Present Value Tables

Present Value Tables APPENDIX TABLE 1 Discount factors: Present value of $1 to be received after t years ⫽ 1/(1 ⫹ r ) t. Interest Rate per Year Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 1 2 3 4 5 .990 .980 .971 .961 .951 .980 .961 .942 .924 .906 .971 .943 .915 .888 .863 .962 .925 .889 .855 .822 .952 .907 .864 .823 .784 .943 .890 .840 .792 .747 .935 .873 .816 .763 .713 .926 .857 .794 .735 .681 .917 .842 .772 .708 .650 .909 .826 .751 .683 .621 .901 .812 .731 .659 .593 .893 .797 .712 .636 .567 .885 .783 .693 .613 .543 .877 .769 .675 .592 .519 .870 .756 .658 .572 .497 6 7 8 9 10 .942 .933 .923 .914 .905 .888 .871 .853 .837 .820 .837 .813 .789 .766 .744 .790 .760 .731 .703 .676 .746 .711 .677 .645 .614 .705 .665 .627 .592 .558 .666 .623 .582 .544 .508 .630 .583 .540 .500 .463 .596 .547 .502 .460 .422 .564 .513 .467 .424 .386 .535 .482 .434 .391 .352 .507 .452 .404 .361 .322 .480 .425 .376 .333 .295 .456 .400 .351 .308 .270 .432 .376 .327 .284 .247 11 12 13 14 15 .896 .887 .879 .870 .861 .804 .788 .773 .758 .743 .722 .701 .681 .661 .642 .650 .625 .601 .577 .555 .585 .557 .530 .505 .481 .527 .497 .469 .442 .417 .475 .444 .415 .388 .362 .429 .397 .368 .340 .315 .388 .356 .326 .299 .275 .350 .319 .290 .263 .239 .317 .286 .258 .232 .209 .287 .257 .229 .205 .183 .261 .231 .204 .181 .160 .237 .208 .182 .160 .140 .215 .187 .163 .141 .123 16 17 18 19 20 .853 .844 .836 .828 .820 .728 .714 .700 .686 .673 .623 .605 .587 .570 .554 .534 .513 .494 .475 .456 .458 .436 .416 .396 .377 .394 .371 .350 .331 .312 .339 .317 .296 .277 .258 .292 .270 .250 .232 .215 .252 .231 .212 .194 .178 .218 .198 .180 .164 .149 .188 .170 .153 .138 .124 .163 .146 .130 .116 .104 .141 .125 .111 .098 .087 .123 .108 .095 .083 .073 .107 .093 .081 .070 .061 16% 17% 18% 19% 20% 21% Interest Rate per Year Number of Years 22% 23% 24% 26% 27% 28% 29% 30% .862 .743 .641 .552 .476 .855 .731 .624 .534 .456 .847 .718 .609 .516 .437 .840 .706 .593 .499 .419 .833 .694 .579 .482 .402 .826 .683 .564 .467 .386 .820 .672 .551 .451 .370 .813 .661 .537 .437 .355 .806 .650 .524 .423 .341 .800 .640 .512 .410 .328 .794 .630 .500 .397 .315 .787 .620 .488 .384 .303 .781 .610 .477 .373 .291 .775 .601 .466 .361 .280 .769 .592 .455 .350 .269 6 7 8 9 10 .410 .354 .305 .263 .227 .390 .333 .285 .243 .208 .370 .314 .266 .225 .191 .352 .296 .249 .209 .176 .335 .279 .233 .194 .162 .319 .263 .218 .180 .149 .303 .249 .204 .167 .137 .289 .235 .191 .155 .126 .275 .222 .179 .144 .116 .262 .210 .168 .134 .107 .250 .198 .157 .125 .099 .238 .188 .148 .116 .092 .227 .178 .139 .108 .085 .217 .168 .130 .101 .078 .207 .159 .123 .094 .073 11 12 13 14 15 .195 .168 .145 .125 .108 .178 .152 .130 .111 .095 .162 .137 .116 .099 .084 .148 .124 .104 .088 .074 .135 .112 .093 .078 .065 .123 .102 .084 .069 .057 .112 .092 .075 .062 .051 .103 .083 .068 .055 .045 .094 .076 .061 .049 .040 .086 .069 .055 .044 .035 .079 .062 .050 .039 .031 .072 .057 .045 .035 .028 .066 .052 .040 .032 .025 .061 .047 .037 .028 .022 .056 .043 .033 .025 .020 16 17 18 19 20 .093 .080 .069 .060 .051 .081 .069 .059 .051 .043 .071 .060 .051 .043 .037 .062 .052 .044 .037 .031 .054 .045 .038 .031 .026 .047 .039 .032 .027 .022 .042 .034 .028 .023 .019 .036 .030 .024 .020 .016 .032 .026 .021 .017 .014 .028 .023 .018 .014 .012 .025 .020 .016 .012 .010 .022 .017 .014 .011 .008 .019 .015 .012 .009 .007 .017 .013 .010 .008 .006 .015 .012 .009 .007 .005 Note: For example, if the interest rate is 10% per year, the present value of $1 received at year 5 is $.621. A 25% 1 2 3 4 5 A-1 Present Value Tables APPENDIX TABLE 2 Future value of $1 after t years ⫽ (1 ⫹ r )t . Interest Rate per Year Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120 1.130 1.140 1.150 2 3 4 5 1.020 1.030 1.041 1.051 1.040 1.061 1.082 1.104 1.061 1.093 1.126 1.159 1.082 1.125 1.170 1.217 1.102 1.158 1.216 1.276 1.124 1.191 1.262 1.338 1.145 1.225 1.311 1.403 1.166 1.260 1.360 1.469 1.188 1.295 1.412 1.539 1.210 1.331 1.464 1.611 1.232 1.368 1.518 1.685 1.254 1.405 1.574 1.762 1.277 1.443 1.630 1.842 1.300 1.482 1.689 1.925 1.323 1.521 1.749 2.011 6 7 8 9 10 1.062 1.072 1.083 1.094 1.105 1.126 1.149 1.172 1.195 1.219 1.194 1.230 1.267 1.305 1.344 1.265 1.316 1.369 1.423 1.480 1.340 1.407 1.477 1.551 1.629 1.419 1.504 1.594 1.689 1.791 1.501 1.606 1.718 1.838 1.967 1.587 1.714 1.851 1.999 2.159 1.677 1.828 1.993 2.172 2.367 1.772 1.949 2.144 2.358 2.594 1.870 2.076 2.305 2.558 2.839 1.974 2.211 2.476 2.773 3.106 2.082 2.353 2.658 3.004 3.395 2.195 2.502 2.853 3.252 3.707 2.313 2.660 3.059 3.518 4.046 11 12 13 14 15 1.116 1.127 1.138 1.149 1.161 1.243 1.268 1.294 1.319 1.346 1.384 1.426 1.469 1.513 1.558 1.539 1.601 1.665 1.732 1.801 1.710 1.796 1.886 1.980 2.079 1.898 2.012 2.133 2.261 2.397 2.105 2.252 2.410 2.579 2.759 2.332 2.518 2.720 2.937 3.172 2.580 2.813 3.066 3.342 3.642 2.853 3.138 3.452 3.797 4.177 3.152 3.498 3.883 4.310 4.785 3.479 3.896 4.363 4.887 5.474 3.836 4.335 4.898 5.535 6.254 4.226 4.818 5.492 6.261 7.138 4.652 5.350 6.153 7.076 8.137 16 17 18 19 20 1.173 1.184 1.196 1.208 1.220 1.373 1.400 1.428 1.457 1.486 1.605 1.653 1.702 1.754 1.806 1.873 1.948 2.026 2.107 2.191 2.183 2.292 2.407 2.527 2.653 2.540 2.693 2.854 3.026 3.207 2.952 3.159 3.380 3.617 3.870 3.426 3.700 3.996 4.316 4.661 3.970 4.328 4.717 5.142 5.604 4.595 5.054 5.560 6.116 6.727 5.311 5.895 6.544 7.263 8.062 6.130 6.866 7.690 8.613 9.646 7.067 8.137 7.986 9.276 9.024 10.58 10.20 12.06 11.52 13.74 9.358 10.76 12.38 14.23 16.37 of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 1 2 3 4 5 1.160 1.346 1.561 1.811 2.100 1.170 1.369 1.602 1.874 2.192 1.180 1.392 1.643 1.939 2.288 1.190 1.416 1.685 2.005 2.386 1.200 1.440 1.728 2.074 2.488 1.210 1.464 1.772 2.144 2.594 1.220 1.488 1.816 2.215 2.703 1.230 1.513 1.861 2.289 2.815 1.240 1.538 1.907 2.364 2.932 1.250 1.563 1.953 2.441 3.052 1.260 1.588 2.000 2.520 3.176 1.270 1.613 2.048 2.601 3.304 1.280 1.638 2.097 2.684 3.436 1.290 1.664 2.147 2.769 3.572 1.300 1.690 2.197 2.856 3.713 6 7 8 9 10 2.436 2.826 3.278 3.803 4.411 2.565 3.001 3.511 4.108 4.807 2.700 3.185 3.759 4.435 5.234 2.840 3.379 4.021 4.785 5.695 2.986 3.583 4.300 5.160 6.192 3.138 3.797 4.595 5.560 6.728 3.297 4.023 4.908 5.987 7.305 3.463 4.259 5.239 6.444 7.926 3.635 4.508 5.590 6.931 8.594 3.815 4.768 5.960 7.451 9.313 4.002 5.042 6.353 8.005 10.09 4.196 5.329 6.768 8.595 10.92 4.398 5.629 7.206 9.223 11.81 4.608 5.945 7.669 9.893 12.76 4.827 6.275 8.157 10.60 13.79 11 12 13 14 15 5.117 5.624 6.176 6.777 7.430 8.140 5.936 6.580 7.288 8.064 8.916 9.850 6.886 7.699 8.599 9.596 10.70 11.92 7.988 9.007 10.15 11.42 12.84 14.42 9.266 10.54 11.97 13.59 15.41 17.45 8.912 10.87 13.26 16.18 19.74 9.749 11.99 14.75 18.14 22.31 10.66 13.21 16.39 20.32 25.20 11.64 14.55 18.19 22.74 28.42 12.71 16.01 20.18 25.42 32.03 13.86 17.61 22.36 28.40 36.06 15.11 19.34 24.76 31.69 40.56 16.46 21.24 27.39 35.34 45.59 17.92 23.30 30.29 39.37 51.19 24.09 29.38 35.85 43.74 53.36 27.45 33.76 41.52 51.07 62.82 31.24 38.74 48.04 59.57 73.86 35.53 44.41 55.51 69.39 86.74 40.36 45.80 50.85 58.17 64.07 73.87 80.73 93.81 101.7 119.1 51.92 66.46 85.07 108.9 139.4 58.81 75.86 97.86 126.2 162.9 66.54 86.50 112.5 146.2 190.0 Interest Rate per Year Number 16 17 18 19 20 10.75 12.47 14.46 16.78 19.46 12.33 14.43 16.88 19.75 23.11 14.13 16.67 19.67 23.21 27.39 16.17 19.24 22.90 27.25 32.43 18.49 22.19 26.62 31.95 38.34 21.11 25.55 30.91 37.40 45.26 Note: For example, if the interest rate is 10% per year, the investment of $1 today will be worth $1.611 at year 5. 30% A-2 Present Value Tables APPENDIX TABLE 3 Annuity table: Present value of $1 per year for each of t years ⫽ 1/ r ⫺ 1/[ r(1 ⫹ r) t ]. Interest Rate per Year Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 1 2 3 4 5 .990 1.970 2.941 3.902 4.853 .980 1.942 2.884 3.808 4.713 .971 1.913 2.829 3.717 4.580 .962 1.886 2.775 3.630 4.452 .952 1.859 2.723 3.546 4.329 .943 1.833 2.673 3.465 4.212 .935 1.808 2.624 3.387 4.100 .926 1.783 2.577 3.312 3.993 .917 1.759 2.531 3.240 3.890 .909 1.736 2.487 3.170 3.791 .901 1.713 2.444 3.102 3.696 .893 1.690 2.402 3.037 3.605 .885 1.668 2.361 2.974 3.517 .877 1.647 2.322 2.914 3.433 .870 1.626 2.283 2.855 3.352 6 7 8 9 10 5.795 6.728 7.652 8.566 9.471 5.601 6.472 7.325 8.162 8.983 5.417 6.230 7.020 7.786 8.530 5.242 6.002 6.733 7.435 8.111 5.076 5.786 6.463 7.108 7.722 4.917 5.582 6.210 6.802 7.360 4.767 5.389 5.971 6.515 7.024 4.623 5.206 5.747 6.247 6.710 4.486 5.033 5.535 5.995 6.418 4.355 4.868 5.335 5.759 6.145 4.231 4.712 5.146 5.537 5.889 4.111 4.564 4.968 5.328 5.650 3.998 4.423 4.799 5.132 5.426 3.889 4.288 4.639 4.946 5.216 3.784 4.160 4.487 4.772 5.019 7.887 8.384 8.853 9.295 9.712 7.499 7.943 8.358 8.745 9.108 7.139 7.536 7.904 8.244 8.559 6.805 7.161 7.487 7.786 8.061 6.495 6.814 7.103 7.367 7.606 6.207 6.492 6.750 6.982 7.191 5.938 6.194 6.424 6.628 6.811 5.687 5.918 6.122 6.302 6.462 5.453 5.660 5.842 6.002 6.142 5.234 5.421 5.583 5.724 5.847 8.851 8.313 9.122 8.544 9.372 8.756 9.604 8.950 9.818 9.129 7.824 8.022 8.201 8.365 8.514 7.379 7.549 7.702 7.839 7.963 6.974 7.120 7.250 7.366 7.469 6.604 6.729 6.840 6.938 7.025 6.265 6.373 6.467 6.550 6.623 5.954 6.047 6.128 6.198 6.259 11 12 13 14 15 10.37 11.26 12.13 13.00 13.87 9.787 9.253 8.760 8.306 10.58 9.954 9.385 8.863 11.35 10.63 9.986 9.394 12.11 11.30 10.56 9.899 12.85 11.94 11.12 10.38 16 17 18 19 20 14.72 15.56 16.40 17.23 18.05 13.58 14.29 14.99 15.68 16.35 12.56 13.17 13.75 14.32 14.88 11.65 12.17 12.66 13.13 13.59 10.84 11.27 11.69 12.09 12.46 10.11 10.48 10.83 11.16 11.47 of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% 1 2 3 4 5 .862 1.605 2.246 2.798 3.274 .855 1.585 2.210 2.743 3.199 .847 1.566 2.174 2.690 3.127 .840 1.547 2.140 2.639 3.058 .833 1.528 2.106 2.589 2.991 .826 1.509 2.074 2.540 2.926 .820 1.492 2.042 2.494 2.864 .813 1.474 2.011 2.448 2.803 .806 1.457 1.981 2.404 2.745 .800 1.440 1.952 2.362 2.689 .794 1.424 1.923 2.320 2.635 .787 1.407 1.896 2.280 2.583 .781 1.392 1.868 2.241 2.532 .775 1.376 1.842 2.203 2.483 .769 1.361 1.816 2.166 2.436 6 7 8 9 10 3.685 4.039 4.344 4.607 4.833 3.589 3.922 4.207 4.451 4.659 3.498 3.812 4.078 4.303 4.494 3.410 3.706 3.954 4.163 4.339 3.326 3.605 3.837 4.031 4.192 3.245 3.508 3.726 3.905 4.054 3.167 3.416 3.619 3.786 3.923 3.092 3.327 3.518 3.673 3.799 3.020 3.242 3.421 3.566 3.682 2.951 3.161 3.329 3.463 3.571 2.885 3.083 3.241 3.366 3.465 2.821 3.009 3.156 3.273 3.364 2.759 2.937 3.076 3.184 3.269 2.700 2.868 2.999 3.100 3.178 2.643 2.802 2.925 3.019 3.092 11 12 13 14 15 5.029 5.197 5.342 5.468 5.575 4.836 4.988 5.118 5.229 5.324 4.656 4.793 4.910 5.008 5.092 4.486 4.611 4.715 4.802 4.876 4.327 4.439 4.533 4.611 4.675 4.177 4.278 4.362 4.432 4.489 4.035 4.127 4.203 4.265 4.315 3.902 3.985 4.053 4.108 4.153 3.776 3.851 3.912 3.962 4.001 3.656 3.725 3.780 3.824 3.859 3.543 3.606 3.656 3.695 3.726 3.437 3.493 3.538 3.573 3.601 3.335 3.387 3.427 3.459 3.483 3.239 3.286 3.322 3.351 3.373 3.147 3.190 3.223 3.249 3.268 16 17 18 19 20 5.668 5.749 5.818 5.877 5.929 5.405 5.475 5.534 5.584 5.628 5.162 5.222 5.273 5.316 5.353 4.938 4.990 5.033 5.070 5.101 4.730 4.775 4.812 4.843 4.870 4.536 4.576 4.608 4.635 4.657 4.357 4.391 4.419 4.442 4.460 4.189 4.219 4.243 4.263 4.279 4.033 4.059 4.080 4.097 4.110 3.887 3.910 3.928 3.942 3.954 3.751 3.771 3.786 3.799 3.808 3.623 3.640 3.654 3.664 3.673 3.503 3.518 3.529 3.539 3.546 3.390 3.403 3.413 3.421 3.427 3.283 3.295 3.304 3.311 3.316 9.447 9.763 10.06 10.34 10.59 Interest Rate per Year Number Note: For example, if the interest rate is 10% per year, the investment of $1 received in each of the next 5 years is $3.791. A-3 Present Value Tables APPENDIX TABLE 4 Values of e rt. Future value of $1 invested at a continuously compounded rate r for t years. .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00 .10 .20 .30 .40 1.000 1.105 1.221 1.350 1.492 1.010 1.116 1.234 1.363 1.507 1.020 1.127 1.246 1.377 1.522 1.030 1.139 1.259 1.391 1.537 1.041 1.150 1.271 1.405 1.553 1.051 1.162 1.284 1.419 1.568 1.062 1.174 1.297 1.433 1.584 1.073 1.185 1.310 1.448 1.600 1.083 1.197 1.323 1.462 1.616 1.094 1.209 1.336 1.477 1.632 .50 .60 .70 .80 .90 1.649 1.822 2.014 2.226 2.460 1.665 1.840 2.034 2.248 2.484 1.682 1.859 2.054 2.271 2.509 1.699 1.878 2.075 2.293 2.535 1.716 1.896 2.096 2.316 2.560 1.733 1.916 2.117 2.340 2.586 1.751 1.935 2.138 2.363 2.612 1.768 1.954 2.160 2.387 2.638 1.786 1.974 2.181 2.411 2.664 1.804 1.994 2.203 2.435 2.691 1.00 1.10 1.20 1.30 1.40 2.718 3.004 3.320 3.669 4.055 2.746 3.034 3.353 3.706 4.096 2.773 3.065 3.387 3.743 4.137 2.801 3.096 3.421 3.781 4.179 2.829 3.127 3.456 3.819 4.221 2.858 3.158 3.490 3.857 4.263 2.886 3.190 3.525 3.896 4.306 2.915 3.222 3.561 3.935 4.349 2.945 3.254 3.597 3.975 4.393 2.974 3.287 3.633 4.015 4.437 1.50 1.60 1.70 1.80 1.90 4.482 4.953 5.474 6.050 6.686 4.527 5.003 5.529 6.110 6.753 4.572 5.053 5.585 6.172 6.821 4.618 5.104 5.641 6.234 6.890 4.665 5.155 5.697 6.297 6.959 4.711 5.207 5.755 6.360 7.029 4.759 5.259 5.812 6.424 7.099 4.807 5.312 5.871 6.488 7.171 4.855 5.366 5.930 6.553 7.243 4.904 5.419 5.989 6.619 7.316 2.00 2.10 2.20 2.30 2.40 7.389 8.166 9.025 9.974 11.02 7.463 8.248 9.116 10.07 11.13 7.538 8.331 9.207 10.18 11.25 7.614 8.415 9.300 10.28 11.36 7.691 8.499 9.393 10.38 11.47 7.768 8.585 9.488 10.49 11.59 7.846 8.671 9.583 10.59 11.70 7.925 8.758 9.679 10.70 11.82 8.004 8.846 9.777 10.80 11.94 8.085 8.935 9.875 10.91 12.06 2.50 2.60 2.70 2.80 2.90 12.18 13.46 14.88 16.44 18.17 12.30 13.60 15.03 16.61 18.36 12.43 13.74 15.18 16.78 18.54 12.55 13.87 15.33 16.95 18.73 12.68 14.01 15.49 17.12 18.92 12.81 14.15 15.64 17.29 19.11 12.94 14.30 15.80 17.46 19.30 13.07 14.44 15.96 17.64 19.49 13.20 14.59 16.12 17.81 19.69 13.33 14.73 16.28 17.99 19.89 3.00 3.10 3.20 3.30 3.40 20.09 22.20 24.53 27.11 29.96 20.29 22.42 24.78 27.39 30.27 20.49 22.65 25.03 27.66 30.57 20.70 22.87 25.28 27.94 30.88 20.91 23.10 25.53 28.22 31.19 21.12 23.34 25.79 28.50 31.50 21.33 23.57 26.05 28.79 31.82 21.54 23.81 26.31 29.08 32.14 21.76 24.05 26.58 29.37 32.46 21.98 24.29 26.84 29.67 32.79 3.50 3.60 3.70 3.80 3.90 33.12 36.60 40.45 44.70 49.40 33.45 36.97 40.85 45.15 49.90 33.78 37.34 41.26 45.60 50.40 34.12 37.71 41.68 46.06 50.91 34.47 38.09 42.10 46.53 51.42 34.81 38.47 42.52 46.99 51.94 35.16 38.86 42.95 47.47 52.46 35.52 39.25 43.38 47.94 52.98 35.87 39.65 43.82 48.42 53.52 36.23 40.04 44.26 48.91 54.05 rt Note: For example, if the continuously compounded interest rate is 10% per year, the investment of $1 today will be worth $1.105 at year 1 and $1.221 at year 2. A-4 Present Value Tables APPENDIX TABLE 5 Present value of $1 per year received in a continuous stream for each of t years (discounted at an annually compounded rate r ) ⫽ {1 ⫺ 1/(1 ⫹ r) t}/ {ln(1 ⫹ r)}. Interest Rate per Year Number of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 1 2 3 4 5 .995 1.980 2.956 3.922 4.878 .990 1.961 2.913 3.846 4.760 .985 1.942 2.871 3.773 4.648 .981 1.924 2.830 3.702 4.540 .976 1.906 2.791 3.634 4.437 .971 1.888 2.752 3.568 4.337 .967 1.871 2.715 3.504 4.242 .962 1.854 2.679 3.443 4.150 .958 1.837 2.644 3.383 4.062 .954 1.821 2.609 3.326 3.977 .950 1.805 2.576 3.270 3.896 .945 1.790 2.543 3.216 3.817 .941 1.774 2.512 3.164 3.741 .937 1.759 2.481 3.113 3.668 .933 1.745 2.450 3.064 3.598 6 7 8 9 10 5.825 6.762 7.690 8.609 9.519 5.657 6.536 7.398 8.243 9.072 5.498 6.323 7.124 7.902 8.657 5.346 6.121 6.867 7.583 8.272 5.202 5.930 6.623 7.284 7.913 5.063 5.748 6.394 7.004 7.579 4.931 5.576 6.178 6.741 7.267 4.805 5.412 5.974 6.494 6.975 4.685 5.256 5.780 6.261 6.702 4.570 5.108 5.597 6.042 6.447 4.459 4.967 5.424 5.836 6.208 4.353 4.832 5.260 5.642 5.983 4.252 4.704 5.104 5.458 5.772 4.155 4.582 4.956 5.285 5.573 4.062 4.465 4.816 5.121 5.386 7.758 8.218 8.647 9.048 9.423 7.421 7.834 8.216 8.570 8.897 7.107 7.478 7.819 8.131 8.418 6.815 7.149 7.453 7.729 7.980 6.542 6.843 7.115 7.359 7.579 6.287 6.559 6.802 7.018 7.212 6.049 6.294 6.512 6.704 6.874 5.826 6.048 6.242 6.413 6.563 5.617 5.818 5.992 6.144 6.276 9.774 9.201 10.10 9.482 10.41 9.742 10.69 9.983 10.96 10.21 8.681 8.923 9.144 9.347 9.533 8.209 8.416 8.605 8.777 8.932 7.778 7.957 8.118 8.263 8.394 7.385 7.539 7.676 7.799 7.909 7.024 7.158 7.275 7.380 7.472 6.694 6.809 6.910 6.999 7.077 6.390 6.490 6.577 6.652 6.718 11 12 13 14 15 10.42 11.31 12.19 13.07 13.93 9.884 10.68 11.46 12.23 12.98 9.391 8.935 8.512 8.121 10.10 9.572 9.083 8.633 10.79 10.18 9.627 9.116 11.46 10.77 10.14 9.571 12.12 11.34 10.64 10.00 16 17 18 19 20 14.79 15.64 16.48 17.31 18.14 13.71 14.43 15.14 15.83 16.51 12.75 13.36 13.96 14.54 15.10 11.88 12.41 12.91 13.39 13.86 11.11 11.55 11.98 12.39 12.77 10.41 10.79 11.15 11.49 11.81 Interest Rate per Year Number of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% 1 2 3 4 5 .929 1.730 2.421 3.016 3.530 .925 1.716 2.392 2.970 3.464 .922 1.703 2.365 2.925 3.401 .918 1.689 2.337 2.882 3.340 .914 1.676 2.311 2.840 3.281 .910 1.663 2.285 2.799 3.223 .907 1.650 2.259 2.759 3.168 .903 1.638 2.235 2.720 3.115 .900 1.625 2.211 2.682 3.063 .896 1.613 2.187 2.646 3.013 .893 1.601 2.164 2.610 2.964 .889 1.590 2.141 2.576 2.917 .886 1.578 2.119 2.542 2.872 .883 1.567 2.098 2.509 2.828 .880 1.556 2.077 2.477 2.785 6 7 8 9 10 3.972 4.354 4.682 4.966 5.210 3.886 4.247 4.555 4.819 5.044 3.804 4.145 4.434 4.680 4.887 3.724 4.048 4.319 4.547 4.739 3.648 3.954 4.209 4.422 4.599 3.574 3.865 4.104 4.302 4.466 3.504 3.779 4.004 4.189 4.340 3.436 3.696 3.909 4.081 4.221 3.370 3.617 3.817 3.978 4.108 3.307 3.542 3.730 3.880 4.000 3.246 3.469 3.646 3.786 3.898 3.187 3.399 3.566 3.697 3.801 3.130 3.331 3.489 3.612 3.708 3.075 3.266 3.415 3.530 3.619 3.022 3.204 3.344 3.452 3.535 11 12 13 14 15 5.421 5.603 5.759 5.894 6.010 5.237 5.401 5.542 5.662 5.765 5.063 5.213 5.339 5.446 5.537 4.900 5.036 5.150 5.245 5.326 4.747 4.870 4.972 5.058 5.129 4.602 4.713 4.806 4.882 4.945 4.465 4.566 4.650 4.718 4.774 4.335 4.428 4.503 4.564 4.614 4.213 4.297 4.365 4.420 4.464 4.096 4.173 4.235 4.284 4.324 3.986 4.057 4.112 4.157 4.192 3.882 3.946 3.997 4.036 4.068 3.783 3.841 3.887 3.923 3.951 3.689 3.742 3.784 3.816 3.841 3.599 3.648 3.686 3.715 3.737 16 17 18 19 20 6.111 6.197 6.272 6.336 6.391 5.853 5.928 5.992 6.047 6.094 5.614 5.679 5.735 5.781 5.821 5.393 5.450 5.498 5.538 5.571 5.188 5.238 5.279 5.313 5.342 4.998 5.041 5.076 5.106 5.130 4.820 4.858 4.889 4.914 4.935 4.655 4.687 4.714 4.736 4.754 4.500 4.529 4.552 4.571 4.586 4.355 4.381 4.401 4.417 4.430 4.220 4.242 4.259 4.273 4.284 4.092 4.112 4.127 4.139 4.149 3.973 3.990 4.003 4.014 4.022 3.860 3.875 3.887 3.896 3.903 3.754 3.767 3.778 3.785 3.791 Note: For example, if the interest rate is 10% per year, a continuous cash flow of $1 a year for each of 5 years is worth $3.977. A continuous flow of $1 in year 5 only is worth $3.977 ⫺ $3.326 ⫽ $.651. A-5 Present Value Tables APPENDIX TABLE 6 Cumulative probability [N( d)] that a normally distributed variable will be less than d standard deviations above the mean. d 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.1 0.2 0.3 0.4 .5000 .5398 .5793 .6179 .6554 .5040 .5438 .5832 .6217 .6591 .5080 .5478 .5871 .6255 .6628 .5120 .5517 .5910 .6293 .6664 .5160 .5557 .5948 .6331 .6700 .5199 .5596 .5987 .6368 .6736 .5239 .5636 .6026 .6406 .6772 .5279 .5675 .6064 .6443 .6808 .5319 .5714 .6103 .6480 .6844 .5359 .5753 .6141 .6517 .6879 0.5 0.6 0.7 0.8 0.9 .6915 .7257 .7580 .7881 .8159 .6950 .7291 .7611 .7910 .8186 .6985 .7324 .7642 .7939 .8212 .7019 .7357 .7673 .7967 .8238 .7054 .7389 .7704 .7995 .8264 .7088 .7422 .7734 .8023 .8289 .7123 .7454 .7764 .8051 .8315 .7157 .7486 .7794 .8078 .8340 .7190 .7517 .7823 .8106 .8365 .7224 .7549 .7852 .8133 .8389 1 1.1 1.2 1.3 1.4 .8413 .8643 .8849 .9032 .9192 .8438 .8665 .8869 .9049 .9207 .8461 .8686 .8888 .9066 .9222 .8485 .8708 .8907 .9082 .9236 .8508 .8729 .8925 .9099 .9251 .8531 .8749 .8944 .9115 .9265 .8554 .8770 .8962 .9131 .9279 .8577 .8790 .8980 .9147 .9292 .8599 .8810 .8997 .9162 .9306 .8621 .8830 .9015 .9177 .9319 1.5 1.6 1.7 1.8 1.9 .9332 .9452 .9554 .9641 .9713 .9345 .9463 .9564 .9649 .9719 .9357 .9474 .9573 .9656 .9726 .9370 .9484 .9582 .9664 .9732 .9382 .9495 .9591 .9671 .9738 .9394 .9505 .9599 .9678 .9744 .9406 .9515 .9608 .9686 .9750 .9418 .9525 .9616 .9693 .9756 .9429 .9535 .9625 .9699 .9761 .9441 .9545 .9633 .9706 .9767 2 2.1 2.2 2.3 2.4 .9772 .9821 .9861 .9893 .9918 .9778 .9826 .9864 .9896 .9920 .9783 .9830 .9868 .9898 .9922 .9788 .9834 .9871 .9901 .9925 .9793 .9838 .9875 .9904 .9927 .9798 .9842 .9878 .9906 .9929 .9803 .9846 .9881 .9909 .9931 .9808 .9850 .9884 .9911 .9932 .9812 .9854 .9887 .9913 .9934 .9817 .9857 .9890 .9916 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 Note: For example, if d ⫽ .22, N( d ) ⫽ .5871 (i.e., there is a .5871 probability that a normally distributed variable will be less than .22 standard deviations above the mean).