You 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 $230,000 per year for the next 40 years (based on family history, you think you will live to age 80). You plan to save by making 10 equal annual installments (from age 30 to age 40) into a fairly risky investment fund that you expect will earn 14% per year. You will leave the money in this fund until it is completely depleted when you are 80 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 $230,000 withdrawals.) (Round your final answer to the nearest whole dollar.) To make the plan work, you must accumulate $ by retirement. Requirements 1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the $230,000 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? Present Value of $1 Periods 2 1% 0.990 0.980 0.971 0.961 0.951 2% 0.980 0.961 0.942 0.924 0.906 3% 0.971 0.943 0.915 0.888 0.863 4% 0.962 0.925 0.889 0.855 0.822 5% 6% 0.952 0.943 0.907 0.890 0.864 0.840 0.823 0.792 0.784 0.747 7% 0.935 0.873 0.816 0.763 0.713 8% 0.926 0.857 0.794 0.735 0.681 9% 0.917 0.842 0.772 0.708 0.650 10% 12% 0.909 0.893 0.826 0.797 0.751 0.712 0.683 0.636 0.621 0.567 14% 0.877 0.769 0.675 0.592 0.519 15% 0.870 0.756 0.658 0.572 0.497 16% 0.862 0.743 0.641 0.552 0.476 3 4 5 18% 20% 0.847 0.833 0.718 0.694 0.609 0.579 0.516 0.482 0.437 0.402 0.370 0.335 0.314 0.279 0.266 0.233 0.225 0.194 0.191 0.162 6 7 8 0.942 0.888 0.933 0.871 0.923 0.853 0.914 0.837 0.905 0.820 0.837 0.813 0.789 0.766 0.744 0.790 0.760 0.731 0.703 0.676 0.746 0.711 0.677 0.645 0.614 0.705 0.665 0.627 0.592 0.558 0.666 0.623 0.582 0.544 0.508 0.630 0.583 0.540 0.500 0.463 0.596 0.547 0.502 0.460 0.422 0.564 0.513 0.467 0.424 0.386 0.507 0.452 0.404 0.361 0.322 0.456 0.400 0.351 0.308 0.270 0.432 0.376 0.327 0.284 0.247 0.410 0.354 0.305 0.263 0.227 9 10 0.475 0.444 11 12 13 14 15 0.896 0.887 0.879 0.870 0.861 0.804 0.788 0.773 0.758 0.743 0.722 0.701 0.681 0.661 0.642 0.650 0.625 0.601 0.577 0.555 0.585 0.557 0.530 0.505 0.481 0.527 0.497 0.469 0.442 0.417 0.415 0.388 0.362 0.429 0.397 0.368 0.340 0.315 0.388 0.356 0.326 0.299 0.275 0.350 0.319 0.290 0.263 0.239 0.287 0.257 0.229 0.205 0.183 0.237 0.208 0.182 0.160 0.140 0.215 0.187 0.163 0.141 0.123 0.195 0.168 0.145 0.125 0.108 0.162 0.135 0.137 0.112 0.116 0.093 0.099 0.078 0.084 0.065 16 17 18 19 20 0.853 0.728 0.844 0.714 0.836 0.700 0.828 0.686 0.820 0.673 0.623 0.605 0.587 0.570 0.554 0.534 0.513 0.494 0.475 0.456 0.458 0.436 0.416 0.396 0.377 0.394 0.371 0.350 0.331 0.312 0.339 0.317 0.296 0.277 0.258 0.292 0.270 0.250 0.232 0.215 0.252 0.231 0.212 0.194 0.178 0.218 0.163 0.198 0.146 0.180 0.130 0.164 0.116 0.149 0.104 0.123 0.108 0.095 0.083 0.073 0.107 0.093 0.081 0.070 0.061 0.093 0.080 0.069 0.060 0.051 0.071 0.054 0.060 0.045 0.051 0.038 0.043 0.031 0.037 0.026 21 22 23 24 25 0.811 0.803 0.795 0.788 0.780 0.660 0.647 0.634 0.622 0.610 0.538 0.522 0.507 0.492 0.478 0.439 0.422 0.406 0.390 0.375 0.359 0.294 0.342 0.278 0.326 0.262 0.310 0.247 0.295 0.233 0.242 0.226 0.211 0.197 0.184 0.199 0.184 0.170 0.158 0.146 0.164 0.150 0.138 0.126 0.116 0.135 0.093 0.123 0.083 0.112 0.074 0.102 0.066 0.092 0.059 0.064 0.056 0.049 0.043 0.038 0.053 0.046 0.040 0.035 0.030 0.044 0.038 0.033 0.028 0.024 0.031 0.022 0.026 0.018 0.022 0.015 0.019 0.013 0.016 0.010 26 27 28 29 30 0.772 0.764 0.757 0.749 0.742 0.598 0.586 0.574 0.563 0.552 0.464 0.450 0.437 0.424 0.412 0.361 0.347 0.333 0.321 0.308 0.281 0.268 0.255 0.243 0.231 0.220 0.207 0.196 0.185 0.174 0.172 0.161 0.150 0.141 0.131 0.135 0.125 0.116 0.107 0.099 0.106 0.098 0.090 0.082 0.075 0.084 0.053 0.076 0.047 0.069 0.042 0.063 0.037 0.057 0.033 0.033 0.029 0.026 0.022 0.020 0.026 0.023 0.020 0.017 0.015 0.021 0.018 0.016 0.014 0.012 0.014 0.009 0.011 0.007 0.010 0.006 0.008 0.005 0.007 0.004 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 50 0.608 0.372 0.228 0.141 0.087 0.054 0.034 0.021 0.013 0.009 0.003 0.001 0.001 0.001 Future Value of $1 Periods 1 2 3 4 5 1% 1.010 1.020 1.030 1.041 1.051 2% 1.020 1.040 1.061 1.082 1.104 3% 1.030 1.061 1.093 1.126 1.159 4% 1.040 1.082 1.125 1.170 1.217 5% 1.050 1.103 1.158 1.216 1.276 6% 1.060 1.124 1.191 1.262 1.338 7% 8% 1.070 | 1.080 1.145 1.166 1.225 1.260 1.311 1.360 1.403 1.469 9% 1.090 1.188 1.295 1.412 1.539 10% 1.100 1.210 1.331 1.464 1.611 12% 1.120 1.254 1.405 1.574 1.762 14% 1.140 1.300 1.482 1.689 1.925 15% 1.150 1.323 1.521 1.749 2.011 6 7 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 1.587 1.606 | 1.714 1.718 1.851 1.838 1.999 1.967 2.159 1.677 1.772 1.828 1.949 1.993 | 2.144 2.172 2.358 2.367 | 2.594 1.974 2.195 | 2.313 2.211 | 2.502 2.660 2.476 2.853 3.059 2.773 3.252 3.518 3.106 3.707 4.046 8 9 10 1 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 1.898 1.796 2.012 1.886 2.133 1.980 | 2.261 2.079 | 2.397 2.105 2.252 2.410 2.579 2.759 2.332 2.580 | 2.853 2.518 | 2.813 13.138 2.720 3.066 | 3.452 2.937 3.342 3.798 3.172 3.642 | 4.177 3.479 4.226 13.896 | 4.818 4.363 5.492 4.887 16.261 5.474 17.138 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 9.358 10.76 12.38 14.23 16.37 21 22 23 24 25 6.130 18.137 6.866 9.276 7.690 10.58 8.613 12.06 9.646 13.74 10.80 15.67 12.10 17.86 13.55 | 20.36 15.18 23.21 17.00 26.46 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 | 4.595 1.400 1.653 1.948 2.292 | 2.693 3.159 3.700 4.328 5.054 1.428 1.702 2.026 | 2.407 | 2.854 3.380 | 3.996 4.717 5.560 1.457 1.754 | 2.107 | 2.527 | 3.026 3.617 | 4.316 5.142 6.116 1.486 1.806 | 2.191 2.653 3.207 3.870 | 4.661 5.604 6.727 1.516 1.860 | 2.279 | 2.786 3.400 | 4.141 5.034 6.109 17.400 1.546 1.916 2.370 2.925 3.604 4.430 5.437 6.659 8.140 1.577 1.974 2.465 | 3.072 | 3.820 | 4.741 | 5.871 7.258 8.954 1.608 2.033 2.563 | 3.225 | 4.049 5.072 6.341 7.911 9.850 1.641 2.094 2.666 3.386 4.292 5.427] 6.848 8.623 10.83 1.673 | 2.157 2.772 3.556 4.549 5.807 7.396 9.399 11.92 1.707 ] 2.221 2.883 3.733 4.822 6.214 17.988 10.25 13.11 1.741 2.288 2.999 3.920 5.112 6.649 8.627 11.17 14.42 1.776 | 2.357 13.119 4.116 5.418 7.114 9.317 12.17 15.86 1.811 2.427 3.243 | 4.322 5.743 7.612 10.06 13.27 17.45 2.208 3.262 4.801 7.040 10.29 14.97 21.72 | 31.41 45.26 2.692 | 4.384 7.107 11.47 18.42 | 29.46 46.90 74.36 117.4 1.232 1.245 1.257 1.270 1.282 18.82 21.64 24.89 28.63 32.92 26 27 28 29 30 1.295 1.308 1.321 1.335 1.348 19.04 30.17 21.32 34.39 23.88 39.20 126.75 | 44.69 29.96 50.95 37.86 43.54 50.07 57.58 66.21 40 1.489 93.05 188.9 267.9 50 1.645 289.0 700.2 1,084 14% 15% 0.877 0.870 1.647 1.626 2.322 2.283 2.914 2.855 3.433 3.352 16% 0.862 1.605 2.246 2.798 3.274 18% 0.847 1.566 2.174 2.690 3.127 20% 0.833 1.528 2.106 2.589 2.991 3 4 7 8 7.325 3.889 4.288 4.639 4.946 5.216 3.784 4.160 4.487 4.772 5.019 3.685 4.039 4.344 4.607 4.833 3.498 3.812 4.078 4.303 4.494 3.326 3.605 3.837 4.031 4.192 5.453 5.660 5.842 6.002 6.142 5.234 5.421 5.583 5.724 5.847 5.029 5.197 5.342 5.468 5.575 4.656 4.793 4.910 5.008 5.092 4.327 4.439 4.533 4.611 4.675 Present Value of Ordinary Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.690 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.402 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.037 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.605 6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.111 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.564 7.652 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 4.968 9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.328 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.650 11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 5.938 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.194 13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.424 14 13.004 12.106 | 11.296 10.563 | 9.899 9.295 8.745 8.244 7.786 7.367 6.628 15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606 6.811 16 14.718 13.578 12.561 | 11.652 10.838 10.106 9.447 8.851 8.313 7.824 6.974 17 15.562 14.292 13.166 12.166 11.274 10.4779.763 9.122 8.544 8.022 7.120 18 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.250 19 17.226 15.678 14.32413.134 12.085 11.158 10.336 9.604 8.950 8.365 7.366 20 18.046 16.351 14.877 13.590 12.462 11.470 10.5949.818 9.129 8.514 7.469 21 18.857 17.011 15.415 14.029 12.821 11.764 10.836 10.017 9.292 8.649 7.562 22 19.660 17.658 15.937 14.451 13.163 12.042 11.061 10.2019.442 8.772 7.645 23 20.456 18.292 16.444 14.857 13.489 12.303 11.272 10.371 9.580 8.883 7.718 24 21.243 18.914 16.936 15.247 13.799 12.550 11.469 10.529 9.707 8.985 7.784 25 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.823 9.077 7.843 26 22.795 20.121 17.877 15.983 14.375 13.003 11.826 10.8109.929 9.161 7.896 27 23.560 20.707 18.327 16.330 14.643 13.211 11.987 10.935 10.027 9.237 7.943 28 24.316 21.281 18.764 16.663 14.898 13.406 12.13711.051 10.116 9.307 7.984 29 25.066 21.844 19.188 16.984 15.141 13.591 | 12.278 11.158 10.1989.370 8.022 30 25.808 22.396 19.600 17.292 15.372 13.765 12.409 11.258 10.274 9.427 8.055 40 32.835 27.355 23.115 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.244 50 39.196 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962 9.915 8.304 6.265 6.373 6.467 6.550 6.623 5.669 5.749 5.818 5.877 5.929 5.162 5.222 5.273 5.316 5.353 4.730 4.775 4.812 4.844 4.870 5.954 6.047 6.128 6.198 6.259 6.312 6.359 6.399 6.434 6.464 6.687 6.743 6.792 6.835 6.873 5.973 6.011 6.044 6.073 6.097 5.384 5.410 5.432 5.451 5.467 4.891 4.909 4.925 4.937 4.948 6.906 6.935 6.961 6.983 7.003 6.491 6.514 6.534 6.551 6.566 6.118 6.136 6.152 6.166 6.177 5.480 5.492 5.502 5.510 5.517 4.956 4.964 4.970 4.975 4.979 7.105 6.642 6.233 5.548 4.997 7.133 6.661 6.246 5.554 4.999 Periods 1 2 3 4 5 1% 1.000 2.010 3.030 4.060 5.101 15% 1.000 2.150 3.473 4.993 6.742 6 7 8 6.152 7.214 8.286 9.369 10.46 8.754 11.07 13.73 16.79 20.30 9 10 1 12 13 14 15 11.57 12.68 13.81 14.95 16.10 24.35 29.00 34.35 40.50 47.58 Future Value of Ordinary Annuity of $1 2% 13% 4% 5% 6% 7% 18% 9% 10% 12% 14% 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.020 | 2.030 2.040 2.050 2.060 2.070 2.080 2.090 | 2.100 2.120 | 2.140 3.060 | 3.091 13.122 13.153 3.184 3.215 3.246 3.278 3.310 3.374 3.440 4.122 14.184 4.246 | 4.310 4.375 4.440 | 4.506 4.573 | 4.641 4.779 4.921 5.204 5.309 15.416 5.526 15.637 5.751 5.867 5.985 6.105 6.353 6.610 6.308 6.468 6.633 6.802 6.97517.153 7.336 7.523 17.716 8.115 8.536 7.434 7.662 7.898 18.142 | 8.394 8.654 8.923 9.200 9.487 10.09 10.73 8.583 8.892 9.214 9.549 9.897 | 10.260 | 10.64 11.03 11.44 12.30 13.23 9.755 10.16 10.58 11.03 11.49 11.98 12.49 13.02 13.58 14.78 16.09 10.95 11.46 12.01 12.58 13.18 13.82 14.49 15.19 15.94 17.55 19.34 12.17 12.81 13.49 14.21 14.97 15.78 16.65 17.56 18.53 20.65 23.04 13.41 14.19 15.03 15.92 16.87 17.89 18.98 20.14 21.38 24.13 27.27 14.68 15.62 16.63 17.71 18.88 20.14 21.50 22.95 24.52 28.03 32.09 15.97 17.09 18.29 19.60 | 21.02 22.55 24.21 26.02 | 27.98 32.39 37.58 17.29 18.60 20.02 | 21.58 23.28 25.13 27.15 29.36 | 31.77 37.28 43.84 18.64 | 20.16 | 21.82 | 23.66 | 25.67 | 27.89 | 30.32 | 33.00 35.95 42.75 50.98 20.01 21.76 23.70] 25.84 28.21 30.84 33.75 36.97 | 40.54 48.88 59.12 21.41 23.41 125.65 | 28.13 30.91 34.00 | 37.45 41.30 | 45.60 55.75 68.39 22.84 25.12 27.67 30.54 33.76 37.38 41.45 46.02 51.16 63.44 78.97 24.30 | 26.87] 29.78 33.07 36.79 | 41.00 45.76 51.16 57.28 72.05 191.02 25.78 | 28.68 31.97 | 35.72 39.99 44.87 50.42 56.76 64.00 | 81.70 104.8 27.30 | 30.54 34.25 38.51 43.39 49.01 55.46 62.87 71.40 92.50 120.4 28.85 32.45 36.62 | 41.43 47.00 53.44 60.89 69.53 79.54 104.6 138.3 30.42 34.43 39.08 44.50 50.82 58.18 66.76 76.79 88.50 118.2 158.7 32.03 36.46 41.65 47.73 54.86 63.25 73.11 84.70 98.35 133.3 181.9 33.67 38.55 44.31 51.11 59.16 68.68 79.95 93.32 109.2 150.3 208.3 35.34 | 40.71 47.08 54.67 63.71 74.48 87.35 102.7 121.1 169.41 238.5 37.05 42.93 49.97 58.40 68.53 80.70 95.34 113.0 134.2 190.7 272.9 38.79 45.22 52.97 62.32 73.64 87.35 104.0 124.1 148.6 | 214.6 312.1 40.57 | 47.58 56.08 | 66.44 | 79.06 94.46 113.3 136.3 164.5 241.3 356.8 60.40 75.40 95.03 120.8 154.8 199.6 259.1 337.9 442.6 767.1 1,342 84.58 112.8 152.7 209.3 290.3 406.5 573.8 815.1 1.164 | 2,400 | 4,995 16 17 18 19 20 17.26 18.43 19.61 20.81 22.02 55.72 65.08 75.84 88.21 102.4 21 22 23 24 25 23.24 24.47 25.72 26.97 28.24 118.8 137.6 159.3 184.2 212.8 26 27 28 129 30 29.53 30.82 32.13 33.45 34.78 245.7 283.6 327.1 377.2 434.7 40 48.89 1,779 50 64.46 7,218