6.659 7.258 7.911 8.623 9.399 10.245 11.167 12.172 13.268 14.462 15.763 17.182 18.728 20.414 31.409 48.327 74.358 114.4 176.0 270.8 416.7 641.2 986.6 1518 2336 3593 5529 ∞

.9174 .8417 .7722 .7084 .6499 .5963 .5470 .5019 .4604 .4224 .3875 .3555 .3262 .2992 .2745 .2519 .2311 .2120 .1945 .1784 .1637 .1502 .1378 .1264 .1160 .1064 .0976 .0895 .0822 .0754 .0691 .0634 .0582 .0534 .0490 .0318 .0207 .0134 .00874 .00568 .00369 .00240 .00156 .00101 .000659 .000428 .000278 .000181 0

1.0900 .5685 .3951 .3087 .2571 .2229 .1987 .1807 .1668 .1558 .1469 .1397 .1336 .1284 .1241 .1203 .1170 .1142 .1117 .1095 .1076 .1059 .1044 .1030 .1018 .1007 .0997 .0989 .0981 .0973 .0967 .0961 .0956 .0951 .0946 .0930 .0919 .0912 .0908 .0905 .0903 .0902 .0901 .0901 .0901 .0900 .0900 .0900 .09

.917 1.759 2.531 3.240 3.890 4.486 5.033 5.535 5.995 6.418 6.805 7.161 7.487 7.786 8.061 8.313 8.544 8.756 8.950 9.129 9.292 9.442 9.580 9.707 9.823 9.929 10.027 10.116 10.198 10.274 10.343 10.406 10.464 10.518 10.567 10.757 10.881 10.962 11.014 11.048 11.070 11.084 11.094 11.100 11.104 11.106 11.108 11.109 11.111

1.0000 .4785 .3051 .2187 .1671 .1329 .1087 .0907 .0768 .0658 .0569 .0497 .0436 .0384 .0341 .0303 .0270 .0242 .0217 .0195 .0176 .0159 .0144 .0130 .0118 .01072 .00973 .00885 .00806 .00734 .00669 .00610 .00556 .00508 .00464 .00296 .00190 .00123 .00079 .00051 .000334 .000216 .000141 .0000913 .0000593 .0000386 .0000251 .0000163 0

1.000 2.090 3.278 4.573 5.985 7.523 9.200 11.028 13.021 15.193 17.560 20.141 22.953 26.019 29.361 33.003 36.974 41.301 46.018 51.160 56.765 62.873 69.532 76.790 84.701 93.3 102.7 113.0 124.1 136.3 149.6 164.0 179.8 197.0 215.7 337.9 525.9 815.1 1260 1945 2998 4619 7113 10951 16855 25939 39917 61423 ∞



N

0 .478 .943 1.393 1.828 2.250 2.657 3.051 3.431 3.798 4.151 4.491 4.818 5.133 5.435 5.724 6.002 6.269 6.524 6.767 7.001 7.223 7.436 7.638 7.832 8.016 8.191 8.357 8.515 8.666 8.808 8.944 9.072 9.193 9.308 9.796 10.160 10.430 10.626 10.768 10.870 10.943 10.994 11.030 11.055 11.073 11.085 11.093 11.111

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞









1.100 1.210 1.331 1.464 1.611 1.772 1.949 2.144 2.358 2.594 2.853 3.138 3.452 3.797 4.177 4.595 5.054 5.560 6.116 6.727 7.400 8.140 8.954 9.850 10.835 11.918 13.110 14.421 15.863 17.449 19.194 21.114 23.225 25.548 28.102 45.259 72.890 117.4 189.1 304.5 490.4 789.7 1272 2048 3299 5313 8557 13781 ∞

.9091 .8264 .7513 .6830 .6209 .5645 .5132 .4665 .4241 .3855 .3505 .3186 .2897 .2633 .2394 .2176 .1978 .1799 .1635 .1486 .1351 .1228 .1117 .1015 .0923 .0839 .0763 .0693 .0630 .0573 .0521 .0474 .0431 .0391 .0356 .0221 .0137 .00852 .00529 .00328 .00204 .00127 .00079 .00049 .00030 .00019 .00012 .00007

1.1000 .5762 .4021 .3155 .2638 .2296 .2054 .1874 .1736 .1627 .1540 .1468 .1408 .1357 .1315 .1278 .1247 .1219 .1195 .1175 .1156 .1140 .1126 .1113 .1102 .1092 .1083 .1075 .1067 .1061 .1055 .1050 .1045 .1041 .1037 .1023 .1014 .1009 .1005 .1003 .1002 .1001 .1001 .1000 .1000 .1000 .1000 .1000 .10

.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 7.367 7.606 7.824 8.022 8.201 8.365 8.514 8.649 8.772 8.883 8.985 9.077 9.161 9.237 9.307 9.370 9.427 9.479 9.526 9.569 9.609 9.644 9.779 9.863 9.915 9.947 9.967 9.980 9.987 9.992 9.995 9.997 9.998 9.999 9.999 10

1.0000 .4762 .3021 .2155 .1638 .1296 .1054 .0874 .0736 .0627 .0540 .0468 .0408 .0357 .0315 .0278 .0247 .0219 .0195 .0175 .0156 .0140 .0126 .0113 .0102 .00916 .00826 .00745 .00673 .00608 .00550 .00497 .00450 .00407 .00369 .00226 .00139 .00086 .00053 .00033 .00020 .00013 .000079 .000049 .000030 .000019 .000012 .000007 0

1.000 2.100 3.310 4.641 6.105 7.716 9.487 11.436 13.579 15.937 18.531 21.384 24.523 27.975 31.772 35.950 40.545 45.599 51.159 57.275 64.002 71.403 79.543 88.497 98.347 109.2 121.1 134.2 148.6 164.5 181.9 201.1 222.3 245.5 271.0 442.6 718.9 1164 1881 3035 4894 7887 12709 20474 32980 53120 85557 137796 ∞

0

565


Uniform Payment Factor A/G 0 .476 .937 1.381 1.810 2.224 2.622 3.004 3.372 3.725 4.064 4.388 4.699 4.996 5.279 5.549 5.807 6.053 6.286 6.508 6.719 6.919 7.108 7.288 7.458 7.619 7.770 7.914 8.049 8.176 8.296 8.409 8.515 8.615 8.709 9.096 9.374 9.570 9.708 9.802 9.867 9.911 9.941 9.961 9.974 9.983 9.989 9.993 10

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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11%


N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞











N

1.110 1.232 1.368 1.518 1.685 1.870 2.076 2.305 2.558 2.839 3.152 3.498 3.883 4.310 4.785 5.311 5.895 6.544 7.263 8.062 8.949 9.934 11.026 12.239 13.585 15.080 16.739 18.580 20.624 22.892 25.410 28.206 31.308 34.752 38.575 65.001 109.5 184.6 311.0 524.1 883.1 1488 2507 4225 7120 11997 20215 34064 ∞

.9009 .8116 .7312 .6587 .5935 .5346 .4817 .4339 .3909 .3522 .3173 .2858 .2575 .2320 .2090 .1883 .1696 .1528 .1377 .1240 .1117 .1007 .0907 .0817 .0736 .0663 .0597 .0538 .0485 .0437 .0394 .0355 .0319 .0288 .0259 .0154 .00913 .00542 .00322 .00191 .00113 .000672 .000399 .000237 .000140 .000083 .000049 .000029

1.1100 .5839 .4092 .3223 .2706 .2364 .2122 .1943 .1806 .1698 .1611 .1540 .1482 .1432 .1391 .1355 .1325 .1298 .1276 .1256 .1238 .1223 .1210 .1198 .1187 .1178 .1170 .1163 .1156 .1150 .1145 .1140 .1136 .1133 .1129 .1117 .1110 .1106 .1104 .1102 .1101 .1101 .1100 .1100 .1100 .1100 .1100 .1100 .11

.901 1.713 2.444 3.102 3.696 4.231 4.712 5.146 5.537 5.889 6.207 6.492 6.750 6.982 7.191 7.379 7.549 7.702 7.839 7.963 8.075 8.176 8.266 8.348 8.422 8.488 8.548 8.602 8.650 8.694 8.733 8.769 8.801 8.829 8.855 8.951 9.008 9.042 9.062 9.074 9.081 9.085 9.087 9.089 9.090 9.090 9.090 9.091 9.091

1.0000 .4739 .2992 .2123 .1606 .1264 .1022 .0843 .0706 .0598 .0511 .0440 .0382 .0332 .0291 .0255 .0225 .0198 .0176 .0156 .0138 .0123 .0110 .00979 .00874 .00781 .00699 .00626 .00561 .00502 .00451 .00404 .00363 .00326 .00293 .00172 .00101 .000599 .000355 .000210 .000125 .0000740 .0000439 .0000260 .0000155 .0000092 .0000054 .0000032 0

1.000 2.110 3.342 4.710 6.228 7.913 9.783 11.859 14.164 16.722 19.561 22.713 26.212 30.095 34.405 39.190 44.501 50.396 56.939 64.203 72.265 81.214 91.148 102.2 114.4 128.0 143.1 159.8 178.4 199.0 221.9 247.3 275.5 306.8 341.6 581.8 986.6 1669 2818 4755 8019 13518 22785 38401 64714 109053 183768 309665 ∞

0 .812 2.274 4.250 6.624 9.297 12.187 15.225 18.352 21.522 24.695 27.839 30.929 33.945 36.871 39.695 42.409 45.007 47.486 49.842 52.077 54.191 56.186 58.066 59.832 61.490 63.043 64.497 65.854 67.121 68.302 69.401 70.423 71.372 72.254 75.779 78.155 79.734 80.771 81.446 81.882 82.161 82.340 82.453 82.524 82.570 82.598 82.616 82.645

0 .474 .931 1.370 1.792 2.198 2.586 2.958 3.314 3.654 3.979 4.288 4.582 4.862 5.127 5.379 5.618 5.844 6.057 6.259 6.449 6.628 6.797 6.956 7.104 7.244 7.375 7.498 7.613 7.721 7.821 7.915 8.002 8.084 8.159 8.466 8.676 8.819 8.913 8.976 9.017 9.044 9.061 9.072 9.079 9.083 9.086 9.088 9.091

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

0

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N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞









1.120 1.254 1.405 1.574 1.762 1.974 2.211 2.476 2.773 3.106 3.479 3.896 4.363 4.887 5.474 6.130 6.866 7.690 8.613 9.646 10.804 12.100 13.552 15.179 17.000 19.040 21.325 23.884 26.750 29.960 33.555 37.582 42.092 47.143 52.800 93.051 164.0 289.0 509.3 897.6 1582 2788 4913 8658 15259 26892 47393 83522 ∞

.8929 .7972 .7118 .6355 .5674 .5066 .4523 .4039 .3606 .3220 .2875 .2567 .2292 .2046 .1827 .1631 .1456 .1300 .1161 .1037 .0926 .0826 .0738 .0659 .0588 .0525 .0469 .0419 .0374 .0334 .0298 .0266 .0238 .0212 .0189 .0107 .00610 .00346 .00196 .00111 .00063 .00036 .00020 .00012 .000066 .000037 .000021 .000012

1.1200 .5917 .4163 .3292 .2774 .2432 .2191 .2013 .1877 .1770 .1684 .1614 .1557 .1509 .1468 .1434 .1405 .1379 .1358 .1339 .1322 .1308 .1296 .1285 .1275 .1267 .1259 .1252 .1247 .1241 .1237 .1233 .1229 .1226 .1223 .1213 .1207 .1204 .1202 .1201 .1201 .1200 .1200 .1200 .1200 .1200 .1200 .1200 .12

.893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 5.650 5.938 6.194 6.424 6.628 6.811 6.974 7.120 7.250 7.366 7.469 7.562 7.645 7.718 7.784 7.843 7.896 7.943 7.984 8.022 8.055 8.085 8.112 8.135 8.157 8.176 8.244 8.283 8.304 8.317 8.324 8.328 8.330 8.332 8.332 8.333 8.333 8.333 8.333 8.333

1.0000 .4717 .2963 .2092 .1574 .1232 .0991 .0813 .0677 .0570 .0484 .0414 .0357 .0309 .0268 .0234 .0205 .0179 .0158 .0139 .0122 .0108 .0096 .0085 .0075 .00665 .00590 .00524 .00466 .00414 .00369 .00328 .00292 .00260 .00232 .00130 .00074 .00042 .00024 .00013 .000076 .000043 .000024 .000014 .0000079 .0000045 .0000025 .0000014 0

1.000 2.120 3.374 4.779 6.353 8.115 10.089 12.300 14.776 17.549 20.655 24.133 28.029 32.393 37.280 42.753 48.884 55.750 63.440 72.052 81.699 92.503 104.603 118.155 133.334 150.3 169.4 190.7 214.6 241.3 271.3 304.8 342.4 384.5 431.7 767.1 1358 2400 4236 7472 13174 23223 40934 72146 127152 224091 394931 696011 ∞

0

567



N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 ∞

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13%



Arithmetic Gradient

N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.130 1.277 1.443 1.630 1.842 2.082 2.353 2.658 3.004 3.395 3.836 4.335 4.898 5.535 6.254 7.067 7.986 9.024 10.197 11.523 13.021 14.714 16.627 18.788 21.231 23.991 27.109 30.633 34.616 39.116 44.201 49.947 56.440 63.777 72.069 132.8 244.6 450.7 830.5 1530 ∞

.8850 .7831 .6931 .6133 .5428 .4803 .4251 .3762 .3329 .2946 .2607 .2307 .2042 .1807 .1599 .1415 .1252 .1108 .0981 .0868 .0768 .0680 .0601 .0532 .0471 .0417 .0369 .0326 .0289 .0256 .0226 .0200 .0177 .0157 .0139 .00753 .00409 .00222 .00120 .00065

1.1300 .5995 .4235 .3362 .2843 .2502 .2261 .2084 .1949 .1843 .1758 .1690 .1634 .1587 .1547 .1514 .1486 .1462 .1441 .1424 .1408 .1395 .1383 .1373 .1364 .1357 .1350 .1344 .1339 .1334 .1330 .1327 .1323 .1321 .1318 .1310 .1305 .1303 .1302 .1301 .13

.885 1.668 2.361 2.974 3.517 3.998 4.423 4.799 5.132 5.426 5.687 5.918 6.122 6.302 6.462 6.604 6.729 6.840 6.938 7.025 7.102 7.170 7.230 7.283 7.330 7.372 7.409 7.441 7.470 7.496 7.518 7.538 7.556 7.572 7.586 7.634 7.661 7.675 7.683 7.687 7.692

1.0000 .4695 .2935 .2062 .1543 .1202 .0961 .0784 .0649 .0543 .0458 .0390 .0334 .0287 .0247 .0214 .0186 .0162 .0141 .0124 .0108 .00948 .00832 .00731 .00643 .00565 .00498 .00439 .00387 .00341 .00301 .00266 .00234 .00207 .00183 .000986 .000534 .000289 .000157 .000085 0

1.000 2.130 3.407 4.850 6.480 8.323 10.405 12.757 15.416 18.420 21.814 25.650 29.985 34.883 40.417 46.672 53.739 61.725 70.749 80.947 92.470 105.5 120.2 136.8 155.6 176.9 200.8 227.9 258.6 293.2 332.3 376.5 426.5 482.9 546.7 1014 1874 3460 6380 11762 ∞

0

13%


0 .783 2.169 4.009 6.180 8.582 11.132 13.765 16.428 19.080 21.687 24.224 26.674 29.023 31.262 33.384 35.388 37.271 39.037 40.685 42.221 43.649 44.972 46.196 47.326 48.369 49.328 50.209 51.018 51.759 52.438 53.059 53.626 54.143 54.615 56.409 57.515 58.187 58.591 58.831 59.172


0 .469 .919 1.348 1.757 2.147 2.517 2.869 3.201 3.516 3.813 4.094 4.357 4.605 4.837 5.055 5.259 5.449 5.627 5.792 5.945 6.088 6.220 6.343 6.457 6.561 6.658 6.747 6.830 6.905 6.975 7.039 7.097 7.151 7.200 7.389 7.508 7.581 7.626 7.653 7.692

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

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N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.140 1.300 1.482 1.689 1.925 2.195 2.502 2.853 3.252 3.707 4.226 4.818 5.492 6.261 7.138 8.137 9.276 10.575 12.056 13.743 15.668 17.861 20.362 23.212 26.462 30.167 34.390 39.204 44.693 50.950 58.083 66.215 75.485 86.053 98.100 188.9 363.7 700.2 1348 2596 ∞

.8772 .7695 .6750 .5921 .5194 .4556 .3996 .3506 .3075 .2697 .2366 .2076 .1821 .1597 .1401 .1229 .1078 .0946 .0829 .0728 .0638 .0560 .0491 .0431 .0378 .0331 .0291 .0255 .0224 .0196 .0172 .0151 .0132 .0116 .0102 .00529 .00275 .00143 .00074 .00039

1.1400 .6073 .4307 .3432 .2913 .2572 .2332 .2156 .2022 .1917 .1834 .1767 .1712 .1666 .1628 .1596 .1569 .1546 .1527 .1510 .1495 .1483 .1472 .1463 .1455 .1448 .1442 .1437 .1432 .1428 .1425 .1421 .1419 .1416 .1414 .1407 .1404 .1402 .1401 .1401 .14

.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.265 6.373 6.467 6.550 6.623 6.687 6.743 6.792 6.835 6.873 6.906 6.935 6.961 6.983 7.003 7.020 7.035 7.048 7.060 7.070 7.105 7.123 7.133 7.138 7.140 7.143

1.0000 .4673 .2907 .2032 .1513 .1172 .0932 .0756 .0622 .0517 .0434 .0367 .0312 .0266 .0228 .0196 .0169 .0146 .0127 .0110 .00954 .00830 .00723 .00630 .00550 .00480 .00419 .00366 .00320 .00280 .00245 .00215 .00188 .00165 .00144 .000745 .000386 .000200 .000104 .000054 0

1.000 2.140 3.440 4.921 6.610 8.536 10.730 13.233 16.085 19.337 23.045 27.271 32.089 37.581 43.842 50.980 59.118 68.394 78.969 91.025 104.8 120.4 138.3 158.7 181.9 208.3 238.5 272.9 312.1 356.8 407.7 465.8 532.0 607.5 693.6 1342 2591 4995 9623 18535 ∞

0

569


0 .769 2.119 3.896 5.973 8.251 10.649 13.103 15.563 17.991 20.357 22.640 24.825 26.901 28.862 30.706 32.430 34.038 35.531 36.914 38.190 39.366 40.446 41.437 42.344 43.173 43.929 44.618 45.244 45.813 46.330 46.798 47.222 47.605 47.952 49.238 49.996 50.438 50.691 50.836 51.020


0 .467 .913 1.337 1.740 2.122 2.483 2.825 3.146 3.449 3.733 4.000 4.249 4.482 4.699 4.901 5.089 5.263 5.424 5.573 5.711 5.838 5.955 6.062 6.161 6.251 6.334 6.410 6.479 6.542 6.600 6.652 6.700 6.743 6.782 6.930 7.019 7.071 7.102 7.120 7.143

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

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15%



Arithmetic Gradient

N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.150 1.323 1.521 1.749 2.011 2.313 2.660 3.059 3.518 4.046 4.652 5.350 6.153 7.076 8.137 9.358 10.761 12.375 14.232 16.367 18.822 21.645 24.891 28.625 32.919 37.857 43.535 50.066 57.575 66.212 76.144 87.565 100.7 115.8 133.2 267.9 538.8 1084 2180 4384 ∞

.8696 .7561 .6575 .5718 .4972 .4323 .3759 .3269 .2843 .2472 .2149 .1869 .1625 .1413 .1229 .1069 .0929 .0808 .0703 .0611 .0531 .0462 .0402 .0349 .0304 .0264 .0230 .0200 .0174 .0151 .0131 .0114 .00993 .00864 .00751 .00373 .00186 .00092 .00046 .00023

1.1500 .6151 .4380 .3503 .2983 .2642 .2404 .2229 .2096 .1993 .1911 .1845 .1791 .1747 .1710 .1679 .1654 .1632 .1613 .1598 .1584 .1573 .1563 .1554 .1547 .1541 .1535 .1531 .1527 .1523 .1520 .1517 .1515 .1513 .1511 .1506 .1503 .1501 .1501 .1500 .15

.870 1.626 2.283 2.855 3.352 3.784 4.160 4.487 4.772 5.019 5.234 5.421 5.583 5.724 5.847 5.954 6.047 6.128 6.198 6.259 6.312 6.359 6.399 6.434 6.464 6.491 6.514 6.534 6.551 6.566 6.579 6.591 6.600 6.609 6.617 6.642 6.654 6.661 6.664 6.665 6.667

1.0000 .4651 .2880 .2003 .1483 .1142 .0904 .0729 .0596 .0493 .0411 .0345 .0291 .0247 .0210 .0179 .0154 .0132 .0113 .00976 .00842 .00727 .00628 .00543 .00470 .00407 .00353 .00306 .00265 .00230 .00200 .00173 .00150 .00131 .00113 .000562 .000279 .000139 .000069 .000034 0

1.000 2.150 3.473 4.993 6.742 8.754 11.067 13.727 16.786 20.304 24.349 29.002 34.352 40.505 47.580 55.717 65.075 75.836 88.212 102.4 118.8 137.6 159.3 184.2 212.8 245.7 283.6 327.1 377.2 434.7 501.0 577.1 664.7 765.4 881.2 1779 3585 7218 14524 29220 ∞

0

15%


0 .756 2.071 3.786 5.775 7.937 10.192 12.481 14.755 16.979 19.129 21.185 23.135 24.972 26.693 28.296 29.783 31.156 32.421 33.582 34.645 35.615 36.499 37.302 38.031 38.692 39.289 39.828 40.315 40.753 41.147 41.501 41.818 42.103 42.359 43.283 43.805 44.096 44.256 44.343 44.444


0 .465 .907 1.326 1.723 2.097 2.450 2.781 3.092 3.383 3.655 3.908 4.144 4.362 4.565 4.752 4.925 5.084 5.231 5.365 5.488 5.601 5.704 5.798 5.883 5.961 6.032 6.096 6.154 6.207 6.254 6.297 6.336 6.371 6.402 6.517 6.583 6.620 6.641 6.653 6.667

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

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N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.160 1.346 1.561 1.811 2.100 2.436 2.826 3.278 3.803 4.411 5.117 5.936 6.886 7.988 9.266 10.748 12.468 14.463 16.777 19.461 22.574 26.186 30.376 35.236 40.874 47.414 55.000 63.800 74.009 85.850 99.586 115.5 134.0 155.4 180.3 378.7 795.4 1671 3509 7370 ∞

.8621 .7432 .6407 .5523 .4761 .4104 .3538 .3050 .2630 .2267 .1954 .1685 .1452 .1252 .1079 .0930 .0802 .0691 .0596 .0514 .0443 .0382 .0329 .0284 .0245 .0211 .0182 .0157 .0135 .0116 .0100 .00866 .00746 .00643 .00555 .00264 .00126 .00060 .00028 .00014

1.1600 .6230 .4453 .3574 .3054 .2714 .2476 .2302 .2171 .2069 .1989 .1924 .1872 .1829 .1794 .1764 .1740 .1719 .1701 .1687 .1674 .1664 .1654 .1647 .1640 .1634 .1630 .1625 .1622 .1619 .1616 .1614 .1612 .1610 .1609 .1604 .1602 .1601 .1600 .1600 .16

.862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 4.833 5.029 5.197 5.342 5.468 5.575 5.668 5.749 5.818 5.877 5.929 5.973 6.011 6.044 6.073 6.097 6.118 6.136 6.152 6.166 6.177 6.187 6.196 6.203 6.210 6.215 6.233 6.242 6.246 6.248 6.249 6.250

1.0000 .4630 .2853 .1974 .1454 .1114 .0876 .0702 .0571 .0469 .0389 .0324 .0272 .0229 .0194 .0164 .0140 .0119 .0101 .00867 .00742 .00635 .00545 .00467 .00401 .00345 .00296 .00255 .00219 .00189 .00162 .00140 .00120 .00104 .000892 .000424 .000201 .000096 .000046 .000022 0

1.000 2.160 3.506 5.066 6.877 8.977 11.414 14.240 17.519 21.321 25.733 30.850 36.786 43.672 51.660 60.925 71.673 84.141 98.603 115.4 134.8 157.4 183.6 214.0 249.2 290.1 337.5 392.5 456.3 530.3 616.2 715.7 831.3 965.3 1121 2361 4965 10436 21925 46058 ∞

0

571


0 .743 2.024 3.681 5.586 7.638 9.761 11.896 14.000 16.040 17.994 19.847 21.590 23.217 24.728 26.124 27.407 28.583 29.656 30.632 31.518 32.320 33.044 33.697 34.284 34.811 35.284 35.707 36.086 36.423 36.725 36.993 37.232 37.444 37.633 38.299 38.660 38.852 38.953 39.006 39.063


0 .463 .901 1.316 1.706 2.073 2.417 2.739 3.039 3.319 3.578 3.819 4.041 4.246 4.435 4.609 4.768 4.913 5.046 5.167 5.277 5.377 5.467 5.549 5.623 5.690 5.750 5.804 5.853 5.896 5.936 5.971 6.002 6.030 6.055 6.144 6.193 6.220 6.234 6.242 6.250

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

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17%




Compound Amount Factor

Present Worth Factor

Capital Recovery Factor


Sinking Fund Factor

Compound Amount Factor


Uniform Payment Factor

N

F/P

P/F

A/P

P/A

A/F

F/A

P/G

A/G

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.170 1.369 1.602 1.874 2.192 2.565 3.001 3.511 4.108 4.807 5.624 6.580 7.699 9.007 10.539 12.330 14.426 16.879 19.748 23.106 27.034 31.629 37.006 43.297 50.658 59.270 69.345 81.134 94.927 111.1 129.9 152.0 177.9 208.1 243.5 533.9 1170 2566 5626 12335 ∞

.8547 .7305 .6244 .5337 .4561 .3898 .3332 .2848 .2434 .2080 .1778 .1520 .1299 .1110 .0949 .0811 .0693 .0592 .0506 .0433 .0370 .0316 .0270 .0231 .0197 .0169 .0144 .0123 .0105 .00900 .00770 .00658 .00562 .00480 .00411 .00187 .000854 .000390 .000178 .000081

1.1700 .6308 .4526 .3645 .3126 .2786 .2549 .2377 .2247 .2147 .2068 .2005 .1954 .1912 .1878 .1850 .1827 .1807 .1791 .1777 .1765 .1756 .1747 .1740 .1734 .1729 .1725 .1721 .1718 .1715 .1713 .1711 .1710 .1708 .1707 .1703 .1701 .1701 .1700 .1700 .17

.855 1.585 2.210 2.743 3.199 3.589 3.922 4.207 4.451 4.659 4.836 4.988 5.118 5.229 5.324 5.405 5.475 5.534 5.584 5.628 5.665 5.696 5.723 5.746 5.766 5.783 5.798 5.810 5.820 5.829 5.837 5.844 5.849 5.854 5.858 5.871 5.877 5.880 5.881 5.882 5.882

1.0000 .4608 .2826 .1945 .1426 .1086 .0849 .0677 .0547 .0447 .0368 .0305 .0254 .0212 .0178 .0150 .0127 .0107 .00907 .00769 .00653 .00555 .00472 .00402 .00342 .00292 .00249 .00212 .00181 .00154 .00132 .00113 .000961 .000821 .000701 .000319 .000145 .000066 .000030 .000014 0

1.000 2.170 3.539 5.141 7.014 9.207 11.772 14.773 18.285 22.393 27.200 32.824 39.404 47.103 56.110 66.649 78.979 93.406 110.3 130.0 153.1 180.2 211.8 248.8 292.1 342.8 402.0 471.4 552.5 647.4 758.5 888.4 1040 1218 1426 3135 6879 15090 33090 72555 ∞

0

0 .731 1.979 3.580 5.405 7.354 9.353 11.346 13.294 15.166 16.944 18.616 20.175 21.618 22.946 24.163 25.272 26.279 27.190 28.013 28.753 29.417 30.011 30.542 31.016 31.438 31.813 32.146 32.441 32.702 32.932 33.136 33.316 33.475 33.614 34.097 34.346 34.474 34.538 34.571 34.602

0 .461 .896 1.305 1.689 2.049 2.385 2.697 2.987 3.255 3.503 3.732 3.942 4.134 4.310 4.470 4.616 4.749 4.869 4.978 5.076 5.164 5.244 5.315 5.379 5.436 5.487 5.533 5.574 5.610 5.642 5.670 5.696 5.718 5.738 5.807 5.844 5.863 5.873 5.877 5.882

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

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N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.180 1.392 1.643 1.939 2.288 2.700 3.185 3.759 4.435 5.234 6.176 7.288 8.599 10.147 11.974 14.129 16.672 19.673 23.214 27.393 32.324 38.142 45.008 53.109 62.669 73.949 87.260 103.0 121.5 143.4 169.2 199.6 235.6 278.0 328.0 750.4 1717 3927 8985 20555 ∞

.8475 .7182 .6086 .5158 .4371 .3704 .3139 .2660 .2255 .1911 .1619 .1372 .1163 .0985 .0835 .0708 .0600 .0508 .0431 .0365 .0309 .0262 .0222 .0188 .0160 .0135 .0115 .00971 .00823 .00697 .00591 .00501 .00425 .00360 .00305 .00133 .000583 .000255 .000111 .000049

1.1800 .6387 .4599 .3717 .3198 .2859 .2624 .2452 .2324 .2225 .2148 .2086 .2037 .1997 .1964 .1937 .1915 .1896 .1881 .1868 .1857 .1848 .1841 .1835 .1829 .1825 .1821 .1818 .1815 .1813 .1811 .1809 .1808 .1806 .1806 .1802 .1801 .1800 .1800 .1800 .18

.847 1.566 2.174 2.690 3.127 3.498 3.812 4.078 4.303 4.494 4.656 4.793 4.910 5.008 5.092 5.162 5.222 5.273 5.316 5.353 5.384 5.410 5.432 5.451 5.467 5.480 5.492 5.502 5.510 5.517 5.523 5.528 5.532 5.536 5.539 5.548 5.552 5.554 5.555 5.555 5.556

1.0000 .4587 .2799 .1917 .1398 .1059 .0824 .0652 .0524 .0425 .0348 .0286 .0237 .0197 .0164 .0137 .0115 .00964 .00810 .00682 .00575 .00485 .00409 .00345 .00292 .00247 .00209 .00177 .00149 .00126 .00107 .000906 .000767 .000650 .000550 .000240 .000105 .0000458 .0000200 .0000088 0

1.000 2.180 3.572 5.215 7.154 9.442 12.142 15.327 19.086 23.521 28.755 34.931 42.219 50.818 60.965 72.939 87.068 103.7 123.4 146.6 174.0 206.3 244.5 289.5 342.6 405.3 479.2 566.5 669.4 790.9 934.3 1103 1303 1539 1817 4163 9532 21813 49910 114190 ∞

0

573


0 .718 1.935 3.483 5.231 7.083 8.967 10.829 12.633 14.352 15.972 17.481 18.877 20.158 21.327 22.389 23.348 24.212 24.988 25.681 26.300 26.851 27.339 27.772 28.155 28.494 28.791 29.054 29.284 29.486 29.664 29.819 29.955 30.074 30.177 30.527 30.701 30.786 30.827 30.846 30.864


0 .459 .890 1.295 1.673 2.025 2.353 2.656 2.936 3.194 3.430 3.647 3.845 4.025 4.189 4.337 4.471 4.592 4.700 4.798 4.885 4.963 5.033 5.095 5.150 5.199 5.243 5.281 5.315 5.345 5.371 5.394 5.415 5.433 5.449 5.502 5.529 5.543 5.549 5.553 5.556

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

esch_app_b.qxd

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19%




N









N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.190 1.416 1.685 2.005 2.386 2.840 3.379 4.021 4.785 5.695 6.777 8.064 9.596 11.420 13.590 16.172 19.244 22.901 27.252 32.429 38.591 45.923 54.649 65.032 77.388 92.092 109.6 130.4 155.2 184.7 219.8 261.5 311.2 370.3 440.7 1052 2510 5989 14292 34105 ∞

.8403 .7062 .5934 .4987 .4190 .3521 .2959 .2487 .2090 .1756 .1476 .1240 .1042 .0876 .0736 .0618 .0520 .0437 .0367 .0308 .0259 .0218 .0183 .0154 .0129 .0109 .00912 .00767 .00644 .00541 .00455 .00382 .00321 .00270 .00227 .000951 .000398 .000167 .000070 .000029

1.1900 .6466 .4673 .3790 .3271 .2933 .2699 .2529 .2402 .2305 .2229 .2169 .2121 .2082 .2051 .2025 .2004 .1987 .1972 .1960 .1951 .1942 .1935 .1930 .1925 .1921 .1917 .1915 .1912 .1910 .1909 .1907 .1906 .1905 .1904 .1902 .1901 .1900 .1900 .1900 .19

.840 1.547 2.140 2.639 3.058 3.410 3.706 3.954 4.163 4.339 4.486 4.611 4.715 4.802 4.876 4.938 4.990 5.033 5.070 5.101 5.127 5.149 5.167 5.182 5.195 5.206 5.215 5.223 5.229 5.235 5.239 5.243 5.246 5.249 5.251 5.258 5.261 5.262 5.263 5.263 5.263

1.0000 .4566 .2773 .1890 .1371 .1033 .0799 .0629 .0502 .0405 .0329 .0269 .0221 .0182 .0151 .0125 .0104 .00868 .00724 .00605 .00505 .00423 .00354 .00297 .00249 .00209 .00175 .00147 .00123 .00103 .000869 .000729 .000612 .000514 .000432 .000181 .0000757 .0000317 .0000133 .0000056 0

1.000 2.190 3.606 5.291 7.297 9.683 12.523 15.902 19.923 24.709 30.404 37.180 45.244 54.841 66.261 79.850 96.022 115.3 138.2 165.4 197.8 236.4 282.4 337.0 402.0 479.4 571.5 681.1 811.5 966.7 1151 1371 1633 1944 2314 5530 13203 31515 75214 179495 ∞

0 .706 1.893 3.389 5.065 6.826 8.601 10.342 12.014 13.594 15.070 16.434 17.684 18.823 19.853 20.781 21.612 22.354 23.015 23.601 24.119 24.576 24.979 25.333 25.643 25.914 26.151 26.358 26.539 26.696 26.832 26.951 27.054 27.143 27.220 27.474 27.595 27.652 27.679 27.691 27.701

0 .457 .885 1.284 1.657 2.002 2.321 2.615 2.886 3.133 3.359 3.564 3.751 3.920 4.072 4.209 4.331 4.441 4.539 4.627 4.705 4.773 4.834 4.888 4.936 4.978 5.015 5.047 5.075 5.100 5.121 5.140 5.157 5.171 5.184 5.225 5.245 5.255 5.259 5.261 5.263

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

0

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N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

1.200 1.440 1.728 2.074 2.488 2.986 3.583 4.300 5.160 6.192 7.430 8.916 10.699 12.839 15.407 18.488 22.186 26.623 31.948 38.338 46.005 55.206 66.247 79.497 95.396 114.5 137.4 164.8 197.8 237.4 284.9 341.8 410.2 492.2 590.7 1470 3657 9100 22645 56348 ∞

.8333 .6944 .5787 .4823 .4019 .3349 .2791 .2326 .1938 .1615 .1346 .1122 .0935 .0779 .0649 .0541 .0451 .0376 .0313 .0261 .0217 .0181 .0151 .0126 .0105 .00874 .00728 .00607 .00506 .00421 .00351 .00293 .00244 .00203 .00169 .000680 .000273 .000110 .000044 .000018

1.2000 .6545 .4747 .3863 .3344 .3007 .2774 .2606 .2481 .2385 .2311 .2253 .2206 .2169 .2139 .2114 .2094 .2078 .2065 .2054 .2044 .2037 .2031 .2025 .2021 .2018 .2015 .2012 .2010 .2008 .2007 .2006 .2005 .2004 .2003 .2001 .2001 .2000 .2000 .2000 .20

.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.730 4.775 4.812 4.843 4.870 4.891 4.909 4.925 4.937 4.948 4.956 4.964 4.970 4.975 4.979 4.982 4.985 4.988 4.990 4.992 4.997 4.999 4.999 5.000 5.000 5

1.0000 .4545 .2747 .1863 .1344 .1007 .0774 .0606 .0481 .0385 .0311 .0253 .0206 .0169 .0139 .0114 .00944 .00781 .00646 .00536 .00444 .00369 .00307 .00255 .00212 .00176 .00147 .00122 .00102 .000846 .000705 .000587 .000489 .000407 .000339 .000136 .0000547 .0000220 .0000088 .0000035 0

1.000 2.200 3.640 5.368 7.442 9.930 12.916 16.499 20.799 25.959 32.150 39.581 48.497 59.196 72.035 87.442 105.9 128.1 154.7 186.7 225.0 271.0 326.2 392.5 472.0 567.4 681.9 819.2 984.1 1182 1419 1704 2046 2456 2948 7344 18281 45497 113219 281733 ∞

0

575


0 .694 1.852 3.299 4.906 6.581 8.255 9.883 11.434 12.887 14.233 15.467 16.588 17.601 18.509 19.321 20.042 20.680 21.244 21.739 22.174 22.555 22.887 23.176 23.428 23.646 23.835 23.999 24.141 24.263 24.368 24.459 24.537 24.604 24.661 24.847 24.932 24.970 24.987 24.994 25


0 .455 .879 1.274 1.641 1.979 2.290 2.576 2.836 3.074 3.289 3.484 3.660 3.817 3.959 4.085 4.198 4.298 4.386 4.464 4.533 4.594 4.647 4.694 4.735 4.771 4.802 4.829 4.853 4.873 4.891 4.906 4.919 4.931 4.941 4.973 4.988 4.995 4.998 4.999 5

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 ∞

esch_app_b.qxd

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25%




N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 ∞

1.250 1.563 1.953 2.441 3.052 3.815 4.768 5.960 7.451 9.313 11.642 14.552 18.190 22.737 28.422 35.527 44.409 55.511 69.389 86.736 108.420 135.525 169.407 211.758 264.698 330.9 413.6 517.0 646.2 807.8 1010 1262 1578 1972 2465 7523 22959 70065 ∞

.8000 .6400 .5120 .4096 .3277 .2621 .2097 .1678 .1342 .1074 .0859 .0687 .0550 .0440 .0352 .0281 .0225 .0180 .0144 .0115 .0092 .0074 .0059 .0047 .0038 .00302 .00242 .00193 .00155 .00124 .000990 .000792 .000634 .000507 .000406 .000133 .000044 .000014 0

1.2500 .6944 .5123 .4234 .3718 .3388 .3163 .3004 .2888 .2801 .2735 .2684 .2645 .2615 .2591 .2572 .2558 .2546 .2537 .2529 .2523 .2519 .2515 .2512 .2509 .2508 .2506 .2505 .2504 .2503 .2502 .2502 .2502 .2501 .2501 .2500 .2500 .2500 .25

.800 1.440 1.952 2.362 2.689 2.951 3.161 3.329 3.463 3.571 3.656 3.725 3.780 3.824 3.859 3.887 3.910 3.928 3.942 3.954 3.963 3.970 3.976 3.981 3.985 3.988 3.990 3.992 3.994 3.995 3.996 3.997 3.997 3.998 3.998 3.999 4.000 4.000 4

1.0000 .4444 .2623 .1734 .1218 .0888 .0663 .0504 .0388 .0301 .0235 .0184 .0145 .0115 .0091 .0072 .00576 .00459 .00366 .00292 .00233 .00186 .00148 .00119 .000948 .000758 .000606 .000485 .000387 .000310 .000248 .000198 .000159 .000127 .000101 .0000332 .0000109 .0000036 0

1.000 2.250 3.813 5.766 8.207 11.259 15.073 19.842 25.802 33.253 42.566 54.208 68.760 86.949 109.687 138.109 173.6 218.0 273.6 342.9 429.7 538.1 673.6 843.0 1055 1319 1650 2064 2581 3227 4035 5045 6307 7885 9857 30089 91831 280256 ∞


0 .640 1.664 2.893 4.204 5.514 6.773 7.947 9.021 9.987 10.846 11.602 12.262 12.833 13.326 13.748 14.108 14.415 14.674 14.893 15.078 15.233 15.362 15.471 15.562 15.637 15.700 15.752 15.796 15.832 15.861 15.886 15.906 15.923 15.937 15.977 15.991 15.997 16


0 .444 .852 1.225 1.563 1.868 2.142 2.387 2.605 2.797 2.966 3.115 3.244 3.356 3.453 3.537 3.608 3.670 3.722 3.767 3.805 3.836 3.863 3.886 3.905 3.921 3.935 3.946 3.955 3.963 3.969 3.975 3.979 3.983 3.986 3.995 3.998 3.999 4

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 ∞

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N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

1.300 1.690 2.197 2.856 3.713 4.827 6.275 8.157 10.604 13.786 17.922 23.298 30.288 39.374 51.186 66.542 86.504 112.5 146.2 190.0 247.1 321.2 417.5 542.8 705.6 917.3 1193 1550 2015 2620 ∞

.7692 .5917 .4552 .3501 .2693 .2072 .1594 .1226 .0943 .0725 .0558 .0429 .0330 .0254 .0195 .0150 .0116 .00889 .00684 .00526 .00405 .00311 .00239 .00184 .00142 .00109 .000839 .000645 .000496 .000382

1.3000 .7348 .5506 .4616 .4106 .3784 .3569 .3419 .3312 .3235 .3177 .3135 .3102 .3078 .3060 .3046 .3035 .3027 .3021 .3016 .3012 .3009 .3007 .3006 .3004 .3003 .3003 .3002 .3001 .3001 .30

.769 1.361 1.816 2.166 2.436 2.643 2.802 2.925 3.019 3.092 3.147 3.190 3.223 3.249 3.268 3.283 3.295 3.304 3.311 3.316 3.320 3.323 3.325 3.327 3.329 3.330 3.331 3.331 3.332 3.332 3.333

1.0000 .4348 .2506 .1616 .1106 .0784 .0569 .0419 .0312 .0235 .0177 .0135 .0102 .00782 .00598 .00458 .00351 .00269 .00207 .00159 .00122 .000937 .000720 .000554 .000426 .000327 .000252 .000194 .000149 .000115 0

1.000 2.300 3.990 6.187 9.043 12.756 17.583 23.858 32.015 42.619 56.405 74.327 97.625 127.9 167.3 218.5 285.0 371.5 484.0 630.2 820.2 1067 1388 1806 2349 3054 3972 5164 6715 8730 ∞

0

577


0 .592 1.502 2.552 3.630 4.666 5.622 6.480 7.234 7.887 8.445 8.917 9.314 9.644 9.917 10.143 10.328 10.479 10.602 10.702 10.783 10.848 10.901 10.943 10.977 11.005 11.026 11.044 11.058 11.069 11.111


0 .435 .827 1.178 1.490 1.765 2.006 2.216 2.396 2.551 2.683 2.795 2.889 2.969 3.034 3.089 3.135 3.172 3.202 3.228 3.248 3.265 3.278 3.289 3.298 3.305 3.311 3.315 3.319 3.322 3.333

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

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35%



Arithmetic Gradient

N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

1.350 1.823 2.460 3.322 4.484 6.053 8.172 11.032 14.894 20.107 27.144 36.644 49.470 66.784 90.158 121.7 164.3 221.8 299.5 404.3 545.8 736.8 994.7 1343 1813 2447 3304 4460 6021 8129 ∞

.7407 .5487 .4064 .3011 .2230 .1652 .1224 .0906 .0671 .0497 .0368 .0273 .0202 .0150 .0111 .00822 .00609 .00451 .00334 .00247 .00183 .00136 .00101 .000745 .000552 .000409 .000303 .000224 .000166 .000123

1.3500 .7755 .5897 .5008 .4505 .4193 .3988 .3849 .3752 .3683 .3634 .3598 .3572 .3553 .3539 .3529 .3521 .3516 .3512 .3509 .3506 .3505 .3504 .3503 .3502 .3501 .3501 .3501 .3501 .3500 .35

.741 1.289 1.696 1.997 2.220 2.385 2.508 2.598 2.665 2.715 2.752 2.779 2.799 2.814 2.825 2.834 2.840 2.844 2.848 2.850 2.852 2.853 2.854 2.855 2.856 2.856 2.856 2.857 2.857 2.857 2.857

1.0000 .4255 .2397 .1508 .1005 .0693 .0488 .0349 .0252 .0183 .0134 .00982 .00722 .00532 .00393 .00290 .00214 .00158 .00117 .000868 .000642 .000476 .000352 .000261 .000193 .000143 .000106 .000078 .000058 .000043 0

1.000 2.350 4.173 6.633 9.954 14.438 20.492 28.664 39.696 54.590 74.697 101.8 138.5 188.0 254.7 344.9 466.6 630.9 852.7 1152 1556 2102 2839 3834 5177 6989 9437 12740 17200 23222 ∞

0

35%



0

0

.549 1.362 2.265 3.157 3.983 4.717 5.352 5.889 6.336 6.705 7.005 7.247 7.442 7.597 7.721 7.818 7.895 7.955 8.002 8.038 8.067 8.089 8.106 8.119 8.130 8.137 8.143 8.148 8.152 8.163

.426 .803 1.134 1.422 1.670 1.881 2.060 2.209 2.334 2.436 2.520 2.589 2.644 2.689 2.725 2.753 2.776 2.793 2.808 2.819 2.827 2.834 2.839 2.843 2.847 2.849 2.851 2.852 2.853 2.857

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

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N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

1.400 1.960 2.744 3.842 5.378 7.530 10.541 14.758 20.661 28.925 40.496 56.694 79.371 111.1 155.6 217.8 304.9 426.9 597.6 836.7 1171 1640 2296 3214 4500 6300 8820 12348 17287 24201 ∞

.7143 .5102 .3644 .2603 .1859 .1328 .0949 .0678 .0484 .0346 .0247 .0176 .0126 .00900 .00643 .00459 .00328 .00234 .00167 .00120 .000854 .000610 .000436 .000311 .000222 .000159 .000113 .000081 .000058 .000041

1.4000 .8167 .6294 .5408 .4914 .4613 .4419 .4291 .4203 .4143 .4101 .4072 .4051 .4036 .4026 .4018 .4013 .4009 .4007 .4005 .4003 .4002 .4002 .4001 .4001 .4001 .4000 .4000 .4000 .4000 .40

.714 1.224 1.589 1.849 2.035 2.168 2.263 2.331 2.379 2.414 2.438 2.456 2.469 2.478 2.484 2.489 2.492 2.494 2.496 2.497 2.498 2.498 2.499 2.499 2.499 2.500 2.500 2.500 2.500 2.500 2.5

1.0000 .4167 .2294 .1408 .0914 .0613 .0419 .0291 .0203 .0143 .0101 .00718 .00510 .00363 .00259 .00185 .00132 .000939 .000670 .000479 .000342 .000244 .000174 .000124 .000089 .000064 .000045 .000032 .000023 .000017 0

1.000 2.400 4.360 7.104 10.946 16.324 23.853 34.395 49.153 69.814 98.739 139.2 195.9 275.3 386.4 542.0 759.8 1065 1492 2089 2926 4097 5737 8033 11247 15747 22047 30867 43214 60501 ∞

0

579



0

0

.510 1.239 2.020 2.764 3.428 3.997 4.471 4.858 5.170 5.417 5.611 5.762 5.879 5.969 6.038 6.090 6.130 6.160 6.183 6.200 6.213 6.222 6.229 6.235 6.239 6.242 6.244 6.245 6.247 6.25

.417 .780 1.092 1.358 1.581 1.766 1.919 2.042 2.142 2.221 2.285 2.334 2.373 2.403 2.426 2.444 2.458 2.468 2.476 2.482 2.487 2.490 2.493 2.494 2.496 2.497 2.498 2.498 2.499 2.5

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

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45%




N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

1.450 2.103 3.049 4.421 6.410 9.294 13.476 19.541 28.334 41.085 59.573 86.381 125.3 181.6 263.3 381.8 553.7 802.8 1164 1688 2448 3549 5146 7462 10819 15688 22748 32984 47827 69349 ∞

.6897 .4756 .3280 .2262 .1560 .1076 .0742 .0512 .0353 .0243 .0168 .0116 .00798 .00551 .00380 .00262 .00181 .00125 .000859 .000592 .000409 .000282 .000194 .000134 .0000924 .0000637 .0000440 .0000303 .0000209 .0000144 0

1.4500 .8582 .6697 .5816 .5332 .5043 .4861 .4743 .4665 .4612 .4577 .4553 .4536 .4525 .4517 .4512 .4508 .4506 .4504 .4503 .4502 .4501 .4501 .4501 .4500 .4500 .4500 .4500 .4500 .4500 .45

.690 1.165 1.493 1.720 1.876 1.983 2.057 2.109 2.144 2.168 2.185 2.196 2.204 2.210 2.214 2.216 2.218 2.219 2.220 2.221 2.221 2.222 2.222 2.222 2.222 2.222 2.222 2.222 2.222 2.222 2.222

1.0000 .4082 .2197 .1316 .0832 .0543 .0361 .0243 .0165 .0112 .00768 .00527 .00362 .00249 .00172 .00118 .000814 .000561 .000387 .000267 .000184 .000127 .0000875 .0000603 .0000416 .0000287 .0000198 .0000136 .0000094 .0000065 0

1.000 2.450 4.553 7.601 12.022 18.431 27.725 41.202 60.743 89.077 130.2 189.7 276.1 401.4 583.0 846.3 1228 1782 2585 3749 5437 7884 11433 16579 24041 34860 50548 73296 106280 154107 ∞



0

0

.476 1.132 1.810 2.434 2.972 3.418 3.776 4.058 4.277 4.445 4.572 4.668 4.740 4.793 4.832 4.861 4.882 4.898 4.909 4.917 4.923 4.927 4.930 4.933 4.934 4.935 4.936 4.937 4.937 4.938

.408 .758 1.053 1.298 1.499 1.661 1.791 1.893 1.973 2.034 2.082 2.118 2.145 2.165 2.180 2.191 2.200 2.206 2.210 2.214 2.216 2.218 2.219 2.220 2.221 2.221 2.221 2.222 2.222 2.222

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ∞

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581 50%

Arithmetic Gradient

N









N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ∞

1.500 2.250 3.375 5.063 7.594 11.391 17.086 25.629 38.443 57.665 86.498 129.7 194.6 291.9 437.9 656.8 985.3 1478 2217 3325 4988 7482 11223 16834 25251 ∞

.6667 .4444 .2963 .1975 .1317 .0878 .0585 .0390 .0260 .0173 .0116 .00771 .00514 .00343 .00228 .00152 .00101 .000677 .000451 .000301 .000200 .000134 .0000891 .0000594 .0000396 0

1.5000 .9000 .7105 .6231 .5758 .5481 .5311 .5203 .5134 .5088 .5058 .5039 .5026 .5017 .5011 .5008 .5005 .5003 .5002 .5002 .5001 .5001 .5000 .5000 .5000 .50

.667 1.111 1.407 1.605 1.737 1.824 1.883 1.922 1.948 1.965 1.977 1.985 1.990 1.993 1.995 1.997 1.998 1.999 1.999 1.999 2.000 2.000 2.000 2.000 2.000 2

1.0000 .4000 .2105 .1231 .0758 .0481 .0311 .0203 .0134 .00882 .00585 .00388 .00258 .00172 .00114 .000762 .000508 .000339 .000226 .000150 .000100 .0000668 .0000446 .0000297 .0000198 0

1.000 2.500 4.750 8.125 13.188 20.781 32.172 49.258 74.887 113.3 171.0 257.5 387.2 581.9 873.8 1312 1969 2954 4432 6649 9974 14962 22443 33666 50500 ∞

0 .444 1.037 1.630 2.156 2.595 2.947 3.220 3.428 3.584 3.699 3.784 3.846 3.890 3.922 3.945 3.961 3.973 3.981 3.987 3.991 3.994 3.996 3.997 3.998 4

0 .400 .737 1.015 1.242 1.423 1.565 1.675 1.760 1.824 1.871 1.907 1.933 1.952 1.966 1.976 1.983 1.988 1.991 1.994 1.996 1.997 1.998 1.999 1.999 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 ∞

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60%




N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ∞

1.600 2.560 4.096 6.554 10.486 16.777 26.844 42.950 68.719 110.0 175.9 281.5 450.4 720.6 1153 1845 2951 4722 7556 12089 ∞

.6250 .3906 .2441 .1526 .0954 .0596 .0373 .0233 .0146 .00909 .00568 .00355 .00222 .00139 .000867 .000542 .000339 .000212 .000132 .000083 0

1.6000 .9846 .7938 .7080 .6633 .6380 .6232 .6143 .6089 .6055 .6034 .6021 .6013 .6008 .6005 .6003 .6002 .6001 .6001 .6000 .60

.625 1.016 1.260 1.412 1.508 1.567 1.605 1.628 1.642 1.652 1.657 1.661 1.663 1.664 1.665 1.666 1.666 1.666 1.666 1.667 1.667

1.0000 .3846 .1938 .1080 .0633 .0380 .0232 .0143 .00886 .00551 .00343 .00214 .00134 .000834 .000521 .000325 .000203 .000127 .000079 .000050 0

1.000 2.600 5.160 9.256 15.810 26.295 43.073 69.916 112.9 181.6 291.5 467.5 748.9 1199 1920 3073 4917 7869 12591 20147 ∞



0

0

.391 .879 1.337 1.718 2.016 2.240 2.403 2.519 2.601 2.658 2.697 2.724 2.742 2.754 2.762 2.767 2.771 2.773 2.775 2.778

.385 .698 .946 1.140 1.286 1.396 1.476 1.534 1.575 1.604 1.624 1.638 1.647 1.654 1.658 1.661 1.663 1.664 1.665 1.667

70% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ∞

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ∞ 70%

1.700 2.890 4.913 8.352 14.199 24.138 41.034 69.758 118.6 201.6 342.7 582.6 990.5 1684 2862 4866 8272 14063 23907 40642 ∞

.5882 .3460 .2035 .1197 .0704 .0414 .0244 .0143 .00843 .00496 .00292 .00172 .00101 .000594 .000349 .000206 .000121 .000071 .000042 .000025 0

1.7000 1.0704 .8789 .7952 .7530 .7303 .7175 .7102 .7060 .7035 .7020 .7012 .7007 .7004 .7002 .7001 .7001 .7000 .7000 .7000 .70

.588 .934 1.138 1.258 1.328 1.369 1.394 1.408 1.417 1.421 1.424 1.426 1.427 1.428 1.428 1.428 1.428 1.428 1.429 1.429 1.429

1.0000 .3704 .1789 .0952 .0530 .0303 .0175 .0102 .00595 .00349 .00205 .00120 .000707 .000416 .000245 .000144 .000085 .000050 .000029 .000017 0

1.000 2.700 5.590 10.503 18.855 33.054 57.191 98.225 168.0 286.6 488.2 830.9 1414 2404 4088 6950 11816 20089 34152 58059 ∞

0

0

.346 .753 1.112 1.394 1.601 1.747 1.848 1.915 1.960 1.989 2.008 2.020 2.028 2.033 2.036 2.038 2.039 2.040 2.040 2.041

.370 .662 .885 1.050 1.169 1.254 1.312 1.352 1.379 1.396 1.408 1.415 1.420 1.423 1.425 1.427 1.427 1.428 1.428 1.429

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ∞

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N







1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ∞

1.800 3.240 5.832 10.498 18.896 34.012 61.222 110.2 198.4 357.0 642.7 1157 2082 3748 6747 ∞

.5556 .3086 .1715 .0953 .0529 .0294 .0163 .00907 .00504 .00280 .00156 .000864 .000480 .000267 .000148

1.8000 1.1571 .9656 .8842 .8447 .8242 .8133 .8073 .8041 .8022 .8012 .8007 .8004 .8002 .8001 .80

.556 .864 1.036 1.131 1.184 1.213 1.230 1.239 1.244 1.246 1.248 1.249 1.249 1.250 1.250 1.25

1.0000 .3571 .1656 .0842 .0447 .0242 .0133 .00733 .00405 .00225 .00125 .000692 .000384 .000213 .000119 0

1.000 2.800 6.040 11.872 22.370 41.265 75.278 136.5 246.7 445.1 802.1 1445 2602 4684 8432 ∞

0



0

0

.309 .652 .937 1.149 1.296 1.394 1.458 1.498 1.523 1.539 1.548 1.554 1.557 1.559 1.563

.357 .629 .829 .971 1.068 1.134 1.177 1.204 1.222 1.233 1.240 1.244 1.246 1.248 1.25

90% 1 2 3 4 5 6 7 8 9 10 ∞

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ∞ 90%

1.900 3.610 6.859 13.032 24.761 47.046 89.387 169.8 322.7 613.1 ∞

.5263 .2770 .1458 .0767 .0404 .0213 .0112 .00589 .00310 .00163 0

1.9000 1.2448 1.0536 0.9748 0.9379 0.9195 0.9102 0.9053 0.9028 0.9015 0.90

.526 .803 .949 1.026 1.066 1.087 1.099 1.105 1.108 1.109 1.111

1.0000 .3448 .1536 .0748 .0379 .0195 .0102 .00533 .00280 .00147 0

1.000 2.900 6.510 13.369 26.401 51.162 98.208 187.6 357.4 680.1 ∞

0. .277 .569 .799 .960 1.067 1.134 1.175 1.200 1.214 1.235

0 .345 .599 .779 .901 .981 1.032 1.064 1.083 1.095 1.111

100% 1 2 3 4 5 6 7 8 9 10 ∞

583

1 2 3 4 5 6 7 8 9 10 ∞ 100%

2.000 4.000 8.000 16.000 32.000 64.000 128.0 256.0 512.0 1024 ∞

.5000 .2500 .1250 .0625 .0313 .0156 .00781 .00391 .00195 .00098 0

2.0000 1.3333 1.1429 1.0667 1.0323 1.0159 1.0079 1.0039 1.0020 1.0010 1

.500 .750 .875 .938 .969 .984 .992 .996 .998 .999 1

1.0000 .3333 .1429 .0667 .0323 .0159 .00787 .00392 .00196 .00098 0

1.000 3.000 7.000 15.000 31.000 63.000 127.0 255.0 511.0 1023 ∞

0

0

.250 .500 .688 .813 .891 .938 .965 .980 .989 1

.333 .571 .733 .839 .905 .945 .969 .982 .990 1

1 2 3 4 5 6 7 8 9 10 ∞

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