- X - X Reference Reference Future Value of $1 Present Value of $1 9% 10% 12% 14% 15% 16% 18% 20% Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% Periods 1% 2% 3% 4% 5% 6% 7% 8% 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 0.877 0.870 0.862 0.847 0.833 Period 1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.120 1.140 1.150 Period 1 Period 2 1.300 1.323 1.020 1.040 1.061 1.082 | 1.103 1.124 1.145 1.166 1.188 1.210 1.254 Period 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.797 0.769 0.756 0.743 0.718 0.694 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.405 1.482 1.521 Period 3 942 0.915 0.889 0.864 0.971 0.942 0.9 0.840 0.816 0.794 0.772 5 0.658 0.641 0.609 0.5 Period 3 2 0.751 0.712 0.675 0.708 0.683 0.636 0.592 0.572 0.552 0.516 0.482 Period 4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.574 1.689 1.749 Period 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 1.403 1.469 1.539 1.611 1.762 1.925 2.011 Period 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.567 0.519 0.497 0.476 0.437 0.402 Period 5 1.051 1.104 1.159 1.217 1.276 1.338 Period 6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 1.974 2.195 2.313 Period 6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.507 0.456 0.432 0.410 0.370 0.335 Period 7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.211 2.502 2.660 Period 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.452 0.400 0.376 0.354 0.314 0.279 0.502 0.467 0.404 0.351 0.327 0.305 0.266 0.233 Period 8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.476 2.853 3.059 Period 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.284 0.263 0. 194 Period 9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 2.773 3.252 3.518 Period 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.361 0.308 0.225 0.191 0.162 Period 10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 3.106 3.707 4.046 Period 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.322 0.270 0.247 0.227 1.539 1.710 1.898 2.105 332 2.580 2.853 3.479 4.226 Period 11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.287 0.237 0.215 0.195 0.162 0.135 Period 11 1.116 1.243 1.384 0.208 0.187 0.168 0.137 0.112 Period 12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 3.896 4.818 5.350 Period 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.257 Period 13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 4.363 5.492 6.153 Period 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.229 0.182 0.163 0.145 0.116 0.093 Period 14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.798 4.887 6.261 7.076 Period 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.205 0.160 0.141 0.125 0.099 0.078 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 5.474 7.138 8.137 Period 15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 6 0.239 0.183 0.140 0.123 0.108 8 0.084 0.065 Period 15 1.161 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 6.130 8.137 9.358 Period 16 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.163 0.123 0.107 0.093 0.071 0.054 Period 16 1.173 10.198 0.146 0.108 0.093 0.080 0.060 0.045 Period 17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 6.866 9.276 10.76 Period 17 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.051 0.038 Period 18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 7.690 10.58 12.38 Period 18 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.130 0.095 0.081 0.069 0.232 0.194 0.164 0.116 0.083 0.070 0.060 0.043 0.031 Period 19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 8.613 12.06 14.23 Period 19 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.215 0.178 0.149 0.104 0.073 0.061 0.051 0.037 Period 20 .220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727 9.646 13.74 16.37 Period 20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.064 0.053 0.044 0.031 0.022 Period 21 1.232 1.516 1.860 2.279 2.786 3.400 4.141 5.034 6.109 7.400 10.80 15.67 18.82 Period 21 0.811 0.660 0.538 0.439 0.359 0.294 0.242 0.199 0.164 4 0.135 0.093 4 0.150 0.123 0.083 0.056 0.046 0.038 0.026 0.018 Period 22 1.245 1.546 1.916 2.370 2.925 3.604 4.430 5.437 6.659 8.140 12.10 17.86 21.64 Period 22 0.803 0.647 0.522 0.422 0.342 0.278 0.226 Period 23 1.257 1.577 1.974 2.465 3.820 4.741 5.871 7.258 8.954 13.55 24.89 795 0.634 0.406 0.326 0.262 0.211 0.170 0.138 0.112 0.074 0.049 0.040 0.033 022 0.015 2.033 2.563 3.225 4.049 5.072 6.341 7.911 9.850 15.18 23.21 28.63 Period 24 0.788 0.622 0.492 0.390 0.310 0.247 0.197 0.158 0.126 0.102 0.066 0.043 0.035 0.028 0.019 0.013 Period 24 1.270 1.608 Period 25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.83 17.00 26.46 32.92 Period 25 0.780 0.610 0.478 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.059 0.038 0.030 0.024 0.016 0.010 Period 26 1.295 1.673 2.157 2.772 3.556 4 4.549 5.807 7.396 9.399 11.92 19.04 30.17 37.86 Period 26 0.772 0.598 0.464 0.361 0.281 0.220 0.172 0.135 0.106 0.084 0.053 0.033 0.026 0.021 0.014 0.009 0.161 0.125 0.098 0.076 0.047 0.029 0.023 0.018 0.011 0.007 Period 27 1.308 1.707 2.221 2.883 3.733 4.822 6.214 7.988 10.25 6 13.11 21.32 34.39 43.54 Period 27 0.764 0.586 0.450 0.347 0.268 0.207 1.741 2.288 2.999 3.920 5.112 6.649 8.627 11.17 14.42 23.88 39.20 50.07 Period 28 0.757 0.574 0.437 0.333 0.255 0.196 0.150 0.116 0.090 0.069 0.042 0.026 0.020 0.016 0.010 0.006 Period 28 1.321 Period 29 1.776 2.357 3.119 4.116 5.418 7.114 9.317 12.17 15.86 26.75 .69 57.58 Period 29 0.749 0.563 0.424 0.321 0.243 0.185 0.141 0.107 0.082 20.063 0.037 0.022 0.017 0.014 0.008 0.005 1.335 Period 30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.06 13.27 17.45 29.96 50.95 66.2 Period 30 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0. 0.033 0.020 0.015 0.012 0.007 0.004 10.29 14.97 21.72 31.41 45.26 93.05 188.9 Period 40 0.672 0.453 0.307 0.208 0.142 0.097 0.067 0.046 0.032 0.022 0.011 0.005 0.004 0.003 0.001 0.001 Period 40 .489 2.208 3.262 4.801 7.040 0.021 0.013 0.009 0.003 0.001 0.001 0.001 Period 50 1.645 2.692 4.384 7.107 7 11.47 18.42 29.46 46.90 74.36 117.4 289.0 700.2 1,084 Period 50 0.608 0.372 0.228 0.141 0.087 0.054 0.034 Print Done Print DoneX - X Reference Reference Future Value of Ordinary Annuity of $1 Present Value of Ordinary Annuity of $1 | 5% 6% 7% 8% 9% 10% 12% 14% 15% Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% Periods 1% 2% 3% 4% 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 0.877 0.870 0.862 0.847 0.833 Period 1 1.000 1.000 1.000 1.000 1.000 2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090 2.100 2.120 2.140 2.150 Period 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.690 1.647 1.626 1.605 1.566 1.528 Period 2 2.246 2.174 2.106 Period 3 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3.310 3.374 3.440 3.473 Period 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.402 2.322 2.283 2.690 2.589 Period 4 4.060 4.122 4.184 4.246 4.310 4.375 4.440 4.506 4.573 4.641 4.779 4.921 | 4.993 Period 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.037 2.914 2.855 2.798 5.637 5.751 5.867 5.985 6.105 6.353 6.610 6.742 3.274 3.127 2.991 Period 5 5.101 5.204 5.309 5.416 5.526 Period 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.605 3.433 3.352 Period 6 6.152 6.308 6.468 6.633 6.802 6.975 7.153 7.336 7.523 7.716 8.115 8.536 8.754 5 417 5.076 4.917 4.767 4.623 4.486 4.355 4.111 3.889 3.784 3.685 3.498 3.32 Period 6 5.795 5.601 5.242 Period 7 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487 10.09 10.73 11.07 Period 7 6.472 6.230 6.002 4.288 4.160 6.728 5.786 5.582 5.389 5.206 5.033 4.868 4.564 4.039 3.812 3.605 8.286 8.583 8.892 9.214 9.549 9.897 10.260 10.64 11.03 11.44 12.30 13.23 13.73 Period 8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 4.968 4.639 |4.487 4.34 4.078 3.837 Period 8 14.78 16.09 16.79 7.108 6.802 6.515 6.247 5.995 5.759 5.328 4.946 4.772 4.607 4.303 4.03 Period 9 9.369 9.755 10.16 10.58 11.03 11.49 11.98 12.49 13.02 13.58 Period 9 8.566 8.162 7.786 7.435 13.18 13.82 14.49 15.19 15.94 17.55 19.34 Period 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.650 5.216 5.019 4.833 4.494 4.192 Period 10 10.46 10.95 11.46 12.01 12.58 8 16.65 17.56 18.53 20.65 23.04 24.35 8.306 7.887 7.499 7.139 6.805 6.495 5.938 5.453 5.234 5.02 4.656 4.32 Period 11 11.57 12.17 12.81 13.49 14.21 14.97 Period 11 10.368 9.787 9.253 8.760 17.89 18.98 20.14 21.38 24.13 27.27 29.00 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.194 5.660 5.421 5.19 4.793 4.439 Period 12 12.68 13.41 14.19 15.03 15.92 16.87 Period 12 11.255 10.575 9.954 4.910 4.533 Period 13 13.81 14.68 15.62 16.63 17.71 18.88 20.14 21.50 22.95 24.52 28.03 32.09 34.35 Period 13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 4 7.487 7.103 6.424 5.842 5.583 5.342 Period 14 14.95 15.97 17.09 18.29 19.60 21.02 22.55 24.21 26.02 27.98 32.39 37.58 40.50 6 10.563 9.899 9.295 8.745 8.244 7.786 7.367 5.724 5.468 4.611 Period 14 13.004 12.106 11.296 6.628 6.002 5.008 23.28 25.13 27.15 29.36 31.77 37.28 43.84 47.5 Period 15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606 6.811 6.142 5.847 5.575 5.092 4.675 Period 15 16.10 17.29 18.60 0 20.02 21.58 55.72 5.669 5.162 4.73 Period 16 17.26 18.64 20.16 21.82 23.66 25.67 27.89 30.32 33.00 35.95 42.75 50.98 Period 16 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.313 7.824 6.974 6.265 5.954 6.047 5.749 4.77 Period 17 3 20.01 21.76 23.70 25.84 7.120 6.373 5.222 28.21 30.84 33.75 36.97 40.54 48.88 59.12 65.08 Period 17 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.022 7.250 6.467 6.128 5.818 5.273 4.812 Period 18 19.61 21.41 23.41 25.65 28.13 30.91 34.00 37.45 41.30 45.60 55.75 68.39 75.84 Period 18 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.366 6.550 6.198 5.877 5.316 4.844 Period 19 20.81 22.84 25.12 27.67 30.54 33.76 37.38 41.45 46.02 51.16 63.44 78.97 88.21 Period 19 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 36.79 41.00 45.76 51.16 57.28 72.05 91.02 102.4 Period 20 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.469 6.623 6.259 5.929 5.353 4.870 Period 20 22.02 24.30 26.87 29.78 33.07 104.8 118.8 18.857 17.011 15.415 14.029 12.821 11.764 10.836 10.017 9.292 8.649 7.562 6.687 6.312 5.973 5.384 4.891 Period 21 23.24 25.78 28.68 31.97 35.72 39.99 44.87 50.42 56.76 64.00 81.70 Period 21 43.39 49.01 55.46 62.87 71.40 92.50 120.4 137.6 Period 22 19.660 17.658 15.937 14.451 13.163 12.042 11.061 10.201 9.442 8.772 7.645 6.743 6.359 6.011 5.410 4.90 Period 22 7 27.30 30.54 34.25 38.51 Period 23 2 28.85 32.45 36.62 41.43 47.00 53.44 60.89 69.53 79.54 104.6 138.3 159.3 20.456 18.292 16.444 14.857 13.489 12.303 11.272 10.371 9.580 8.883 7.718 6.792 6.399 6.044 5.432 4.925 Period 23 158.7 184.2 21.243 18.914 16.936 15.247 13.799 12.550 11.469 10.529 9.707 8.985 7.784 6.835 6.434 6.073 5.451 4.937 Period 24 26.97 30.42 34.43 39.0 3 39.08 44.50 50.82 58.18 66.76 76.79 88.50 118.2 Period 24 6.097 5.467 4.948 Period 25 28.24 32.03 36.46 41.65 47.73 54.86 63.25 73.11 84.70 98.35 133.3 181.9 212.8 Period 25 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.823 9.077 7.843 6.873 6.464 22.795 20.121 17.877 15.983 14.375 13.003 11.826 10.810 9.929 9.161 7.896 6.906 6.491 6.118 5.480 4.95 Period 26 29.53 33.67 38.55 44.31 51.11 59.16 68.68 79.95 93.32 109.2 150.3 208.3 245.7 Period 26 121.1 169.4 238.5 283.6 23.560 20.707 18.327 16.330 14.643 13.211 11.987 10.935 10.027 9.237 7.943 6.935 6.514 6.136 5.492 4.96 Period 27 30.82 35.34 40.71 8 54.67 63.71 74.48 87.35 102.7 Period 27 7.984 6.961 6.534 6.152 5.502 4.97 Period 28 32.13 37.05 42.93 49.97 58.40 68.53 80.70 95.34 113.0 134.2 190.7 272.9 327.1 Period 28 24.316 21.281 18.764 16.663 14.898 13.406 12.137 11.051 10.116 9.307 6.551 6.16 5.510 4.975 Period 29 33.45 38.79 45.22 52.97 62.32 73.64 87.35 104.0 124.1 6 214.6 312.1 377.2 Period 29 25.066 21.844 19.188 16.984 15.141 13.591 12.278 11.158 10.198 9.370 8.022 6.983 113.3 136.3 164.5 241.3 356.8 434.7 25.808 22.396 19.600 17.292 15.372 13.765 12.409 11.258 10.274 9.427 8.055 7.003 6.566 6.177 5.517 4.979 Period 30 34.78 40.57 47.58 56.08 66.44 79.06 94.46 Period 30 7.105 6.642 6.233 5.548 4.997 Period 40 9 60.40 75.40 95.03 120.8 154.8 199.6 259.1 337.9 442.6 767.1 1,342 1,779 Period 40 32.835 27.355 23.115 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.244 39.196 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962 9.915 8.304 7.133 6.661 6.246 5.554 4.999 Period 50 64.46 84.58 112.8 152.7 209.3 290.3 406.5 573.8 815.1 1,164 2,400 4,995 7,218 Period 50 Print Done Print DoneYou are planning for a very early retirement. You would like to retire at age 40 and have enough money saved to be able to withdraw $235,000 per year for the next 30 years (based on family history, you think you will live to age 70). You plan to save by making 20 equal annual installments (from age 20 to age 40) into a fairly risky investment fund that you expect will earn 12% per year. You will leave the money in this fund until it is completely depleted when you are 70 years old. (Click the icon to view Present Value of $1 table.) (Click the icon to view Present Value of Ordinary Annuity of $1 table.) (Click the icon to view Future Value of $1 table.) (Click the icon to view Future Value of Ordinary Annuity of $1 table.) Read the requirements. Requirement 1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the $235,000 withdrawals.) (Round your final answer to the nearest whole dollar.) To make the plan work, you must accumulate this amount by retirement Requirement 2. How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different? Over the course of your retirement you will be withdrawing However, by age 40 you only need to have invested These numbers are different because: O A. You need to have far less accumulated than what you will withdraw because you only withdraw a portion of the investment every year-the balance remains invested where it continues to earn 12% interest. O B. You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every year-the balance remains invested where it continues to earn 12% interest. O C. You need to have the same amount accumulated as you will withdraw because you will not earn further interest on your investment when you reach retirement. O D. None of the above X Requirements 1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the $235,000 withdrawals.) 2. How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different? Print Done