# Appendix one: tables

Table 1. Discount factors.

The present value of I received or spent in a given future year 'n' at a given discount 'i'.
Discount factor: 1/(1 + i)n

 % 2 4 5 6 8 9 10 12 14 15 16 18 20 25 30 35 40 45 50 Yrs 1 .980 .962 .952 .943 .926 .917 .909 .893 .877 .870 .862 .847 .833 .800 .769 .741 .714 .690 ,667 2 .961 .925 .907 .890 .857 .842 .826 .797 .769 .756 .743 .718 .694 .640 .592 .549 .510 .476 .444 3 .942 .889 .864 .840 .794 .772 .751 .712 .675 .658 .641 .609 .579 .512 .455 .406 .364 .328 .296 4 .924 .855 .823 .792 .735 .708 .683 .636 .592 .572 .552 .516 .482 .410 .350 .301 .260 .226 .198 5 .906 .822 .784 .747 .681 .650 .621 .567 .519 .497 .476 .437 .402 .328 .269 .223 .186 .156 .132 6 .888 .790 .746 .705 .630 .596 .564 .507 .456 .432 .410 .370 .335 .262 .207 .165 .133 .108 .088 7 .871 .760 .711 .665 .583 .547 .513 .452 .400 .376 .354 .314 .279 .210 .159 .122 .095 .074 .059 8 .853 .731 .677 .627 .540 .502 .467 .404 .351 .327 .305 .266 .233 .168 .123 .091 .068 .051 .039 9 .837 .703 .645 .592 .500 .460 .424 .361 .308 .284 .263 .225 .194 .134 .094 .067 .048 .035 .026 10 .820 .676 .614 .558 .463 .422 .386 .322 .270 .247 .227 .191 .162 .107 .073 .050 .035 .024 .017 11 .804 .650 .585 .527 .429 .388 .350 .287 .237 .215 .195 .162 .135 .086 .056 .037 .025 .017 .012 12 .788 .625 .557 .497 .397 .356 .319 .257 .208 .187 .168 .137 .112 .069 .043 .027 .018 .012 .008 13 .773 .601 .530 .469 .368 .326 .290 .229 .182 .163 .145 .116 .093 .055 .033 .020 .013 .008 .005 14 .758 .577 .505 .442 .340 .299 .263 .205 .160 .141 .125 .099 .078 .044 .025 .015 .009 .006 .003 15 .743 .555 .481 .417 .315 .275 .239 .183 .140 .123 .108 .084 .065 .035 .020 .011 .006 .004 .002 16 .728 .534 .458 .394 .292 .252 .218 .163 .123 .107 .093 .071 .054 .028 .015 .008 .005 .003 .002 17 .714 .513 .436 .371 .270 .231 .198 .146 .108 .093 .080 .060 .045 .023 .012 .006 .003 .002 .001 18 .700 .494 .416 .350 .250 .212 .180 .130 .095 .081 .069 .051 .038 .018 .009 .005 .002 .001 .001 19 .686 .475 .396 .331 .232 .194 .164 .116 .083 .070 .060 .043 .031 .014 .007 .003 .002 .001 .000 20 .673 .456 .377 .312 .215 .178 .149 .104 .073 .061 .051 .037 .026 .012 .005 .002 .001 .001 .000 21 .660 .439 .359 .294 .199 .164 .135 .093 .064 .053 .044 .031 .022 .009 .004 .002 .001 .000 .000 22 .647 .422 342 .278 .184 .150 .123 .083 .056 .046 .038 .026 .018 .007 .003 .001 .001 .000 .000 23 .634 .406 .326 .262 .170 .138 .112 .074 .049 .040 .033 .022 .015 .006 .002 .001 .000 .000 .000 24 .622 .390 .310 .247 .158 .126 .102 .066 .043 .035 .028 .019 .013 .005 .002 .001 .000 .000 .000 25 .610 .375 .295 .233 .146 .116 .092 .059 .038 .030 .024 .016 .010 .004 .001 .001 .000 .000 .000 30 .552 .308 .231 .174 .099 .075 .057 .033 .020 .015 .012 .007 .004 .001 .000 .000 .000 .000 .000 35 .500 .253 .181 .130 .068 .049 .036 .019 .010 .008 .006 .003 .002 .000 .000 .000 .000 .000 .000 40 .453 .208 .142 .097 .046 .032 .022 .011 .005 .004 .003 .001 .001 .000 .000 .000 .000 .000 .000 45 .410 .171 .111 .073 .031 .021 .014 .006 .003 .002 .001 .001 .000 .000 .000 .000 .000 .000 .000 50 .372 .141 .087 .054 .021 .013 .009 .003 .001 .001 .001 .000 .000 .000 .000 .000 .000 .000 .000

Table 2. Present value of an annuity.

The present value of I received or spent annually at a given rate of interest 'i' for a given number of years 'n'.
Present value of an annuity factor: S 1/(1 + i)n

 % 2 4 5 6 8 9 10 12 14 15 16 18 20 25 30 35 40 50 Yrs 1 .9804 .9615 .9524 .9434 .9259 .9174 .9091 .8929 .8772 .8696 .8621 .8475 .8333 .8000 .7692 .7407 .7143 .6667 2 1.942 1.886 1.859 1.833 1.783 1.759 1.736 1.690 1.647 1.626 1.605 1.566 1.528 1.440 1.361 1.289 1.224 1.111 3 2.884 2.775 2.723 2.673 2.577 2.531 2.487 2.402 2.322 2.283 2.246 2.174 2.106 1.952 1.816 1.696 1.589 1.407 4 3.808 3.630 3.546 3.465 3.312 3.240 3.170 3.037 2.914 2.855 2.798 2.690 2.589 2.362 2.166 1.997 1.849 1.605 5 4.713 4.452 4.329 4.212 3.993 3.890 3.791 3.605 3.433 3.352 3.274 3,127 2.991 2.689 2.436 2.220 2.035 1.737 6 5.601 5.242 5.076 4.917 4.623 4.486 4.355 4.111 3.889 3.784 3.685 3.498 3.326 2.951 2.643 2.385 2.168 1.824 7 6.472 6.002 5.786 5.582 5.206 5.033 4.868 4.564 4.288 4.160 4.039 3.812 3.605 3.161 2.802 2.508 2.263 1.883 8 7.325 6.733 6.463 6.210 5.747 5.535 5.335 4.968 4.639 4.487 4.344 4.078 3.837 3.329 2.925 2.598 2.331 1.922 9 8.162 7.435 7.108 6.802 6.247 5.995 5.759 5.328 4.946 4.772 4.607 4.303 4.031 3.463 3.019 2.665 2.379 1.948 10 8.983 8.111 7.722 7.360 6.710 6.418 6.145 5.650 5.216 5.019 4.833 4.494 4.192 3.571 3.092 2.715 2.414 1.965 11 9.787 8.760 8.306 7.887 7.139 6.805 6.495 5.938 5.453 5.234 5.029 4.656 4.327 3.656 3.147 2.752 2.438 1.977 12 10.58 9.385 8.863 8.384 7.536 7.161 6.814 6.194 5.660 5.421 5.197 4.793 4.439 3.725 3.190 2.779 2.456 1.985 13 11.35 9.986 9.394 8.853 7.904 7.487 7.103 6.424 5.842 5.583 5.342 4.910 4.533 3.780 3.223 2.799 2.469 1.990 14 12.11 10.56 9.899 9.295 8.244 7.786 7.367 6.628 6.002 5.724 5.468 5.008 4.611 3.824 3.249 2.814 2.478 1.993 15 12.85 11.12 10.38 9.712 8.559 8.061 7.606 6.811 6.142 5.847 5.575 5.092 4.675 3.859 3.268 2.825 2.484 1.995 16 13.58 11.65 10.84 10.11 8.851 8.313 7.824 6.974 6.265 5.954 5.668 5.162 4.730 3.887 3.283 2.834 2.489 1.997 17 14.29 12.17 11.27 10.48 9.122 8.544 8.022 7.120 6.373 6.047 5.749 5.222 4.77 3.910 3.295 2.840 2.492 1.998 18 14.99 12.66 11.69 10.83 9.372 8.756 8.201 7.250 6.467 6.128 5.818 5.273 4.813 3.928 3.304 2.844 2.494 1.999 19 15.68 13.13 12.09 11.16 9.604 8.950 8.365 71366 6.550 6.198 5.877 5.316 4.843 3.942 3.311 2.848 2.496 1.999 20 16.35 13.59 12.46 11.47 9.818 9.129 8.514 7.469 6.623 6.259 5.929 5.353 4.870 3.954 3.316 2.850 2.497 1.999 21 17.01 14.03 12.82 11.76 10.02 9.292 8.649 7.562 6.687 6.312 5.973 5.384 4.891 3.963 3.320 2.852 2.498 2.000 22 17.66 14.45 13.16 12.04 10.20 9.442 8.772 7.645 6.743 6.359 6.011 5.410 4.909 3.970 3.323 2.853 2.498 2.000 23 18.29 14.86 13.49 12'30 10.37 9.580 8.883 7.718 6.792 6.399 6.044 5.432 4.925 3.976 3.325 2.854 2.499 2.000 24 18.91 15.25 13.80 12.55 10.53 9.707 8.985 7.784 6.835 6.434 6.073 5.451 4.937 3.981 3.327 2.855 2.499 2.000 25 19.52 15.62 14.09 12.78 10.67 9.823 9.077 7.843 6.873 6.464 6.097 5.467 4.948 3.985 3.329 2.856 2.499 2.000 30 22.40 17.29 15.37 13.76 11.26 10.27 9.427 8.055 7.003 6.566 6.177 5.517 4.979 3.995 3.332 2.857 2.500 2.000 35 25.00 18.66 16.37 14.50 11.65 10.57 9.644 8.176 7.070 6.617 6.215 5.539 4.992 3.998 3.333 2.857 2.500 2.000 40 27.36 19.79 17.16 15.05 11.92 10.76 9.779 8.244 7.105 6.642 6.233 5.548 4.997 3.999 3.333 2.857 2.500 2.000 45 29.49 20.72 17.77 15.46 12.11 10.88 9.863 8.283 7.123 6.654 6.242 5.552 4.999 4.000 3.333 2.857 2.500 2.000 50 31.42 21.48 18.26 15.76 12.23 10.96 9.915 8.304 7.133 6.661 6.246 5.554 4.999 4.000 3.333 2.857 2.500 2.000

Table 3. Compound interest factors.

The future value of I invested at a given rate of interest 'i' for a given number of years 'n'.
Compounding factor: 1 x (1 + i)n

 % 2 4 5 6 8 9 10 12 14 15 16 18 20 25 30 35 40 45 50 Yrs 1 1.020 1.040 1.050 1.060 1.080 1.090 1.100 1.120 1.140 1.150 1.160 .1.180 1.200 1.250 1.300 1.350 1.400 1.450 1.500 2 1.040 1.082 1.103 1.124 1.166 1.188 1.210 1.254 1.300 1.323 1.346 1.392 1.440 1.563 1.690 1.823 1.960 2.103 2.250 3 1.061 1.125 1.158 1.191 1.260 1.295 1.331 1.405 1.482 1.521 1.561 1.643 1.728 1.953 2.197 2.460 2.744 3.049 3.375 4 1.082 1.170 1.216 1.262 1.360 1.412 1.464 1.574 1.689 1.749 1.811 1.939 2.074 2.441 2.856 3.322 3.842 4.421 5.063 5 1.104 1.217 1.276 1.338 1.469 1.539 1.611 1.762 1.925 2.011 2.100 2.288 2.488 3.052 3.713 4.484 5.378 6.410 7.594 6 1.126 1.265 1.340 1.419 1.587 1.677 1.772 1.974 2.195 2.313 2.436 2.700 2.986 3.815 4.827 6.053 7.530 9.294 11.39 7 1.149 1.316 1.407 1.504 1.714 1.828 1.949 2.211 2.502 2.660 2.826 3.185 3.583 4.768 6.275 8.172 10.54 13.48 17.09 8 1.172 1.369 1.477 1.594 1.851 1.993 2.144 2.476 2.853 3.059 3.278 3.759 4.300 5.960 8.157 11.03 14.76 19.54 25.63 9 1.195 1.423 1.551 1.689 1.999 2.172 2.358 2.773 3.252 3.518 3.803 4.435 5.160 7.451 10.60 14.89 20.66 28.33 38.44 10 1.219 1.480 1.629 1.791 2.159 2.367 2.594 3.106 3.707 4.046 4.411 5.234 6.192 9.313 13.79 20.11 28.93 41.08 57.67 11 1.243 1.539 1.710 1.898 2.332 2.580 2.853 3.479 4.226 4.652 5.117 6.176 7.430 11.64 17.92 27.14 40.50 59.57 86.50 12 1.268 1.601 1.796 2.012 2.518 2.813 3.138 3.896 4.818 5.350 5.936 7.288 8.916 14.55 23.30 36.64 56.69 86.38 129.7 13 1.294 1.665 1.886 2.133 2.720 3.066 3.452 4.363 5.492 6.153 6.886 8.599 10.70 18.19 30.29 49.47 79.37 125.3 194.6 14 1.319 1.732 1.980 2.261 2.937 3.342 3.797 4.887 6.261 7.076 7.988 10.15 12.84 22.74 39.37 66.78 111.1 181.6 291.9 15 1.346 1.801 2.079 2.397 3.172 3.642 4.177 5.474 7.138 8.137 9.266 11.97 15.41 28.42 51.19 90.16 155.6 263.3 437.9 16 1.373 1.873 2.183 2.540 3.426 3.970 4.595 6.130 8.137 9.358 10.75 14.13 18.49 35.53 66.54 121.7 217.8 381.8 656.8 17 1.400 1.948 2.292 2.693 3.700 4.328 5.054 6.866 9.276 10.76 12.47 16.67 22.19 44.41 86.50 164.3 304.9 553.7 985.3 18 1.428 2.026 2.407 2.854 3.996 4.717 5.560 7.690 10.58 12.38 14.46 19.67 26.62 55.51 112.5 221.8 426.9 802.8 1478. 19 1.457 2.107 2.527 3.026 4.316 5.142 6.116 8.613 12.06 14.23 16.78 23.21 31.95 69.39 146.2 299.5 597.6 1164. 2217. 20 1.486 2.191 2.653 3.207 4.661 5.604 6.727 9.646 13.74 16.37 19.46 27.39 38.34 86.74 190.0 404.3 836.7 1688. 3325. 21 1.516 2.279 2.786 3.400 5.034 6.109 7.400 10.80 15.67 18.82 22.57 32.32 46.01 108.4 247.1 545.8 1171. 2448. 4988. 22 1.546 2.370 2.925 3.604 5.437 6.659 8.140 12.10 17,86 21.64 26.19 38.14 55.21 135.5 321.2 736.8 1640. 3549. 7482. 23 1.577 2.465 3.072 3.820 5.871 7.258 8.954 13.55 20.36 24.89 30.38 45.01 66.25 169.4 417.5 994.7 2296. 5146. 11223 24 1.608 2.563 3.225 4.049 6.341 7.911 9.850 15.18 23.21 28.63 35.24 53.11 79.50 211.8 542.8 1343. 3214. 7462. 16834 25 1.641 2.666 3.386 4.292 6.848 8.623 10.83 17.00 26.46 32.92 40.87 62.67 95.40 264.7 705.6 1813. 4500. 10819 25251 30 1.811 3.243 4.322 5.743 10.06 13.27 17.45 29.96 50.95 66.21 85.85 143.4 237.4 807.8 2620. 8129. 24210 69349 >100t 35 2.000 3.946 5.516 7.686 14.79 20.41 28.10 52.80 98.10 133.2 180.3 328.0 590.7 2465. 9728. 36449 >100t >100t >100t 40 2.208 4.801 7.040 10.29 21.72 31.41 45.26 93.05 188.9 267.9 378.7 750.4 1470. 7523. 36119 >100t >100t >100t >100t 45 2.438 5.841 8.985 13.76 31.92 48.33 72.89 164.0 363.7 538.8 795.4 1717. 3657. 22959 >100t >100t >100t >100t >100t 50 2.692 7.107 11.47 18.42 46.90 74.36 117.4 289.0 700.2 1084. 1671. 3927. 9100. 70065 >100t >100t >100t >100t >100t

>100t indicates that the number exceeds 100 000.

Table 4. Future value of annuity.

The future value of I invested annually at a given rate of interest 'i' for a given number of years 'n'.
Future value of an annuity factor: S (1 + i)n

 % 2 4 5 6 8 9 10 12 14 15 16 18 120 25 30 35 40 50 Yrs 1 1.02 1.04 1.05 1.06 1.08 1.09 1.1 1.12 1.14 1.15 1.16 1.18 1.2 1.25 1.3 1.35 1.4 1.5 2 2.060 2.122 2.153 2.184 2.246 2.278 2.310 2.374 2.440 2.473 2.506 2.572 2.640 2.813 2.990 3.173 3.360 3.750 3 3.122 3.246 3.310 3.375 3.506 3.573 3.641 3.779 3.921 3.993 4.066 4.215 4.368 4.766 5.187 5.633 6.104 7.125 4 4.204 4.416 4.526 4.637 4.867 4.985 5.105 5.353 5.610 5.742 5.877 6.154 6.442 7.207 8.043 8.954 9.946 12.19 5 5.308 5.633 5.802 5.975 6.336 6.523 6.716 7.115 7.536 7.754 7.977 8.442 8.930 10.26 11.76 13.44 15.32 19.78 6 6.434 6.898 7.142 7.394 7.923 8.200 8.487 9.089 9.730 10.07 10.41 11.14 11.92 14.07 16.58 19.49 22.85 31.17 7 7.583 8.214 8.549 8.897 9.637 10.03 10.44 11.30 12.23 12.73 13.24 14.33 15.50 18.84 22.86 27.66 33.39 48.26 8 8.755 9.583 10.03 10.49 11.49 12.02 12.58 13.78 15.09 15.79 16.52 18.09 19.80 24.80 31.01 38.70 48.15 73.89 9 9.950 11.01 11.58 12.18 13.49 14.19 14.94 16.55 18.34 19.30 20.32 22.52 24.96 32.25 41.62 53.59 68.81 112.3 10 11.17 12.49 13.21 13.97 15.65 16.56 17.53 19.65 22.04 23.35 24.73 27.76 31.15 41.57 55.41 73.70 97.74 170.0 11 12.41 14.03 14.92 15.87 17.98 19.14 20.38 23.13 26.27 28.00 29.85 33.93 38.58 53.21 73.33 100.8 138.2 256.5 12 13.68 15.63 16.71 17.88 20.50 21.95 23.52 27.03 31.09 33.35 35.79 41.22 47.50 67.76 96.63 137.5 194.9 386.2 13 14.97 17.29 18.60 20.02 23.21 25.02 26.97 31.39 36.58 39.50 42.67 49.82 58.20 85.95 126.9 187.0 274.3 580.9 14 16.29 19.02 20.58 22.28 26.15 28.36 30.77 36.28 42.84 46.58 50.66 59.97 71.04 108.7 166.3 253.7 385.4 872.8 15 17.64 20.82 22.66 24.67 29.32 32.00 34.95 41.75 49.98 54.72 59.93 71.94 86.44 137.1 217.5 343.9 541.0 1311. 16 19.01 22.70 24.84 27.21 32.75 35.97 39.54 47.88 58.12 64.08 70.67 86.07 104.9 172.6 284.0 465.6 758.8 1968. 17 20.41 24.65 27.13 29.91 36.45 40.30 44.60 54.75 67.39 74.84 83.14 102.7 127.1 217.0 370.5 629.9 1064. 2953. 18 21.84 26.67 29.54 32.76 40.45 45.02 50.16 62.44 77.97 87.21 97.60 122.4 153.7 272.6 483.0 851.7 1491. 4431. 19 23.30 28.78 32.07 35.79 44.76 50.16 56.27 71.05 90.02 101.4 114.4 145.6 195.7 341.9 629.2 1151. 2088. 6648. 20 24.78 30.97 34.72 38.99 49.42 55.76 63.00 80.70 103.8 117.8 133.8 173.0 224.0 428.7 819.2 1555. 2925. 9973. 21 26.30 33.25 37.51 42.39 54.46 61.87 70.40 91.50 119.4 136.6 156.4 205.3 270.0 537.1 1066. 2101. 4096. 14961 22 27.84 35.62 40.43 46.00 59.89 68.53 78.54 103.6 137.3 158.3 182.6 243.5 325.2 672.6 1387. 2838. 5736. 22442 23 29.42 38.08 43.50 49.82 65.76 75.79 87.50 117.2 157.7 183.2 213.0 288.5 391.5 842.0 1805. 3833. 8032. 33665 24 31.03 40.65 46.73 53.86 72.11 83.70 97.35 132.3 180.9 211.8 248.2 341.6 471.0 1054. 2348. 5176. 11246 50499 25 32.67 43.31 50.11 58.16 78.95 92.32 108.2 149.3 207.3 244.7 289.1 404.3 566.4 1318. 3053. 6988. 15746 75751 30 41.38 58.33 69.76 83.80 122.3 148.6 180.9 270.3 406.7 500.0 615.2 933.3 1418. 4034. 11349 31349 84702 >100t 35 50.99 76.60 94.84 118.1 186.1 235.1 298.1 483.5 790.7 1013. 1300. 2144. 3538. 12321 42150 >100t >100t >100t 40 61.61 98.83 126.8 164.0 279.8 368.3 486.9 859.1 1530. 2046. 2738. 4913. 8813. 37611 >100t >100t >100t >100t 45 73.33 125.9 167.7 223.5 417.4 573.2 790.8 1521. 2953. 4123. 5760. 11247 21938 >100t >100t >100t >100t >100t 50 86.27 158.8 219.8 307.8 619.7 888.4 1280. 2688. 5694. 8300. 12105 25739 54597 >100t >100t >100t >100t >100t

> 100t indicates that the number exceeds 100 000. !

Table 5. Annual repayments or capital recovery factors.

The amount that must be repaid annually for every I unit borrowed for 'n' years at 'i' rate of interest.
Capital recovery factor: 1/ [S (1 + i)n]

 % 2 4 5 6 8 9 10 12 14 15 16 18 20 25 30 35 40 45 50 Yrs 1 1.02 1.04 1.05 1.06 1.08 1.09 1.10 1.12 1.14 1.15 1.16 1.18 1.20 1.25 1.30 1.35 1.40 1.45 1.50 2 .515 .530 .538 .545 .561 .568 .576 .592 .607 .615 .623 .639 .655 .694 .735 .776 .817 .858 .900 3 .347 .360 .367 .374 .388 .395 .402 .416 .431 .438 .445 .460 .475 .512 .551 .590 .629 .670 .711 4 .263 .275 .282 .289 .302 .309 .315 .329 .343 .350 .357 .372 .386 .423 .462 .501 .541 .582 .623 5 .212 .225 .231 .237 .250 .257 .264 .277 .291 .298 .305 .320 .334 .372 .411 .450 .491 .533 .576 6 .179 .191 .197 .203 .216 .223 .230 .243 .257 .264 .271 .286 .301 .339 .378 .419 .461 .504 .548 7 .155 .167 .173 .179 .192 .199 .205 .219 .233 .240 .248 .262 .277 .316 .357 .399 .442 .486 .531 8 .137 .149 .155 .161 .174 .181 .187 .201 .216 .223 .230 .245 .261 .300 .342 .385 .429 .474 .520 9 .123 .134 .141 .147 .160 .167 .174 .188 .202 .210 .217 .232 .248 .289 .331 .375 .420 .466 .513 10 .111 .123 .130 .136 .149 .156 .163 .177 .192 .199 .207 .223 .239 .280 .323 .368 .414 .461 .509 11 .102 .114 .120 .127 .140 .147 .154 .168 .183 .191 .199 .215 .231 .273 .318 .363 .410 .458 .506 12 .095 .107 .113 .119 .133 .140 .147 .161 .177 .184 .192 .209 .225 .268 .313 .360 .407 .455 .504 13 .088 .100 .106 .113 .127 .134 .141 .156 .171 .179 .187 .204 .221 .265 .310 .357 .405 .454 .503 14 .083 .095 .101 .108 .121 .128 .136 .151 .167 .175 .183 .200 .217 .262 .308 .355 .404 .452 .502 15 .078 .090 .096 .103 .117 .124 .131 .147 .163 .171 .179 .196 .214 .259 .306 .354 .403 .452 .501 16 .074 .086 .092 .099 .113 .120 .128 .143 .160 .168 .176 .194 .211 .257 .305 .353 .402 .451 .501 17 .070 .082 .089 .095 .110 .117 .125 .140 .157 .165 .174 .191 .209 .256 .304 .352 .401 .451 .501 18 .067 .079 .086 .092 .107 .114 .122 .138 .155 .163 .172 .190 .208 .255 .303 .352 .401 .451 .500 19 .064 .076 .083 .090 .104 .112 .120 .136 .153 .161 .170 .188 .206 .254 .302 .351 .401 .450 .500 20 .061 .074 .080 .087 .102 .110 .117 .134 .151 .160 .169 .187 .205 .253 .302 .351 .400 .450 .500 21 .059 .071 .078 .085 .100 .109 .116 .132 .150 .158 .167 .186 .204 .252 .301 .351 .400 .450 .500 22 .057 .069 .076 .083 .098 .106 .114 .131 .148 .157 .166 .185 .204 .252 .301 .350 .400 .450 .500 23 .055 .067 .074 .081 .096 .104 .113 .130 .147 .156 .165 .184 .203 .251 .301 .350 .400 .450 .500 24 .053 .066 .072 .080 .095 .103 .111 .128 .146 .155 .165 .183 .203 .251 .301 .350 .400 .450 .500 25 .051 .064 .071 .078 .094 .102 .110 .127 .145 .155 .164 .183 .202 .251 .300 .350 .400 .450 .500 30 .045 .058 .065 .073 .089 .097 .106 .124 .143 .152 .162 .181 .201 .250 .300 .350 A00 .450 .500 35 .040 .054 .061 .069 .086 .095 .104 .122 .141 .151 .161 .181 .200 .250 .300 .350 .400 .450 .500 40 .037 .051 .058 .066 .084 .093 .102 .121 .141 .151 .161 .181 .200 .250 .300 .350 .400 .450 .500 45 .034 .048 .056 .065 .083 .092 .101 .121 .140 .150 .160 .180 .200 .250 .300 .350 .400 .450 .500 50 .032 .047 .055 .063 .082 .091 .101 .120 .140 .150 .160 .180 .200 .250 .300 .350 .400 .450 .500

Table 6. Random numbers.

 52687 36466 31250 10750 81154 76239 02937 00804 14571 35636 99891 39300 20363 81053 87126 68315 66018 99258 23050 51628 95686 65633 03927 49542 62015 76279 30667 47457 08370 55493 80297 42941 53954 89751 81720 75500 52079 18983 09517 54467 43840 05978 64461 88503 13868 38579 51074 06421 11489 91794 58253 16172 43289 36508 92507 19955 47069 69382 72355 41264 76842 44975 72445 60619 76206 78458 57261 20480 14159 77540 11049 93629 75978 09284 74560 35337 41350 19829 72905 81083 18417 09269 04931 02875 66460 78901 90850 56802 64686 00483 84721 02891 04851 28690 78929 55718 76640 34683 24470 72028 81587 94552 19714 14725 30418 50040 10905 21456 96274 21497 71360 84488 27826 38847 42635 00011 44324 87077 86266 36286 52016 02138 99081 33774 60456 86-051 92892 00108 80450 08016 34409 63265 03569 53389 94802 78443 14874 34622 01461 12809 75493 85249 68259 78254 04969 90573 80572 22936 75494 65843 54777 82846 07602 12542 13438 38729 51739 21464 23261 50418 88106 84632 13687 13245 91385 54043 49706 01643 92906 70078 94555 90339 44937 93688 03769 35063 29841 00717 55934 92701 55639 92813 52547 32590 50596 85757 17311 50801 05721 06699 59503 06371 57022 46540 51404 87963 87201 72295 93739 92461 86958 93697 84126 18507 15149 68452 10995 18637 63589 10291 34068 50072 01118 19281 78744 46676 26528 60506 84982 55870 85367 84104 62187 75449 71417 95366 24359 76252 95341 59073 91119 15355 25554 72685 71664 41397 85554 18196 80180 91959 07223 59851 13118 7,8283 55640 89046 36486 58435 91206 29737 73846 81192 03205 96028 75043 51927 06520 35374 13506 86271 17397 38235 89714 63479 99097 57960 64607 89019 08505 68026 46860 04838 47212 07890 53116 61106 64073 75536 37865 65796