K 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 $160,000 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 10 equal annual installments (from age 30 to age 40) into a fairly risky investment fund that you expect will earn 10% per year. You will leave the money in this fund until it is completely depleted when you are 70 years p old. Read the requirements. View the Present Value of $1 table. View the Future Value of $1 table. View the Present Value of Ordinary Annuity of $1 table. View the Future Value of Ordinary Annuity of $1 table. Requirement 1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the $160,000 withdrawals.) (Round your final answer to the nearest whole dollar.) Money to be accumulated by the time of retirement = $ 1,508,320 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 Present Value of $1 e 0.415 0 0 0.388 0.340 0.362 0.315 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 0.191 0.162| 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 12 0.887 0.788 0.701 0.625 0,557 0.497 0.444 0.397 0.356 0.319 0.257 0.208 0.187 0.168 0.137 0.112 Period 13 0.879 0.773 0.681 0.601 0.530 0.469 0.368 0.326 0.290 0.229 0.182 0.163 0.145 0.116 0.093 Period 14 0.870 0.758 0.661 0.577 0.505 0.442 0.299 0.263 0.205 0.160 0.141 0.125 0.099 0.078 Period 15 0.861 0.743 0.642 0.555 0.481 0.417 0.275 0.239 0.183 0.140 0.123 0.108 0.084 0.065 Period 16 0.853 0.728 0.623 0.534 0.458 Period 17 0.844 0.714 0.605 0.513 0.436 0.371 Period 18 0.836 0.700 0.587 0.494 0.416 0.350 Period 19 0.828 0.686 0.570 0.475 0.396 0.331 Period 20 0.820 0.673 0.554 0.456 0.377 0.394 0.339 0.292 0.317 0.296 0.277 0.312 0.258 0.215 0.252 0.218 0.163 0.123 0.107 0.093 0.071 0.054 0.270 0.231 0.198 0.146 0.108 0.093 0.080 0.060 0.045 0.250 0.212 0.180 0.130 0.095 0.081 0.069 0.051 0.038 0.232 0.194 0.164 0.116 0.083 0.070 0.060 0.043 0.031 0.178 0.149 0.104 0.073 0.061 0.051 0.037 0.026 D Period 21 0.811 0.660 0.538 0.439 0.359 Period 22 0.803 0.647 0.522 0.422 0.342 Period 23 0.795 0.634 0.507 0.406 0.326 0.262 Period 24 0.788 0.622 0.492 0.390 0.310 0.247 Period 25 0.780 0.610 0.478 0.375 0.295 0.233 0.294 0.242 0.199 0.278 0.226 0.211 0.197 0.184 0.164 0.135 0.093 0.064 0.184 0.150 0.123 0.083 0.056 0.170 0.138 0.112 0.074 0.049 0.158 0.126 0.102 0.066 0.043 0.146 0.116 0.092 0.059 0.053 0.044 0.031 0.022 0.046 0.038 0.026 0.018 0.040 0.033 0.022 0.015 0.035 0.028 0.019 0.013 0.038 0.030 0.024 0.016 0.010 Period 26 0.772 0.598 0.464 0.361 0.281 0.220 Period 27 0.764 0.586 0.450 0.347 0.268 0.207 Period 28 0.757 0.574 0.437 0.333 0.255 0.196 Period 29 0.749 0.563 0.424 0.321 0.243 0.185 0.172 0.135 0.161 0.125 0.150 0.116 0.141 0.107 Period 30 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 Period 40 0.672 0.453 0.307 0.208 0.142 0.097 0.067 0.046 0.106 0.084 0.053 0.033 0.026 0.021 0.014 0.009 0.098 0.076 0.047 0.029 0.023 0.018 0.011 0.007 0.090 0.069 0.042 0.026 0.020 0.016 0.010 0.006 0.082 0.063 0.037 0.022 0.017 0.014 0.008 0.005 0.075 0.057 0.033 0.020 0.015 0.012 0.007 0.004 0.032 0.022 0.011 0.005 0.004 0.003 0.001 0.001 ve be able u plan years resent Future Value of $1 Period 11 Period 12 Period 13 Period 14 Period 15 1.161 Period 16. 1.173 Period 17 Period 18 Period 19 Period 20 Period 21 1.184 1.196 1.208 1.220 1.400 Period 22 Period 23 Period 24 Period 25 2.427 3.243 4.322 5.743 7.612 3.262 4.801 7.040 10.29 14.97 Period 10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.798 1.346 1.558 1.801 2.079 2.397 1.373 1.605 1.873 2.3 2.540 6.130 8.137 9.358 1.653 1.948 2.292 2.693 3.159 6.866 9.276 10.76 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 7.690 10.58 12.38 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 1.232 1.516 1.860 2.279 2.786 3.400 4.141 5.034 6.109 7.400 1.245 1.546 1.916 2.370 2.925 3.604 4.430 5.437 6.659 8.140 1.257 1.577 1.974 2.465 3.072 3.820 4.741 5.871 7.258 8.954 1.270 1.608 2.033 2.563 3.225 4.049 5.072 6.341 7.911 9.850 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.83 Period 26 1.295 1.673 2.157 2.772 3.556 4.549 5.807 7.396 9.399 11.92 19.04 30.17 37.86 Period 27 1.308 1.707 2.221 2.883 3.733 4.822 6.214 7.988 10.25 13.11 21.32 34.39 43.54 Period 28 1.321 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 29 1.335 1.776 2.357 3.119 4.116 5.418 7.114 9.317 12.17 15.86 26.75 44.69 57.58 Period 30 1.348 1.811 29.96 50.95 66.21 Period 40 1.489 2.208 3.106 3.707 4.046 3.479 4.226 4.652 3.896 4.818 5.350 4.363 5.492 6.153 2.759 3.172 3.642 4.177 4.887 6.261 7.076 5.474 7.138 8.137 2.952 3.426 3.970 4.595 3.700 4.328 5.054 8.613 12.06 14.23 9.646 13.74 16.37 10.80 15.67 18.82 12.10 17.86 21.64 13.55 20.36 24.89 15.18 23.21 28.63 17.00 26.46 32.92 10.06 13.27 17.45 21.72 31.41 45.26 93.05 188.9 267.9 - X Present Value of Ordinary Annuity of $1 8.111 Period 10 9.471 8.983 8.530 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 11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 5.938 5.453 5.234 5.029 4.656 4.327 Period 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.194 5.660 5.421 5.197 4.793 4.439 Period 13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.424 5.842 5.583 5.342 4.910 4.533 Period 14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.628 6.002 5.724 5.468 5.008 4.6111 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 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 5.669 5.162 4.730 Period 17 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.022 7.120 6.373 6.047 5.749 5.222 4.775 Period 18 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.250 6.467 6.128 5.818 5.273 4.812 Period 19 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.366 6.550 6.198 5.877 5.316 4.844 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 21 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 22 19.660 17.658 15.937 14.451 13.163 12.042 11.061 10.201 9.442 8.772 .645 6.743 6.359 6.011 5.410 4.909 Period 23 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 Period 24 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 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 6.097 5.467 4.948 Period 26 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 4.956 Period 27 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 4.964 Period 28 24.316 21.281 18.764 16.663 14.898 13.406 12.137 11.051 10.116 9.307 7.984 6.961 6.534 6.152 5.502 4.970 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 6.551 6.166 5.510 4.975 Period 30 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 40 32.835 27.355 23.115 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.244 7.105 6.642 6.233 5.548 4.997 6.044 5.432 4.925 6.073 5.451 4.937 X Future Value of Ordinary Annuity of $1 X I sav Period 12 12.68 13.41 14.19 15.03 15.92 16.87 Period 13 13.81 14.68 15.62 16.63 17.71 Period 14 14.95 15.97 17.09 18.29 19.60 Period 15 16.10 17.29 18.60 20.02 21.58 18.88 21.02 23.28 Period 10 10.46 10.95 11.46 12.01 12.58 13.18 13.82 14.49 15.19 15.94 17.55 19.34 20.30 Period 11 11.57 12.17 12.81 13.49 14.21 14.97 15.78 16.65 17.56 18.53 20.65 23.04 24.35 17.89 18.98 20.14 21.38 24.13 27.27 29.00 20.14 21.50 22.95 24.52 28.03 32.09 34.35 22.55 24.21 26.02 27.98 32.39 37.58 40.50 25.13 27.15 29.36 31.77 37.28 43.84 47.58 e 7 d th Ou $ Period 16 17.26 18.64 20.16 21.82 23.66 25.67 Period 17 18.43 20.01 21.76 23.70 25.84 Period 18 19.61 21.41 23.41 25.65 28.13 Period 19 20.81 22.84 25.12 27.67 30.54 Period 20 22.02 24.30 26.87 29.78 33.07 28.21 30.91 33.76 36.79 27.89 30.32 33.00 35.95 42.75 50.98 55.72 30.84 33.75 36.97 40.54 48.88 59.12 65.08 34.00 37.45 41.30 45.60 55.75 68.39 75.84 37.38 41.45 46.02 51.16 63.44 78.97 88.21 41.00 45.76 51.16 57.28 72.05 91.02 102.4 $1 Period 21 Period 22 23.24 25.78 28.68 31.97 35.72 24.47 27.30 30.54 34.25 38.51 39.99 43.39 Period 23 25.72 28.85 32.45 36.62 41.43 47.00 Period 24 Period 25 26.97 30.42 34.43 39.08 44.50 28.24 32.03 36.46 41.65 47.73 50.82 54.86 Period 26 29.53 33.67 38.55 44.31 51.11 59.16 Period 27 30.82 35.34 40.71 47.08 54.67 Period 28 32.13 37.05 42.93 49.97 58.40 Period 29 33.45 38.79 45.22 52.97 62.32 63.71 68.53 Period 30 34.78 40.57 47.58 56.08 66.44 73.64 79.06 Period 40 48.89 60.40 75.40 95.03 120.8 44.87 50.42 56.76 64.00 81.70 104.8 118.8 49.01 55.46 62.87 71.40 92.50 120.4 137.6 53.44 60.89 69.53 79.54 58.18 66.76 76.79 88.50 63.25 73.11 84.70 98.35 68.68 79.95 93.32 74.48 87.35 102.7 121.1 80.70 95.34 113.0 134.2 87.35 104.0 124.1 148.6 214.6 312.1 377.2 94.46 113.3 136.3 164.5 241.3 356.8 434.7 154.8 199.6 259.1 337.9 442.6 767.1 1,342 1,779 inc 104.6 138.3 159.3 118.2 158.7 184.2 133.3 181.9 212.8 109.2 150.3 208.3 245.7 nt 169.4 238.5 283.6 190.7 272.9 327.1