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APPENDIX A
i 0.5%
Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0050 1.0100 1.0151 1.0202 1.0253 1.0304 1.0355 1.0407 1.0459 1.0511 1.0564 1.0617 1.0670 1.0723 1.0777 1.0831 1.0885 1.0939 1.0994 1.1049 1.1104 1.1160 1.1216 1.1272 1.1328 1.1385 1.1442 1.1499 1.1556 1.1614 1.1672 1.1730 1.1789 1.1848 1.1907 1.2208 1.2516 1.2832 1.3156 1.3489 1.3829 1.4178 1.4536 1.4903 1.5280 1.5666 1.6061 1.6467
0.99502 0.99007 0.98515 0.98025 0.97537 0.97052 0.96569 0.96089 0.95610 0.95135 0.94661 0.94191 0.93722 0.93256 0.92792 0.92330 0.91871 0.91414 0.90959 0.90506 0.90056 0.89608 0.89162 0.88719 0.88277 0.87838 0.87401 0.86966 0.86533 0.86103 0.85675 0.85248 0.84824 0.84402 0.83982 0.81914 0.79896 0.77929 0.76009 0.74137 0.72311 0.70530 0.68793 0.67099 0.65446 0.63834 0.62262 0.60729
1.0000 0.49875 0.33167 0.24813 0.19801 0.16460 0.14073 0.12283 0.10891 0.09777 0.08866 0.08107 0.07464 0.06914 0.06436 0.06019 0.05651 0.05323 0.05030 0.04767 0.04528 0.04311 0.04113 0.03932 0.03765 0.03611 0.03469 0.03336 0.03213 0.03098 0.02990 0.02889 0.02795 0.02706 0.02622 0.02265 0.01987 0.01765 0.01584 0.01433 0.01306 0.01197 0.01102 0.01020 0.00947 0.00883 0.00825 0.00773
1.0000 2.0050 3.0150 4.0301 5.0503 6.0755 7.1059 8.1414 9.1821 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 44.159 50.324 56.645 63.126 69.770 76.582 83.566 90.727 98.068 105.59 113.31 121.22 129.33
1.0050 0.50375 0.33667 0.25313 0.20301 0.16960 0.14573 0.12783 0.11391 0.10277 0.09366 0.08607 0.07964 0.07414 0.06936 0.06519 0.06151 0.05823 0.05530 0.05267 0.05028 0.04811 0.04613 0.04432 0.04265 0.04111 0.03969 0.03836 0.03713 0.03598 0.03490 0.03389 0.03295 0.03206 0.03122 0.02765 0.02487 0.02265 0.02084 0.01933 0.01806 0.01697 0.01602 0.01520 0.01447 0.01383 0.01325 0.01273
0.99502 1.9851 2.9702 3.9505 4.9259 5.8964 6.8621 7.8230 8.7791 9.7304 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 36.172 40.207 44.143 47.981 51.726 55.377 58.939 62.414 65.802 69.108 72.331 75.476 78.543
0.00000 0.49875 0.99667 1.4938 1.9900 2.4855 2.9801 3.4738 3.9668 4.4589 4.9501 5.4406 5.9302 6.4190 6.9069 7.3940 7.8803 8.3658 8.8504 9.3342 9.8172 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 18.836 21.159 23.462 25.745 28.006 30.247 32.468 34.668 36.847 39.006 41.145 43.263 45.361
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Discrete Compounding, Discrete Cash Flows SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.0721 1.0829 1.0937 1.1046 1.1157 1.1268 1.1381 1.1495 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2324 1.2447 1.2572 1.2697 1.2824 1.2953 1.3082 1.3213 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 1.4166 1.4889 1.5648 1.6446 1.7285 1.8167 1.9094 2.0068 2.1091 2.2167 2.3298 2.4486 2.5735 2.7048
0.99010 0.98030 0.97059 0.96098 0.95147 0.94205 0.93272 0.92348 0.91434 0.90529 0.89632 0.88745 0.87866 0.86996 0.86135 0.85282 0.84438 0.83602 0.82774 0.81954 0.81143 0.80340 0.79544 0.78757 0.77977 0.77205 0.76440 0.75684 0.74934 0.74192 0.73458 0.72730 0.72010 0.71297 0.70591 0.67165 0.63905 0.60804 0.57853 0.55045 0.52373 0.49831 0.47413 0.45112 0.42922 0.40839 0.38857 0.36971
1.0000 0.49751 0.33002 0.24628 0.19604 0.16255 0.13863 0.12069 0.10674 0.09558 0.08645 0.07885 0.07241 0.06690 0.06212 0.05794 0.05426 0.05098 0.04805 0.04542 0.04303 0.04086 0.03889 0.03707 0.03541 0.03387 0.03245 0.03112 0.02990 0.02875 0.02768 0.02667 0.02573 0.02484 0.02400 0.02046 0.01771 0.01551 0.01373 0.01224 0.01100 0.00993 0.00902 0.00822 0.00752 0.00690 0.00636 0.00587
1.0000 2.0100 3.0301 4.0604 5.1010 6.1520 7.2135 8.2857 9.3685 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 48.886 56.481 64.463 72.852 81.670 90.937 100.68 110.91 121.67 132.98 144.86 157.35 170.48
1.0100 0.50751 0.34002 0.25628 0.20604 0.17255 0.14863 0.13069 0.11674 0.10558 0.09645 0.08885 0.08241 0.07690 0.07212 0.06794 0.06426 0.06098 0.05805 0.05542 0.05303 0.05086 0.04889 0.04707 0.04541 0.04387 0.04245 0.04112 0.03990 0.03875 0.03768 0.03667 0.03573 0.03484 0.03400 0.03046 0.02771 0.02551 0.02373 0.02224 0.02100 0.01993 0.01902 0.01822 0.01752 0.01690 0.01636 0.01587
0.99010 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 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 32.835 36.095 39.196 42.147 44.955 47.627 50.169 52.587 54.888 57.078 59.161 61.143 63.029
0.00000 0.49751 0.99337 1.4876 1.9801 2.4710 2.9602 3.4478 3.9337 4.4179 4.9005 5.3815 5.8607 6.3384 6.8143 7.2886 7.7613 8.2323 8.7017 9.1694 9.6354 10.100 10.563 11.024 11.483 11.941 12.397 12.852 13.304 13.756 14.205 14.653 15.099 15.544 15.987 18.178 20.327 22.436 24.505 26.533 28.522 30.470 32.379 34.249 36.080 37.872 39.626 41.343
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APPENDIX A
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Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0150 1.0302 1.0457 1.0614 1.0773 1.0934 1.1098 1.1265 1.1434 1.1605 1.1779 1.1956 1.2136 1.2318 1.2502 1.2690 1.2880 1.3073 1.3270 1.3469 1.3671 1.3876 1.4084 1.4295 1.4509 1.4727 1.4948 1.5172 1.5400 1.5631 1.5865 1.6103 1.6345 1.6590 1.6839 1.8140 1.9542 2.1052 2.2679 2.4432 2.6320 2.8355 3.0546 3.2907 3.5450 3.8189 4.1141 4.4320
0.98522 0.97066 0.95632 0.94218 0.92826 0.91454 0.90103 0.88771 0.87459 0.86167 0.84893 0.83639 0.82403 0.81185 0.79985 0.78803 0.77639 0.76491 0.75361 0.74247 0.73150 0.72069 0.71004 0.69954 0.68921 0.67902 0.66899 0.65910 0.64936 0.63976 0.63031 0.62099 0.61182 0.60277 0.59387 0.55126 0.51171 0.47500 0.44093 0.40930 0.37993 0.35268 0.32738 0.30389 0.28209 0.26185 0.24307 0.22563
1.0000 0.49628 0.32838 0.24444 0.19409 0.16053 0.13656 0.11858 0.10461 0.09343 0.08429 0.07668 0.07024 0.06472 0.05994 0.05577 0.05208 0.04881 0.04588 0.04325 0.04087 0.03870 0.03673 0.03492 0.03326 0.03173 0.03032 0.02900 0.02778 0.02664 0.02557 0.02458 0.02364 0.02276 0.02193 0.01843 0.01572 0.01357 0.01183 0.01039 0.00919 0.00817 0.00730 0.00655 0.00589 0.00532 0.00482 0.00437
1.0000 2.0150 3.0452 4.0909 5.1523 6.2296 7.3230 8.4328 9.5593 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 54.268 63.614 73.683 84.530 96.215 108.80 122.36 136.97 152.71 169.67 187.93 207.61 228.80
1.0150 0.51128 0.34338 0.25944 0.20909 0.17553 0.15156 0.13358 0.11961 0.10843 0.09929 0.09168 0.08524 0.07972 0.07494 0.07077 0.06708 0.06381 0.06088 0.05825 0.05587 0.05370 0.05173 0.04992 0.04826 0.04673 0.04532 0.04400 0.04278 0.04164 0.04057 0.03958 0.03864 0.03776 0.03693 0.03343 0.03072 0.02857 0.02683 0.02539 0.02419 0.02317 0.02230 0.02155 0.02089 0.02032 0.01982 0.01937
0.98522 1.9559 2.9122 3.8544 4.7826 5.6972 6.5982 7.4859 8.3605 9.2222 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 29.916 32.552 35.000 37.271 39.380 41.338 43.155 44.842 46.407 47.861 49.210 50.462 51.625
0.00000 0.49628 0.99007 1.4814 1.9702 2.4566 2.9405 3.4219 3.9008 4.3772 4.8512 5.3227 5.7917 6.2582 6.7223 7.1839 7.6431 8.0997 8.5539 9.0057 9.4550 9.9018 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 17.528 19.507 21.428 23.289 25.093 26.839 28.529 30.163 31.742 33.268 34.740 36.160 37.530
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Discrete Compounding, Discrete Cash Flows SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190 1.2434 1.2682 1.2936 1.3195 1.3459 1.3728 1.4002 1.4282 1.4568 1.4859 1.5157 1.5460 1.5769 1.6084 1.6406 1.6734 1.7069 1.7410 1.7758 1.8114 1.8476 1.8845 1.9222 1.9607 1.9999 2.2080 2.4379 2.6916 2.9717 3.2810 3.6225 3.9996 4.4158 4.8754 5.3829 5.9431 6.5617 7.2446
0.98039 0.96117 0.94232 0.92385 0.90573 0.88797 0.87056 0.85349 0.83676 0.82035 0.80426 0.78849 0.77303 0.75788 0.74301 0.72845 0.71416 0.70016 0.68643 0.67297 0.65978 0.64684 0.63416 0.62172 0.60953 0.59758 0.58586 0.57437 0.56311 0.55207 0.54125 0.53063 0.52023 0.51003 0.50003 0.45289 0.41020 0.37153 0.33650 0.30478 0.27605 0.25003 0.22646 0.20511 0.18577 0.16826 0.15240 0.13803
1.0000 0.49505 0.32675 0.24262 0.19216 0.15853 0.13451 0.11651 0.10252 0.09133 0.08218 0.07456 0.06812 0.06260 0.05783 0.05365 0.04997 0.04670 0.04378 0.04116 0.03878 0.03663 0.03467 0.03287 0.03122 0.02970 0.02829 0.02699 0.02578 0.02465 0.02360 0.02261 0.02169 0.02082 0.02000 0.01656 0.01391 0.01182 0.01014 0.00877 0.00763 0.00667 0.00586 0.00516 0.00456 0.00405 0.00360 0.00320
1.0000 2.0200 3.0604 4.1216 5.2040 6.3081 7.4343 8.5830 9.7546 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 60.402 71.893 84.579 98.587 114.05 131.13 149.98 170.79 193.77 219.14 247.16 278.08 312.23
1.0200 0.51505 0.34675 0.26262 0.21216 0.17853 0.15451 0.13651 0.12252 0.11133 0.10218 0.09456 0.08812 0.08260 0.07783 0.07365 0.06997 0.06670 0.06378 0.06116 0.05878 0.05663 0.05467 0.05287 0.05122 0.04970 0.04829 0.04699 0.04578 0.04465 0.04360 0.04261 0.04169 0.04082 0.04000 0.03656 0.03391 0.03182 0.03014 0.02877 0.02763 0.02667 0.02586 0.02516 0.02456 0.02405 0.02360 0.02320
0.98039 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 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 27.355 29.490 31.424 33.175 34.761 36.197 37.499 38.677 39.745 40.711 41.587 42.380 43.098
0.00000 0.49505 0.98680 1.4752 1.9604 2.4423 2.9208 3.3961 3.8681 4.3367 4.8021 5.2642 5.7231 6.1786 6.6309 7.0799 7.5256 7.9681 8.4073 8.8433 9.2760 9.7050 10.1320 10.5550 10.9740 11.391 11.804 12.214 12.621 13.025 13.426 13.823 14.217 14.608 14.996 16.889 18.703 20.442 22.106 23.696 25.215 26.663 28.043 29.357 30.606 31.793 32.919 33.986
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APPENDIX A
i 3%
Discrete Compounding, Discrete Cash Flows 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 40 45 50 55 60 65 70 75 80 85 90 95 100
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,N)
0.97087 0.94260 0.91514 0.88849 0.86261 0.83748 0.81309 0.78941 0.76642 0.74409 0.72242 0.70138 0.68095 0.66112 0.64186 0.62317 0.60502 0.58739 0.57029 0.55368 0.53755 0.52189 0.50669 0.49193 0.47761 0.46369 0.45019 0.43708 0.42435 0.41199 0.39999 0.38834 0.37703 0.36604 0.35538 0.30656 0.26444 0.22811 0.19677 0.16973 0.14641 0.12630 0.10895 0.09398 0.08107 0.06993 0.06032 0.05203
1.0000 0.49261 0.32353 0.23903 0.18835 0.15460 0.13051 0.11246 0.09843 0.08723 0.07808 0.07046 0.06403 0.05853 0.05377 0.04961 0.04595 0.04271 0.03981 0.03722 0.03487 0.03275 0.03081 0.02905 0.02743 0.02594 0.02456 0.02329 0.02211 0.02102 0.02000 0.01905 0.01816 0.01732 0.01654 0.01326 0.01079 0.00887 0.00735 0.00613 0.00515 0.00434 0.00367 0.00311 0.00265 0.00226 0.00193 0.00165
1.0000 2.0300 3.0909 4.1836 5.3091 6.4684 7.6625 8.8923 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 92.720 112.80 136.07 163.05 194.33 230.59 272.63 321.36 377.86 443.35 519.27 607.29
1.0300 0.52261 0.35353 0.26903 0.21835 0.18460 0.16051 0.14246 0.12843 0.11723 0.10808 0.10046 0.09403 0.08853 0.08377 0.07961 0.07595 0.07271 0.06981 0.06722 0.06487 0.06275 0.06081 0.05905 0.05743 0.05594 0.05456 0.05329 0.05211 0.05102 0.05000 0.04905 0.04816 0.04732 0.04654 0.04326 0.04079 0.03887 0.03735 0.03613 0.03515 0.03434 0.03367 0.03311 0.03265 0.03226 0.03193 0.03165
0.97087 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 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
0.00000 0.49261 0.98030 1.4631 1.9409 2.4138 2.8819 3.3450 3.8032 4.2565 4.7049 5.1485 5.5872 6.0210 6.4500 6.8742 7.2936 7.7081 8.1179 8.5229 8.9231 9.3186 9.7093 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
1.0300 1.0609 1.0927 1.1255 1.1593 1.1941 1.2299 1.2668 1.3048 1.3439 1.3842 1.4258 1.4685 1.5126 1.5580 1.6047 1.6528 1.7024 1.7535 1.8061 1.8603 1.9161 1.9736 2.0328 2.0938 2.1566 2.2213 2.2879 2.3566 2.4273 2.5001 2.5751 2.6523 2.7319 2.8139 3.2620 3.7816 4.3839 5.0821 5.8916 6.8300 7.9178 9.1789 10.641 12.336 14.300 16.578 19.219
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Discrete Compounding, Discrete Cash Flows 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 40 45 50 55 60 65 70 75 80 85 90 95 100
501
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,N)
0.96154 0.92456 0.88900 0.85480 0.82193 0.79031 0.75992 0.73069 0.70259 0.67556 0.64958 0.62460 0.60057 0.57748 0.55526 0.53391 0.51337 0.49363 0.47464 0.45639 0.43883 0.42196 0.40573 0.39012 0.37512 0.36069 0.34682 0.33348 0.32065 0.30832 0.29646 0.28506 0.27409 0.26355 0.25342 0.20829 0.17120 0.14071 0.11566 0.09506 0.07813 0.06422 0.05278 0.04338 0.03566 0.02931 0.02409 0.01980
1.0000 0.49020 0.32035 0.23549 0.18463 0.15076 0.12661 0.10853 0.09449 0.08329 0.07415 0.06655 0.06014 0.05467 0.04994 0.04582 0.04220 0.03899 0.03614 0.03358 0.03128 0.02920 0.02731 0.02559 0.02401 0.02257 0.02124 0.02001 0.01888 0.01783 0.01686 0.01595 0.01510 0.01431 0.01358 0.01052 0.00826 0.00655 0.00523 0.00420 0.00339 0.00275 0.00223 0.00181 0.00148 0.00121 0.00099 0.00081
1.0000 2.0400 3.1216 4.2465 5.4163 6.6330 7.8983 9.2142 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 95.026 121.03 152.67 191.16 237.99 294.97 364.29 448.63 551.24 676.09 827.98 1012.8 1237.6
1.0400 0.53020 0.36035 0.27549 0.22463 0.19076 0.16661 0.14853 0.13449 0.12329 0.11415 0.10655 0.10014 0.09467 0.08994 0.08582 0.08220 0.07899 0.07614 0.07358 0.07128 0.06920 0.06731 0.06559 0.06401 0.06257 0.06124 0.06001 0.05888 0.05783 0.05686 0.05595 0.05510 0.05431 0.05358 0.05052 0.04826 0.04655 0.04523 0.04420 0.04339 0.04275 0.04223 0.04181 0.04148 0.04121 0.04099 0.04081
0.96154 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 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
0.00000 0.49020 0.97386 1.4510 1.9216 2.3857 2.8433 3.2944 3.7391 4.1773 4.6090 5.0343 5.4533 5.8659 6.2721 6.6720 7.0656 7.4530 7.8342 8.2091 8.5779 8.9407 9.2973 9.6479 9.9925 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
1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009 1.8730 1.9479 2.0258 2.1068 2.1911 2.2788 2.3699 2.4647 2.5633 2.6658 2.7725 2.8834 2.9987 3.1187 3.2434 3.3731 3.5081 3.6484 3.7943 3.9461 4.8010 5.8412 7.1067 8.6464 10.520 12.799 15.572 18.945 23.050 28.044 34.119 41.511 50.505
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APPENDIX A
i 5%
Discrete Compounding, Discrete Cash Flows SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 1.7103 1.7959 1.8856 1.9799 2.0789 2.1829 2.2920 2.4066 2.5270 2.6533 2.7860 2.9253 3.0715 3.2251 3.3864 3.5557 3.7335 3.9201 4.1161 4.3219 4.5380 4.7649 5.0032 5.2533 5.5160 7.0400 8.9850 11.467 14.636 18.679 23.840 30.426 38.833 49.561 63.254 80.730 103.03 131.50
0.95238 0.90703 0.86384 0.82270 0.78353 0.74622 0.71068 0.67684 0.64461 0.61391 0.58468 0.55684 0.53032 0.50507 0.48102 0.45811 0.43630 0.41552 0.39573 0.37689 0.35894 0.34185 0.32557 0.31007 0.29530 0.28124 0.26785 0.25509 0.24295 0.23138 0.22036 0.20987 0.19987 0.19035 0.18129 0.14205 0.11130 0.08720 0.06833 0.05354 0.04195 0.03287 0.02575 0.02018 0.01581 0.01239 0.00971 0.00760
1.0000 0.48780 0.31721 0.23201 0.18097 0.14702 0.12282 0.10472 0.09069 0.07950 0.07039 0.06283 0.05646 0.05102 0.04634 0.04227 0.03870 0.03555 0.03275 0.03024 0.02800 0.02597 0.02414 0.02247 0.02095 0.01956 0.01829 0.01712 0.01605 0.01505 0.01413 0.01328 0.01249 0.01176 0.01107 0.00828 0.00626 0.00478 0.00367 0.00283 0.00219 0.00170 0.00132 0.00103 0.00080 0.00063 0.00049 0.00038
1.0000 2.0500 3.1525 4.3101 5.5256 6.8019 8.1420 9.5491 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 90.320 120.80 159.70 209.35 272.71 353.58 456.80 588.53 756.65 971.23 1245.1 1594.6 2040.7 2610.0
1.0500 0.53780 0.36721 0.28201 0.23097 0.19702 0.17282 0.15472 0.14069 0.12950 0.12039 0.11283 0.10646 0.10102 0.09634 0.09227 0.08870 0.08555 0.08275 0.08024 0.07800 0.07597 0.07414 0.07247 0.07095 0.06956 0.06829 0.06712 0.06605 0.06505 0.06413 0.06328 0.06249 0.06176 0.06107 0.05828 0.05626 0.05478 0.05367 0.05283 0.05219 0.05170 0.05132 0.05103 0.05080 0.05063 0.05049 0.05038
0.95238 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 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
0.00000 0.48780 0.96749 1.4391 1.9025 2.3579 2.8052 3.2445 3.6758 4.0991 4.5144 4.9219 5.3215 5.7133 6.0973 6.4736 6.8423 7.2034 7.5569 7.9030 8.2416 8.5730 8.8971 9.2140 9.5238 9.8266 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
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Discrete Compounding, Discrete Cash Flows SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 1.5036 1.5938 1.6895 1.7908 1.8983 2.0122 2.1329 2.2609 2.3966 2.5404 2.6928 2.8543 3.0256 3.2071 3.3996 3.6035 3.8197 4.0489 4.2919 4.5494 4.8223 5.1117 5.4184 5.7435 6.0881 6.4534 6.8406 7.2510 7.6861 10.286 13.765 18.420 24.650 32.988 44.145 59.076 79.057 105.80 141.58 189.46 253.55 339.30
0.94340 0.89000 0.83962 0.79209 0.74726 0.70496 0.66506 0.62741 0.59190 0.55839 0.52679 0.49697 0.46884 0.44230 0.41727 0.39365 0.37136 0.35034 0.33051 0.31180 0.29416 0.27751 0.26180 0.24698 0.23300 0.21981 0.20737 0.19563 0.18456 0.17411 0.16425 0.15496 0.14619 0.13791 0.13011 0.09722 0.07265 0.05429 0.04057 0.03031 0.02265 0.01693 0.01265 0.00945 0.00706 0.00528 0.00394 0.00295
1.0000 0.48544 0.31411 0.22859 0.17740 0.14336 0.11914 0.10104 0.08702 0.07587 0.06679 0.05928 0.05296 0.04758 0.04296 0.03895 0.03544 0.03236 0.02962 0.02718 0.02500 0.02305 0.02128 0.01968 0.01823 0.01690 0.01570 0.01459 0.01358 0.01265 0.01179 0.01100 0.01027 0.00960 0.00897 0.00646 0.00470 0.00344 0.00254 0.00188 0.00139 0.00103 0.00077 0.00057 0.00043 0.00032 0.00024 0.00018
1.0000 2.0600 3.1836 4.3746 5.6371 6.9753 8.3938 9.8975 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 97.343 104.18 111.43 154.76 212.74 290.34 394.17 533.13 719.08 967.93 1300.9 1746.6 2343.0 3141.1 4209.1 5638.4
1.0600 0.54544 0.37411 0.28859 0.23740 0.20336 0.17914 0.16104 0.14702 0.13587 0.12679 0.11928 0.11296 0.10758 0.10296 0.09895 0.09544 0.09236 0.08962 0.08718 0.08500 0.08305 0.08128 0.07968 0.07823 0.07690 0.07570 0.07459 0.07358 0.07265 0.07179 0.07100 0.07027 0.06960 0.06897 0.06646 0.06470 0.06344 0.06254 0.06188 0.06139 0.06103 0.06077 0.06057 0.06043 0.06032 0.06024 0.06018
0.94340 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 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
0.00000 0.48544 0.96118 1.4272 1.8836 2.3304 2.7676 3.1952 3.6133 4.0220 4.4213 4.8113 5.1920 5.5635 5.9260 6.2794 6.6240 6.9597 7.2867 7.6051 7.9151 8.2166 8.5099 8.7951 9.0722 9.3414 9.6029 9.8568 10.103 10.342 10.574 10.799 11.017 11.228 11.432 12.359 13.141 13.796 14.341 14.791 15.160 15.461 15.706 15.903 16.062 16.189 16.290 16.371
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APPENDIX A
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Discrete Compounding, Discrete Cash Flows SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 4.1406 4.4304 4.7405 5.0724 5.4274 5.8074 6.2139 6.6488 7.1143 7.6123 8.1451 8.7153 9.3253 9.9781 10.677 14.974 21.002 29.457 41.315 57.946 81.273 113.99 159.88 224.23 314.50 441.10 618.67 867.72
0.93458 0.87344 0.81630 0.76290 0.71299 0.66634 0.62275 0.58201 0.54393 0.50835 0.47509 0.44401 0.41496 0.38782 0.36245 0.33873 0.31657 0.29586 0.27651 0.25842 0.24151 0.22571 0.21095 0.19715 0.18425 0.17220 0.16093 0.15040 0.14056 0.13137 0.12277 0.11474 0.10723 0.10022 0.09366 0.06678 0.04761 0.03395 0.02420 0.01726 0.01230 0.00877 0.00625 0.00446 0.00318 0.00227 0.00162 0.00115
1.0000 0.48309 0.31105 0.22523 0.17389 0.13980 0.11555 0.09747 0.08349 0.07238 0.06336 0.05590 0.04965 0.04434 0.03979 0.03586 0.03243 0.02941 0.02675 0.02439 0.02229 0.02041 0.01871 0.01719 0.01581 0.01456 0.01343 0.01239 0.01145 0.01059 0.00980 0.00907 0.00841 0.00780 0.00723 0.00501 0.00350 0.00246 0.00174 0.00123 0.00087 0.00062 0.00044 0.00031 0.00022 0.00016 0.00011 0.00008
1.0000 2.0700 3.2149 4.4399 5.7507 7.1533 8.6540 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 94.461 102.07 110.22 118.93 128.26 138.24 199.64 285.75 406.53 575.93 813.52 1146.8 1614.1 2269.7 3189.1 4478.6 6287.2 8823.9 12 382.0
1.0700 0.55309 0.38105 0.29523 0.24389 0.20980 0.18555 0.16747 0.15349 0.14238 0.13336 0.12590 0.11965 0.11434 0.10979 0.10586 0.10243 0.09941 0.09675 0.09439 0.09229 0.09041 0.08871 0.08719 0.08581 0.08456 0.08343 0.08239 0.08145 0.08059 0.07980 0.07907 0.07841 0.07780 0.07723 0.07501 0.07350 0.07246 0.07174 0.07123 0.07087 0.07062 0.07044 0.07031 0.07022 0.07016 0.07011 0.07008
0.93458 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 7.4987 7.9427 8.3577 8.7455 9.1079 9.4466 9.7632 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
0.00000 0.48309 0.95493 1.4155 1.8650 2.3032 2.7304 3.1465 3.5517 3.9461 4.3296 4.7025 5.0648 5.4167 5.7583 6.0897 6.4110 6.7225 7.0242 7.3163 7.5990 7.8725 8.1369 8.3923 8.6391 8.8773 9.1072 9.3289 9.5427 9.7487 9.9471 10.138 10.322 10.499 10.669 11.423 12.036 12.529 12.921 13.232 13.476 13.666 13.814 13.927 14.015 14.081 14.132 14.170
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Discrete Compounding, Discrete Cash Flows SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722 3.4259 3.7000 3.9960 4.3157 4.6610 5.0338 5.4365 5.8715 6.3412 6.8485 7.3964 7.9881 8.6271 9.3173 10.063 10.868 11.737 12.676 13.690 14.785 21.725 31.920 46.902 68.914 101.26 148.78 218.61 321.20 471.95 693.46 1018.9 1497.1 2199.8
0.92593 0.85734 0.79383 0.73503 0.68058 0.63017 0.58349 0.54027 0.50025 0.46319 0.42888 0.39711 0.36770 0.34046 0.31524 0.29189 0.27027 0.25025 0.23171 0.21455 0.19866 0.18394 0.17032 0.15770 0.14602 0.13520 0.12519 0.11591 0.10733 0.09938 0.09202 0.08520 0.07889 0.07305 0.06763 0.04603 0.03133 0.02132 0.01451 0.00988 0.00672 0.00457 0.00311 0.00212 0.00144 0.00098 0.00067 0.00045
1.0000 0.48077 0.30803 0.22192 0.17046 0.13632 0.11207 0.09401 0.08008 0.06903 0.06008 0.05270 0.04652 0.04130 0.03683 0.03298 0.02963 0.02670 0.02413 0.02185 0.01983 0.01803 0.01642 0.01498 0.01368 0.01251 0.01145 0.01049 0.00962 0.00883 0.00811 0.00745 0.00685 0.00630 0.00580 0.00386 0.00259 0.00174 0.00118 0.00080 0.00054 0.00037 0.00025 0.00017 0.00012 0.00008 0.00005 0.00004
1.0000 2.0800 3.2464 4.5061 5.8666 7.3359 8.9228 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 95.339 103.97 113.28 123.35 134.21 145.95 158.63 172.32 259.06 386.51 573.77 848.92 1253.2 1847.2 2720.1 4002.6 5886.9 8655.7 12 724.0 18 702.0 27 485.0
1.0800 0.56077 0.38803 0.30192 0.25046 0.21632 0.19207 0.17401 0.16008 0.14903 0.14008 0.13270 0.12652 0.12130 0.11683 0.11298 0.10963 0.10670 0.10413 0.10185 0.09983 0.09803 0.09642 0.09498 0.09368 0.09251 0.09145 0.09049 0.08962 0.08883 0.08811 0.08745 0.08685 0.08630 0.08580 0.08386 0.08259 0.08174 0.08118 0.08080 0.08054 0.08037 0.08025 0.08017 0.08012 0.08008 0.08005 0.08004
0.92593 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 7.1390 7.5361 7.9038 8.2442 8.5595 8.8514 9.1216 9.3719 9.6036 9.8181 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
0.00000 0.48077 0.94874 1.4040 1.8465 2.2763 2.6937 3.0985 3.4910 3.8713 4.2395 4.5957 4.9402 5.2731 5.5945 5.9046 6.2037 6.4920 6.7697 7.0369 7.2940 7.5412 7.7786 8.0066 8.2254 8.4352 8.6363 8.8289 9.0133 9.1897 9.3584 9.5197 9.6737 9.8208 9.9611 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
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APPENDIX A
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Discrete Compounding, Discrete Cash Flows SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 2.5804 2.8127 3.0658 3.3417 3.6425 3.9703 4.3276 4.7171 5.1417 5.6044 6.1088 6.6586 7.2579 7.9111 8.6231 9.3992 10.245 11.167 12.172 13.268 14.462 15.763 17.182 18.728 20.414 31.409 48.327 74.358 114.41 176.03 270.85 416.73 641.19 986.55 1517.9 2335.5 3593.5 5529.0
0.91743 0.84168 0.77218 0.70843 0.64993 0.59627 0.54703 0.50187 0.46043 0.42241 0.38753 0.35553 0.32618 0.29925 0.27454 0.25187 0.23107 0.21199 0.19449 0.17843 0.16370 0.15018 0.13778 0.12640 0.11597 0.10639 0.09761 0.08955 0.08215 0.07537 0.06915 0.06344 0.05820 0.05339 0.04899 0.03184 0.02069 0.01345 0.00874 0.00568 0.00369 0.00240 0.00156 0.00101 0.00066 0.00043 0.00028 0.00018
1.0000 0.47847 0.30505 0.21867 0.16709 0.13292 0.10869 0.09067 0.07680 0.06582 0.05695 0.04965 0.04357 0.03843 0.03406 0.03030 0.02705 0.02421 0.02173 0.01955 0.01762 0.01590 0.01438 0.01302 0.01181 0.01072 0.00973 0.00885 0.00806 0.00734 0.00669 0.00610 0.00556 0.00508 0.00464 0.00296 0.00190 0.00123 0.00079 0.00051 0.00033 0.00022 0.00014 0.00009 0.00006 0.00004 0.00003 0.00002
1.0000 2.0900 3.2781 4.5731 5.9847 7.5233 9.2004 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 93.324 102.72 112.97 124.14 136.31 149.58 164.04 179.80 196.98 215.71 337.88 525.86 815.08 1260.1 1944.8 2998.3 4619.2 7113.2 10 951.0 16 855.0 25 939.0 39 917.0 61 423.0
1.0900 0.56847 0.39505 0.30867 0.25709 0.22292 0.19869 0.18067 0.16680 0.15582 0.14695 0.13965 0.13357 0.12843 0.12406 0.12030 0.11705 0.11421 0.11173 0.10955 0.10762 0.10590 0.10438 0.10302 0.10181 0.10072 0.09973 0.09885 0.09806 0.09734 0.09669 0.09610 0.09556 0.09508 0.09464 0.09296 0.09190 0.09123 0.09079 0.09051 0.09033 0.09022 0.09014 0.09009 0.09006 0.09004 0.09003 0.09002
0.91743 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 6.8052 7.1607 7.4869 7.7862 8.0607 8.3126 8.5436 8.7556 8.9501 9.1285 9.2922 9.4424 9.5802 9.7066 9.8226 9.9290 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
0.00000 0.47847 0.94262 1.3925 1.8282 2.2498 2.6574 3.0512 3.4312 3.7978 4.1510 4.4910 4.8182 5.1326 5.4346 5.7245 6.0024 6.2687 6.5236 6.7674 7.0006 7.2232 7.4357 7.6384 7.8316 8.0156 8.1906 8.3571 8.5154 8.6657 8.8083 8.9436 9.0718 9.1933 9.3083 9.7957 10.160 10.430 10.626 10.768 10.870 10.943 10.994 11.030 11.055 11.073 11.085 11.093
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Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 7.4002 8.1403 8.9543 9.8497 10.835 11.918 13.110 14.421 15.863 17.449 19.194 21.114 23.225 25.548 28.102 45.259 72.890 117.39 189.06 304.48 490.37 789.75 1271.9
0.90909 0.82645 0.75131 0.68301 0.62092 0.56447 0.51316 0.46651 0.42410 0.38554 0.35049 0.31863 0.28966 0.26333 0.23939 0.21763 0.19784 0.17986 0.16351 0.14864 0.13513 0.12285 0.11168 0.10153 0.09230 0.08391 0.07628 0.06934 0.06304 0.05731 0.05210 0.04736 0.04306 0.03914 0.03558 0.02209 0.01372 0.00852 0.00529 0.00328 0.00204 0.00127 0.00079
1.0000 0.47619 0.30211 0.21547 0.16380 0.12961 0.10541 0.08744 0.07364 0.06275 0.05396 0.04676 0.04078 0.03575 0.03147 0.02782 0.02466 0.02193 0.01955 0.01746 0.01562 0.01401 0.01257 0.01130 0.01017 0.00916 0.00826 0.00745 0.00673 0.00608 0.00550 0.00497 0.00450 0.00407 0.00369 0.00226 0.00139 0.00086 0.00053 0.00033 0.00020 0.00013 0.00008
1.0000 2.1000 3.3100 4.6410 6.1051 7.7156 9.4872 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 98.347 109.18 121.10 134.21 148.63 164.49 181.94 201.14 222.25 245.48 271.02 442.59 718.90 1163.9 1880.6 3034.8 4893.7 7887.5 12 709.0
1.1000 0.57619 0.40211 0.31547 0.26380 0.22961 0.20541 0.18744 0.17364 0.16275 0.15396 0.14676 0.14078 0.13575 0.13147 0.12782 0.12466 0.12193 0.11955 0.11746 0.11562 0.11401 0.11257 0.11130 0.11017 0.10916 0.10826 0.10745 0.10673 0.10608 0.10550 0.10497 0.10450 0.10407 0.10369 0.10226 0.10139 0.10086 0.10053 0.10033 0.10020 0.10013 0.10008
0.90909 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 8.6487 8.7715 8.8832 8.9847 9.0770 9.1609 9.2372 9.3066 9.3696 9.4269 9.4790 9.5264 9.5694 9.6086 9.6442 9.7791 9.8628 9.9148 9.9471 9.9672 9.9796 9.9873 9.9921
0.00000 0.47619 0.93656 1.3812 1.8101 2.2236 2.6216 3.0045 3.3724 3.7255 4.0641 4.3884 4.6988 4.9955 5.2789 5.5493 5.8071 6.0526 6.2861 6.5081 6.7189 6.9189 7.1085 7.2881 7.4580 7.6186 7.7704 7.9137 8.0489 8.1762 8.2962 8.4091 8.5152 8.6149 8.7086 9.0962 9.3740 9.5704 9.7075 9.8023 9.8672 9.9113 9.9410
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APPENDIX A
i 11%
Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.1100 1.2321 1.3676 1.5181 1.6851 1.8704 2.0762 2.3045 2.5580 2.8394 3.1518 3.4985 3.8833 4.3104 4.7846 5.3109 5.8951 6.5436 7.2633 8.0623 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 65.001 109.53 184.56 311.00
0.90090 0.81162 0.73119 0.65873 0.59345 0.53464 0.48166 0.43393 0.39092 0.35218 0.31728 0.28584 0.25751 0.23199 0.20900 0.18829 0.16963 0.15282 0.13768 0.12403 0.11174 0.10067 0.09069 0.08170 0.07361 0.06631 0.05974 0.05382 0.04849 0.04368 0.03935 0.03545 0.03194 0.02878 0.02592 0.01538 0.00913 0.00542 0.00322
1.0000 0.47393 0.29921 0.21233 0.16057 0.12638 0.10222 0.08432 0.07060 0.05980 0.05112 0.04403 0.03815 0.03323 0.02907 0.02552 0.02247 0.01984 0.01756 0.01558 0.01384 0.01231 0.01097 0.00979 0.00874 0.00781 0.00699 0.00626 0.00561 0.00502 0.00451 0.00404 0.00363 0.00326 0.00293 0.00172 0.00101 0.00060 0.00035
1.0000 2.1100 3.3421 4.7097 6.2278 7.9129 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 91.15 102.17 114.41 128.00 143.08 159.82 178.40 199.02 221.91 247.32 275.53 306.84 341.59 581.83 986.6 1668.8 2818.2
1.1100 0.58393 0.40921 0.32233 0.27057 0.23638 0.21222 0.19432 0.18060 0.16980 0.16112 0.15403 0.14815 0.14323 0.13907 0.13552 0.13247 0.12984 0.12756 0.12558 0.12384 0.12231 0.12097 0.11979 0.11874 0.11781 0.11699 0.11626 0.11561 0.11502 0.11451 0.11404 0.11363 0.11326 0.11293 0.11172 0.11101 0.11060 0.11035
0.90090 1.7125 2.4437 3.1024 3.6959 4.2305 4.7122 5.1461 5.5370 5.8892 6.2065 6.4924 6.7499 6.9819 7.1909 7.3792 7.5488 7.7016 7.8393 7.9633 8.0751 8.1757 8.2664 8.3481 8.4217 8.4881 8.5478 8.6016 8.6501 8.6938 8.7331 8.7686 8.8005 8.8293 8.8552 8.9511 9.0079 9.0417 9.0617
0.00000 0.47393 0.93055 1.3700 1.7923 2.1976 2.5863 2.9585 3.3144 3.6544 3.9788 4.2879 4.5822 4.8619 5.1275 5.3794 5.6180 5.8439 6.0574 6.2590 6.4491 6.6283 6.7969 6.9555 7.1045 7.2443 7.3754 7.4982 7.6131 7.7206 7.8210 7.9147 8.0021 8.0836 8.1594 8.4659 8.6763 8.8185 8.9135
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Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8.6128 9.6463 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 93.051 163.99 289.00 509.32
0.89286 0.79719 0.71178 0.63552 0.56743 0.50663 0.45235 0.40388 0.36061 0.32197 0.28748 0.25668 0.22917 0.20462 0.18270 0.16312 0.14564 0.13004 0.11611 0.10367 0.09256 0.08264 0.07379 0.06588 0.05882 0.05252 0.04689 0.04187 0.03738 0.03338 0.02980 0.02661 0.02376 0.02121 0.01894 0.01075 0.00610 0.00346 0.00196
1.0000 0.47170 0.29635 0.20923 0.15741 0.12323 0.09912 0.08130 0.06768 0.05698 0.04842 0.04144 0.03568 0.03087 0.02682 0.02339 0.02046 0.01794 0.01576 0.01388 0.01224 0.01081 0.00956 0.00846 0.00750 0.00665 0.00590 0.00524 0.00466 0.00414 0.00369 0.00328 0.00292 0.00260 0.00232 0.00130 0.00074 0.00042 0.00024
1.0000 2.1200 3.3744 4.7793 6.3528 8.1152 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 92.503 104.60 118.16 133.33 150.33 169.37 190.70 214.58 241.33 271.29 304.85 342.43 384.52 431.66 767.09 1358.2 2400.0 4236.0
1.1200 0.59170 0.41635 0.32923 0.27741 0.24323 0.21912 0.20130 0.18768 0.17698 0.16842 0.16144 0.15568 0.15087 0.14682 0.14339 0.14046 0.13794 0.13576 0.13388 0.13224 0.13081 0.12956 0.12846 0.12750 0.12665 0.12590 0.12524 0.12466 0.12414 0.12369 0.12328 0.12292 0.12260 0.12232 0.12130 0.12074 0.12042 0.12024
0.89286 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.5620 7.6446 7.7184 7.7843 7.8431 7.8957 7.9426 7.9844 8.0218 8.0552 8.0850 8.1116 8.1354 8.1566 8.1755 8.2438 8.2825 8.3045 8.3170
0.00000 0.47170 0.92461 1.3589 1.7746 2.1720 2.5515 2.9131 3.2574 3.5847 3.8953 4.1897 4.4683 4.7317 4.9803 5.2147 5.4353 5.6427 5.8375 6.0202 6.1913 6.3514 6.5010 6.6406 6.7708 6.8921 7.0049 7.1098 7.2071 7.2974 7.3811 7.4586 7.5302 7.5965 7.6577 7.8988 8.0572 8.1597 8.2251
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APPENDIX A
i 13%
Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.1300 1.2769 1.4429 1.6305 1.8424 2.0820 2.3526 2.6584 3.0040 3.3946 3.8359 4.3345 4.8980 5.5348 6.2543 7.0673 7.9861 9.0243 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 72.069 132.78 244.64 450.74 830.45
0.88496 0.78315 0.69305 0.61332 0.54276 0.48032 0.42506 0.37616 0.33288 0.29459 0.26070 0.23071 0.20416 0.18068 0.15989 0.14150 0.12522 0.11081 0.09806 0.08678 0.07680 0.06796 0.06014 0.05323 0.04710 0.04168 0.03689 0.03264 0.02889 0.02557 0.02262 0.02002 0.01772 0.01568 0.01388 0.00753 0.00409 0.00222 0.00120
1.0000 0.46948 0.29352 0.20619 0.15431 0.12015 0.09611 0.07839 0.06487 0.05429 0.04584 0.03899 0.03335 0.02867 0.02474 0.02143 0.01861 0.01620 0.01413 0.01235 0.01081 0.00948 0.00832 0.00731 0.00643 0.00565 0.00498 0.00439 0.00387 0.00341 0.00301 0.00266 0.00234 0.00207 0.00183 0.00099 0.00053 0.00029 0.00016
1.0000 2.1300 3.4069 4.8498 6.4803 8.3227 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 92.470 105.49 120.20 136.83 155.62 176.85 200.84 227.95 258.58 293.20 332.32 376.52 426.46 482.90 546.68 1013.7 1874.2 3459.5 6380.4
1.1300 0.59948 0.42352 0.33619 0.28431 0.25015 0.22611 0.20839 0.19487 0.18429 0.17584 0.16899 0.16335 0.15867 0.15474 0.15143 0.14861 0.14620 0.14413 0.14235 0.14081 0.13948 0.13832 0.13731 0.13643 0.13565 0.13498 0.13439 0.13387 0.13341 0.13301 0.13266 0.13234 0.13207 0.13183 0.13099 0.13053 0.13029 0.13016
0.88496 1.6681 2.3612 2.9745 3.5172 3.9975 4.4226 4.7988 5.1317 5.4262 5.6869 5.9176 6.1218 6.3025 6.4624 6.6039 6.7291 6.8399 6.9380 7.0248 7.1016 7.1695 7.2297 7.2829 7.3300 7.3717 7.4086 7.4412 7.4701 7.4957 7.5183 7.5383 7.5560 7.5717 7.5856 7.6344 7.6609 7.6752 7.6830
0.00000 0.46948 0.91872 1.3479 1.7571 2.1468 2.5171 2.8685 3.2014 3.5162 3.8134 4.0936 4.3573 4.6050 4.8375 5.0552 5.2589 5.4491 5.6265 5.7917 5.9454 6.0881 6.2205 6.3431 6.4566 6.5614 6.6582 6.7474 6.8296 6.9052 6.9747 7.0385 7.0971 7.1507 7.1998 7.3888 7.5076 7.5811 7.6260
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Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.1400 1.2996 1.4815 1.6890 1.9254 2.1950 2.5023 2.8526 3.2519 3.7072 4.2262 4.8179 5.4924 6.2613 7.1379 8.1372 9.2765 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 98.100 188.88 363.68 700.23 1348.2
0.87719 0.76947 0.67497 0.59208 0.51937 0.45559 0.39964 0.35056 0.30751 0.26974 0.23662 0.20756 0.18207 0.15971 0.14010 0.12289 0.10780 0.09456 0.08295 0.07276 0.06383 0.05599 0.04911 0.04308 0.03779 0.03315 0.02908 0.02551 0.02237 0.01963 0.01722 0.01510 0.01325 0.01162 0.01019 0.00529 0.00275 0.00143 0.00074
1.0000 0.46729 0.29073 0.20320 0.15128 0.11716 0.09319 0.07557 0.06217 0.05171 0.04339 0.03667 0.03116 0.02661 0.02281 0.01962 0.01692 0.01462 0.01266 0.01099 0.00954 0.00830 0.00723 0.00630 0.00550 0.00480 0.00419 0.00366 0.00320 0.00280 0.00245 0.00215 0.00188 0.00165 0.00144 0.00075 0.00039 0.00020 0.00010
1.0000 2.1400 3.4396 4.9211 6.6101 8.5355 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 91.025 104.77 120.44 138.30 158.66 181.87 208.33 238.50 272.89 312.09 356.79 407.74 465.82 532.04 607.52 693.57 1342.0 2590.6 4994.5 9623.1
1.1400 0.60729 0.43073 0.34320 0.29128 0.25716 0.23319 0.21557 0.20217 0.19171 0.18339 0.17667 0.17116 0.16661 0.16281 0.15962 0.15692 0.15462 0.15266 0.15099 0.14954 0.14830 0.14723 0.14630 0.14550 0.14480 0.14419 0.14366 0.14320 0.14280 0.14245 0.14215 0.14188 0.14165 0.14144 0.14075 0.14039 0.14020 0.14010
0.87719 1.6467 2.3216 2.9137 3.4331 3.8887 4.2883 4.6389 4.9464 5.2161 5.4527 5.6603 5.8424 6.0021 6.1422 6.2651 6.3729 6.4674 6.5504 6.6231 6.6870 6.7429 6.7921 6.8351 6.8729 6.9061 6.9352 6.9607 6.9830 7.0027 7.0199 7.0350 7.0482 7.0599 7.0700 7.1050 7.1232 7.1327 7.1376
0.00000 0.46729 0.91290 1.3370 1.7399 2.1218 2.4832 2.8246 3.1463 3.4490 3.7333 3.9998 4.2491 4.4819 4.6990 4.9011 5.0888 5.2630 5.4243 5.5734 5.7111 5.8381 5.9549 6.0624 6.1610 6.2514 6.3342 6.4100 6.4791 6.5423 6.5998 6.6522 6.6998 6.7431 6.7824 6.9300 7.0188 7.0714 7.1020
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APPENDIX A
i 15%
Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.1500 1.3225 1.5209 1.7490 2.0114 2.3131 2.6600 3.0590 3.5179 4.0456 4.6524 5.3503 6.1528 7.0757 8.1371 9.3576 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 87.565 100.70 115.80 133.18 267.86 538.77 1083.7 2179.6
0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 0.28426 0.24718 0.21494 0.18691 0.16253 0.14133 0.12289 0.10686 0.09293 0.08081 0.07027 0.06110 0.05313 0.04620 0.04017 0.03493 0.03038 0.02642 0.02297 0.01997 0.01737 0.01510 0.01313 0.01142 0.00993 0.00864 0.00751 0.00373 0.00186 0.00092 0.00046
1.0000 0.46512 0.28798 0.20027 0.14832 0.11424 0.09036 0.07285 0.05957 0.04925 0.04107 0.03448 0.02911 0.02469 0.02102 0.01795 0.01537 0.01319 0.01134 0.00976 0.00842 0.00727 0.00628 0.00543 0.00470 0.00407 0.00353 0.00306 0.00265 0.00230 0.00200 0.00173 0.00150 0.00131 0.00113 0.00056 0.00028 0.00014 0.00007
1.0000 2.1500 3.4725 4.9934 6.7424 8.7537 11.067 13.727 16.786 20.304 24.349 29.002 34.352 40.505 47.580 55.717 65.075 75.836 88.212 102.44 118.81 137.63 159.28 184.17 212.79 245.71 283.57 327.10 377.17 434.75 500.96 577.10 664.67 765.37 881.17 1779.1 3585.1 7217.7 14 524.0
1.1500 0.61512 0.43798 0.35027 0.29832 0.26424 0.24036 0.22285 0.20957 0.19925 0.19107 0.18448 0.17911 0.17469 0.17102 0.16795 0.16537 0.16319 0.16134 0.15976 0.15842 0.15727 0.15628 0.15543 0.15470 0.15407 0.15353 0.15306 0.15265 0.15230 0.15200 0.15173 0.15150 0.15131 0.15113 0.15056 0.15028 0.15014 0.15007
0.86957 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.3125 6.3587 6.3988 6.4338 6.4641 6.4906 6.5135 6.5335 6.5509 6.5660 6.5791 6.5905 6.6005 6.6091 6.6166 6.6418 6.6543 6.6605 6.6636
0.00000 0.46512 0.90713 1.3263 1.7228 2.0972 2.4498 2.7813 3.0922 3.3832 3.6549 3.9082 4.1438 4.3624 4.5650 4.7522 4.9251 5.0843 5.2307 5.3651 5.4883 5.6010 5.7040 5.7979 5.8834 5.9612 6.0319 6.0960 6.1541 6.2066 6.2541 6.2970 6.3357 6.3705 6.4019 6.5168 6.5830 6.6205 6.6414
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Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.2000 1.4400 1.7280 2.0736 2.4883 2.9860 3.5832 4.2998 5.1598 6.1917 7.4301 8.9161 10.699 12.839 15.407 18.488 22.186 26.623 31.948 38.338 46.005 55.206 66.247 79.497 95.396 114.48 137.37 164.84 197.81 237.38 284.85 341.82 410.19 492.22 590.67
0.83333 0.69444 0.57870 0.48225 0.40188 0.33490 0.27908 0.23257 0.19381 0.16151 0.13459 0.11216 0.09346 0.07789 0.06491 0.05409 0.04507 0.03756 0.03130 0.02608 0.02174 0.01811 0.01509 0.01258 0.01048 0.00874 0.00728 0.00607 0.00506 0.00421 0.00351 0.00293 0.00244 0.00203 0.00169
1.0000 0.45455 0.27473 0.18629 0.13438 0.10071 0.07742 0.06061 0.04808 0.03852 0.03110 0.02526 0.02062 0.01689 0.01388 0.01144 0.00944 0.00781 0.00646 0.00536 0.00444 0.00369 0.00307 0.00255 0.00212 0.00176 0.00147 0.00122 0.00102 0.00085 0.00070 0.00059 0.00049 0.00041 0.00034
1.0000 2.2000 3.6400 5.3680 7.4416 9.9299 12.916 16.499 20.799 25.959 32.150 39.581 48.497 59.196 72.035 87.442 105.93 128.12 154.74 186.69 225.03 271.03 326.24 392.48 471.98 567.38 681.85 819.22 984.07 1181.9 1419.3 1704.1 2045.9 2456.1 2948.3
1.2000 0.65455 0.47473 0.38629 0.33438 0.30071 0.27742 0.26061 0.24808 0.23852 0.23110 0.22526 0.22062 0.21689 0.21388 0.21144 0.20944 0.20781 0.20646 0.20536 0.20444 0.20369 0.20307 0.20255 0.20212 0.20176 0.20147 0.20122 0.20102 0.20085 0.20070 0.20059 0.20049 0.20041 0.20034
0.83333 1.5278 2.1065 2.5887 2.9906 3.3255 3.6046 3.8372 4.0310 4.1925 4.3271 4.4392 4.5327 4.6106 4.6755 4.7296 4.7746 4.8122 4.8435 4.8696 4.8913 4.9094 4.9245 4.9371 4.9476 4.9563 4.9636 4.9697 4.9747 4.9789 4.9824 4.9854 4.9878 4.9898 4.9915
0.00000 0.45455 0.87912 1.2742 1.6405 1.9788 2.2902 2.5756 2.8364 3.0739 3.2893 3.4841 3.6597 3.8175 3.9588 4.0851 4.1976 4.2975 4.3861 4.4643 4.5334 4.5941 4.6475 4.6943 4.7352 4.7709 4.8020 4.8291 4.8527 4.8731 4.8908 4.9061 4.9194 4.9308 4.9406
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APPENDIX A
i 25%
Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.2500 1.5625 1.9531 2.4414 3.0518 3.8147 4.7684 5.9605 7.4506 9.3132 11.642 14.552 18.190 22.737 28.422 35.527 44.409 55.511 69.389 86.736 108.42 135.53 169.41 211.76 264.70 330.87 413.59 516.99 646.23 807.79 1009.7 1262.2 1577.7 1972.2 2465.2
0.80000 0.64000 0.51200 0.40960 0.32768 0.26214 0.20972 0.16777 0.13422 0.10737 0.08590 0.06872 0.05498 0.04398 0.03518 0.02815 0.02252 0.01801 0.01441 0.01153 0.00922 0.00738 0.00590 0.00472 0.00378 0.00302 0.00242 0.00193 0.00155 0.00124 0.00099 0.00079 0.00063 0.00051 0.00041
1.0000 0.44444 0.26230 0.17344 0.12185 0.08882 0.06634 0.05040 0.03876 0.03007 0.02349 0.01845 0.01454 0.01150 0.00912 0.00724 0.00576 0.00459 0.00366 0.00292 0.00233 0.00186 0.00148 0.00119 0.00095 0.00076 0.00061 0.00048 0.00039 0.00031 0.00025 0.00020 0.00016 0.00013 0.00010
1.0000 2.2500 3.8125 5.7656 8.2070 11.259 15.073 19.842 25.802 33.253 42.566 54.208 68.760 86.949 109.69 138.11 173.64 218.04 273.56 342.94 429.68 538.10 673.63 843.03 1054.8 1319.5 1650.4 2064.0 2580.9 3227.2 4035.0 5044.7 6306.9 7884.6 9856.8
1.2500 0.69444 0.51230 0.42344 0.37185 0.33882 0.31634 0.30040 0.28876 0.28007 0.27349 0.26845 0.26454 0.26150 0.25912 0.25724 0.25576 0.25459 0.25366 0.25292 0.25233 0.25186 0.25148 0.25119 0.25095 0.25076 0.25061 0.25048 0.25039 0.25031 0.25025 0.25020 0.25016 0.25013 0.25010
0.80000 1.4400 1.9520 2.3616 2.6893 2.9514 3.1611 3.3289 3.4631 3.5705 3.6564 3.7251 3.7801 3.8241 3.8593 3.8874 3.9099 3.9279 3.9424 3.9539 3.9631 3.9705 3.9764 3.9811 3.9849 3.9879 3.9903 3.9923 3.9938 3.9950 3.9960 3.9968 3.9975 3.9980 3.9984
0.00000 0.44444 0.85246 1.2249 1.5631 1.8683 2.1424 2.3872 2.6048 2.7971 2.9663 3.1145 3.2437 3.3559 3.4530 3.5366 3.6084 3.6698 3.7222 3.7667 3.8045 3.8365 3.8634 3.8861 3.9052 3.9212 3.9346 3.9457 3.9551 3.9628 3.9693 3.9746 3.9791 3.9828 3.9858
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SINGLE PAYMENT
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
N
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,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
1.3000 1.6900 2.1970 2.8561 3.7129 4.8268 6.2749 8.1573 10.604 13.786 17.922 23.298 30.288 39.374 51.186 66.542 86.504 112.46 146.19 190.05 247.06 321.18 417.54 542.80 705.64 917.33 1192.5 1550.3 2015.4 2620.0 3406.0 4427.8 5756.1 7483.0 9727.9
0.76923 0.59172 0.45517 0.35013 0.26933 0.20718 0.15937 0.12259 0.09430 0.07254 0.05580 0.04292 0.03302 0.02540 0.01954 0.01503 0.01156 0.00889 0.00684 0.00526 0.00405 0.00311 0.00239 0.00184 0.00142 0.00109 0.00084 0.00065 0.00050 0.00038 0.00029 0.00023 0.00017 0.00013 0.00010
1.0000 0.43478 0.25063 0.16163 0.11058 0.07839 0.05687 0.04192 0.03124 0.02346 0.01773 0.01345 0.01024 0.00782 0.00598 0.00458 0.00351 0.00269 0.00207 0.00159 0.00122 0.00094 0.00072 0.00055 0.00043 0.00033 0.00025 0.00019 0.00015 0.00011 0.00009 0.00007 0.00005 0.00004 0.00003
1.0000 2.3000 3.9900 6.1870 9.0431 12.756 17.583 23.858 32.015 42.619 56.405 74.327 97.625 127.91 167.29 218.47 285.01 371.52 483.97 630.17 820.22 1067.3 1388.5 1806.0 2348.8 3054.4 3971.8 5164.3 6714.6 8730.0 11 350.0 14 756.0 19 184.0 24 940.0 32 423.0
1.3000 0.73478 0.55063 0.46163 0.41058 0.37839 0.35687 0.34192 0.33124 0.32346 0.31773 0.31345 0.31024 0.30782 0.30598 0.30458 0.30351 0.30269 0.30207 0.30159 0.30122 0.30094 0.30072 0.30055 0.30043 0.30033 0.30025 0.30019 0.30015 0.30011 0.30009 0.30007 0.30005 0.30004 0.30003
0.76923 1.3609 1.8161 2.1662 2.4356 2.6427 2.8021 2.9247 3.0190 3.0915 3.1473 3.1903 3.2233 3.2487 3.2682 3.2832 3.2948 3.3037 3.3105 3.3158 3.3198 3.3230 3.3254 3.3272 3.3286 3.3297 3.3305 3.3312 3.3317 3.3321 3.3324 3.3326 3.3328 3.3329 3.3330
0.00000 0.43478 0.82707 1.1783 1.4903 1.7654 2.0063 2.2156 2.3963 2.5512 2.6833 2.7952 2.8895 2.9685 3.0344 3.0892 3.1345 3.1718 3.2025 3.2275 3.2480 3.2646 3.2781 3.2890 3.2979 3.3050 3.3107 3.3153 3.3189 3.3219 3.3242 3.3261 3.3276 3.3288 3.3297
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APPENDIX A
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Discrete Compounding, Discrete Cash Flows
SINGLE PAYMENT
N
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,N)
0.71429 0.51020 0.36443 0.26031 0.18593 0.13281 0.09486 0.06776 0.04840 0.03457 0.02469 0.01764 0.01260 0.00900 0.00643 0.00459 0.00328 0.00234 0.00167 0.00120 0.00085 0.00061 0.00044 0.00031 0.00022 0.00016 0.00011 0.00008 0.00006 0.00004 0.00003 0.00002 0.00002 0.00001 0.00001
1.0000 0.41667 0.22936 0.14077 0.09136 0.06126 0.04192 0.02907 0.02034 0.01432 0.01013 0.00718 0.00510 0.00363 0.00259 0.00185 0.00132 0.00094 0.00067 0.00048 0.00034 0.00024 0.00017 0.00012 0.00009 0.00006 0.00005 0.00003 0.00002 0.00002 0.00001 0.00001 0.00001 0.00000 0.00000
1.0000 2.4000 4.3600 7.1040 10.946 16.324 23.853 34.395 49.153 69.814 98.739 139.23 195.93 275.30 386.42 541.99 759.78 1064.70 1491.58 2089.21 2925.89 4097.24 5737.14 8033.00 11 247.0 15 747.0 22 047.0 30 867.0 43 214.0 60 501.0 84 703.0 118 585.0 166 019.0 232 428.0 325 400.0
1.4000 0.81667 0.62936 0.54077 0.49136 0.46126 0.44192 0.42907 0.42034 0.41432 0.41013 0.40718 0.40510 0.40363 0.40259 0.40185 0.40132 0.40094 0.40067 0.40048 0.40034 0.40024 0.40017 0.40012 0.40009 0.40006 0.40005 0.40003 0.40002 0.40002 0.40001 0.40001 0.40001 0.40000 0.40000
0.71429 1.2245 1.5889 1.8492 2.0352 2.1680 2.2628 2.3306 2.3790 2.4136 2.4383 2.4559 2.4685 2.4775 2.4839 2.4885 2.4918 2.4941 2.4958 2.4970 2.4979 2.4985 2.4989 2.4992 2.4994 2.4996 2.4997 2.4998 2.4999 2.4999 2.4999 2.4999 2.5000 2.5000 2.5000
0.00000 0.41667 0.77982 1.0923 1.3580 1.5811 1.7664 1.9185 2.0422 2.1419 2.2215 2.2845 2.3341 2.3729 2.4030 2.4262 2.4441 2.4577 2.4682 2.4761 2.4821 2.4866 2.4900 2.4925 2.4944 2.4959 2.4969 2.4977 2.4983 2.4988 2.4991 2.4993 2.4995 2.4996 2.4997
1 1.4000 2 1.9600 3 2.7440 4 3.8416 5 5.3782 6 7.5295 7 10.541 8 14.758 9 20.661 10 28.925 11 40.496 12 56.694 13 79.371 14 111.12 15 155.57 16 217.80 17 304.91 18 426.88 19 597.63 20 836.68 21 1171.36 22 1639.90 23 2295.86 24 3214.20 25 4499.88 26 6299.83 27 8819.76 28 12 348.0 29 17 287.0 30 24 201.0 31 33 882.0 32 47 435.0 33 66 409.0 34 92 972.0 35 130 161.0
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SINGLE PAYMENT
N
517
UNIFORM SERIES
Compound Amount Factor
Present Worth Factor
Sinking Fund Factor
Uniform Series Factor
Capital Recovery Factor
Series Present Worth Factor
Arithmetic Gradient Series Factor
(F/P,i,N)
(P/F,i,N)
(A/F,i,N)
(F/A,i,N)
(A/P,i,N)
(P/A,i,N)
(A/G,i,N)
0.66667 0.44444 0.29630 0.19753 0.13169 0.08779 0.05853 0.03902 0.02601 0.01734 0.01156 0.00771 0.00514 0.00343 0.00228 0.00152 0.00101 0.00068 0.00045 0.00030 0.00020 0.00013 0.00009 0.00006 0.00004 0.00003 0.00002 0.00001 0.00001 0.00001 0.00000 0.00000 0.00000 0.00000 0.00000
1.0000 0.40000 0.21053 0.12308 0.07583 0.04812 0.03108 0.02030 0.01335 0.00882 0.00585 0.00388 0.00258 0.00172 0.00114 0.00076 0.00051 0.00034 0.00023 0.00015 0.00010 0.00007 0.00004 0.00003 0.00002 0.00001 0.00001 0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
1.0000 2.5000 4.7500 8.1250 13.1875 20.781 32.172 49.258 74.887 113.330 170.995 257.493 387.239 581.86 873.79 1311.68 1968.52 2953.78 4431.68 6648.51 9973.77 14 962.0 22 443.0 33 666.0 50 500.0 75 752.0 113 628.0 170 443.0 255 666.0 383 500.0 575 251.0 862 878.0 1 294 318.0 1 941 477.0 2 912 217.0
1.5000 0.90000 0.71053 0.62308 0.57583 0.54812 0.53108 0.52030 0.51335 0.50882 0.50585 0.50388 0.50258 0.50172 0.50114 0.50076 0.50051 0.50034 0.50023 0.50015 0.50010 0.50007 0.50004 0.50003 0.50002 0.50001 0.50001 0.50001 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
0.66667 1.1111 1.4074 1.6049 1.7366 1.8244 1.8829 1.9220 1.9480 1.9653 1.9769 1.9846 1.9897 1.9931 1.9954 1.9970 1.9980 1.9986 1.9991 1.9994 1.9996 1.9997 1.9998 1.9999 1.9999 1.9999 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000
0.00000 0.40000 0.73684 1.0154 1.2417 1.4226 1.5648 1.6752 1.7596 1.8235 1.8713 1.9068 1.9329 1.9519 1.9657 1.9756 1.9827 1.9878 1.9914 1.9940 1.9958 1.9971 1.9980 1.9986 1.9990 1.9993 1.9995 1.9997 1.9998 1.9998 1.9999 1.9999 1.9999 2.0000 2.0000
1 1.5000 2 2.2500 3 3.3750 4 5.0625 5 7.5938 6 11.3906 7 17.0859 8 25.6289 9 38.443 10 57.665 11 86.498 12 129.746 13 194.620 14 291.929 15 437.894 16 656.841 17 985.261 18 1477.89 19 2216.84 20 3325.26 21 4987.89 22 7481.83 23 11 223.0 24 16 834.0 25 25 251.0 26 37 877.0 27 56 815.0 28 85 223.0 29 127 834.0 30 191 751.0 31 287 627.0 32 431 440.0 33 647 160.0 34 970 740.0 35 1 456 110.0
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