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 $225,000 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 15 equal annual installments (from age 25 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 old.

Requirement 1. How much money must you accumulate by retirement to make your plan work? (Hint: to find the present value of $225,000 withdrawals) Round the answer to the nearest dollar.

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?

These numbers are different because:

(all of these tables keep going, if you need me to post more of one of them please let me know)

Over the course of your retirement you will be withdrawing However, by age 40 you only need to have invested O A. 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 B. You need to have far less accumulated than what you will withdraw because you only withdraw a portion of the investment every yearthe balance remains invested where it continues to earn 10% interest. O C. You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every yearthe balance remains invested where it continues to earn 10% interest. OD. None of the above Present Value of $1 3% Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 2% 4% 5% 0.990 0.980 0.971 0.962 0.952 0.980 0.961 0.943 0.925 0.907 0.971 0.942 0.915 0.889 0.864 0.961 0.924 0.888 0.855 0.823 0.951 0.906 0.863 0.822 0.784 6% 0.943 0.890 0.840 0.792 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% 10% 0.917 0.909 0.842 0.826 0.772 0.751 0.708 0.683 0.650 0.621 12% 0.893 0.797 0.712 0.636 0.567 14% 15% 16% 0.877 0.870 0.862 0.769 0.756 0.743 0.675 0.658 0.641 0.592 0.572 0.552 0.519 0.497 0.476 18% 20% 0.847 0.833 0.7180.694 0.609 0.579 0.516 0.482 0.437 0.402 Period 6 Period 7 Period 8 Period 9 Period 10 0.942 0.888 0.837 0.790 0.746 0.933 0.871 0.813 0.760 0.711 0.923 0.853 0.789 0.731 0.677 0.914 0.837 0.766 0.703 0.645 0.905 0.820 0.744 0.676 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 0.564 0.507 0.547 0.513 0.452 0.502 0.467 0.404 0.460 0.424 0.361 0.422 0.386 0.322 0.456 0.432 0.410 0.400 0.376 0.354 0.351 0.327 0.305 0.308 0.284 0.263 0.270 0.247 0.227 0.370 0.335 0.3140.279 0.266 0.233 0.225 0.194 0.191 0.162 Period 11 Period 12 Period 13 Period 14 Period 15 0.896 0.804 0.722 0.650 0.585 0.887 0.788 0.701 0.625 0.557 0.879 0.773 0.681 0.601 0.530 0.870 0.7580.661 0.577 0.505 0.861 0.743 0.642 0.555 0.481 0.527 0.497 0.469 0.442 0.417 0.475 0.444 0.415 0.388 0.362 0.429 0.397 0.368 0.340 0.315 0.388 0.350 0.356 0.319 0.326 0.290 0.299 0.263 0.275 0.239 0.287 0.257 0.229 0.205 0.183 0.237 0.215 0.195 0.208 0.187 0.168 0.182 0.163 0.145 0.1600.141 0.125 0.140 0.123 0.108 0.162 0.135 0.137 0.112 0.116 0.093 0.099 0.078 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 Period 18 0.836 0.7000.587 0.494 0.416 Period 19 0.828 0.686 0.570 0.475 0.396 Period 20 0.820 0.673 0.554 0.456 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 0.218 0.163 0.231 0.1980.146 0.212 0.180 0.130 0.194 0.164 0.116 0.178 0.149 0.104 0.123 0.107 0.093 0.108 0.093 0.080 0.095 0.081 0.069 0.083 0.070 0.060 0.073 0.061 0.051 0.071 0.054 0.060 0.045 0.051 0.038 0.043 0.031 0.037 0.026 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 Period 24 10.788 0.622 0.492 0.390 0.310 Period 25 0.780 0.610 0.478 0.375 0.295 0.294 0.278 0.262 0.247 0.233 0.242 0.226 0.211 0.197 0.184 0.199 0.184 0.170 0.158 0.146 0.164 0.135 0.093 0.150 0.123 0.083 0.138 0.112 0.074 0.126 0.102 0.066 0.116 0.092 0.059 0.064 0.053 0.044 0.056 0.046 0.038 0.049 0.040 0.033 0.043 0.035 0.028 0.038 0.030 0.024 0.031 0.022 0.026 0.018 0.022 0.015 0.019 0.013 0.016 0.010 Future Value of $1 Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 1.010 1.020 1.030 1.041 1.051 2% 1.020 1.040 1.061 1.082 1.104 3% 4% 5% 6% 7% 8% 9% 10% 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.061 1.0821.103 1.1241.145 1.166 1.1881.210 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.159 | 1.217 1.276 | 1.338 1.403 1.469 1.539 1.611 12% 14% 15% 1.120 1.140 1.150 1.254 1.300 1.323 1.405 1.482 1.521 1.574 1.689 1.749 1.762 1.925 2.011 Period 6 Period 7 Period 8 Period 9 Period 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 1.340 1.419 1.501 1.587 1.677 1.772 1.316 1.407 1.504 1.606 1.714 1.828 1.949 1.369 1.477 | 1.594 1.718 1.851 | 1.993 2.144 1.423 1.551 1.689 1.838 1.999 2.172 2.358 1.480 1.629 1.791 1.967 2.159 2.367 2.594 1.974 2.1952.313 2.211 2.502 2.660 2.476 2.853 3.059 2.773 3.252 3.518 3.106 3.707 4.046 Period 11 Period 12 Period 13 Period 14 Period 15 1.116 1.127 1.138 1.149 1.161 1.243 1.268 1.294 1.319 1.346 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 1.469 1.665 1.886 2.133 | 2.410 2.720 3.066 3.452 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.798 1.558 1.801 2.079 2.3972.759 3.172 3.642 4.177 3.479 4.226 4.652 3.896 4.818 5.350 4.363 5.492 6.153 4.887 6.261 7.076 5.474 7.1388.137 Period 16 Period 17 Period 18 Period 19 Period 20 1.173 1.184 1.196 1.208 1.220 1.373 1.400 1.428 1.457 1.486 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 1.653 1.948 2.292 2.6933.159 3.700 4.3285.054 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 1.806 2.191 | 2.653 3.207 3.870 4.661 5.6046.727 6.130 6.866 7.690 8.613 9.646 8.1379.358 9.276 10.76 10.58 12.38 12.06 14.23 13.74 16.37 Period 21 Period 22 Period 23 Period 24 Period 25 1.232 1.245 1.257 1.270 1.282 1.516 1.860 2.279 2.786 3.400 4.141 5.034 6.109 7.400 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 6.3417.911 9.850 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.83 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 Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 2% 0.990 0.980 1.970 1.942 2.941 2.884 3.902 3.808 4.853 4.713 3% 0.971 1.913 2.829 3.717 4.580 Present Value of Ordinary Annuity of $1 4% 5% 6% 7% 8% 9% 10% 0.962 0.952 0.943 0.935 0.926 0.917 0.909 1.886 1.859 1.833 1.808 1.783 1.759 1.736 2.775 2.723 2.673 2.624 2.577 2.531 2.487 3.630 3.546 3.465 3.387 3.312 3.240 3.170 4.452 4.329 4.212 4.100 3.993 3.890 3.791 12% 14% 0.893 0.877 1.690 1.647 2.402 2.322 3.037 2.914 3.605 3.433 15% 0.870 1.626 2.283 2.855 3.352 16% 0.862 1.605 2.246 2.798 3.274 18% 20% 0.847 0.833 1.566 1.528 2.174 2.106 2.690 2.589 3.127 2.991 Period 6 Period 7 Period 8 Period 9 Period 10 5.795 5.601 5.417 6.728 6.472 6.230 7.652 7.325 7.020 8.5668.162 7.786 9.471 8.983 8.530 5.242 5.076 4.917 4.767 6.002 5.786 5.582 5.389 6.733 6.463 6.210 5.971 7.435 7.108 6.802 6.515 8.111 7.722 7.360 7.024 4.623 4.4864.355 4.111 3.889 5.206 5.033 4.868 4.564 | 4.288 5.747 5.535 5.335 4.968 4.639 6.247 5.995 5.759 5.328 4.946 6.710 6.418 6.145 5.6505.216 3.784 4.160 4.487 4.772 5.019 3.685 3.498 3.326 4.039 3.812 3.605 4.344 4.078 3.837 4.607 4.303 4.031 4.833 4.494 4.192 Period 11 Period 12 Period 13 Period 14 Period 15 10.368 9.787 9.253 8.760 8.306 7.887 7.499 11.255 | 10.575 9.954 9.385 8.863 8.384 7.943 12.134 11.348 10.635 9.986 9.394 8.853 8.358 13.004 | 12.106 | 11.296 | 10.563 9.899 9.295 8.745 13.865 12.849 11.93811.118 10.380 9.712 9.108 7.139 6.805 6.495 7.536 | 7.161 6.814 7.904 | 7.487 7.103 8.244 | 7.786 7.367 8.559 8.061 7.606 5.938 5.453 6.194 5.660 6.424 5.842 6.628 6.002 6.811 6.142 5.234 5.421 5.583 5.724 5.847 5.029 5.197 5.342 5.468 5.575 4.656 4.327 4.793 4.439 4.910 4.533 5.008 4.611 5.092 4.675 Period 16 Period 17 Period 18 Period 19 Period 20 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.313 7.824 6.974 15.562 14.292 13.166 12.166 11.274 10.477) 9.763 9.122 8.544 8.022 7.120 16.398 14.992 | 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.250 17.226 15.678 14.32413.134 12.085 11.158 10.336 9.604 8.950 8.365 7.366 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.469 6.265 6.373 6.467 6.550 6.623 5.954 6.047 6.128 6.198 6.259 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 Period 21 Period 22 Period 23 Period 24 Period 25 18.857 | 17.01115.415 14.029 12.821 11.764 10.836 10.017 9.292 8.649 7.562 6.687 19.660 17.658 15.937 14.451 13.163 12.042 11.061 10.2019.442 8.772 7.645 6.743 20.456 18.292 16.444 14.857 13.489 12.303 11.272 10.371 9.580 8.883 7.718 6.792 8.985 7.784 21.243 18.914 16.936 15.247 13.799 12.550 11.469 10.529 9.707 6.835 7.843 6.873 22.023 19.523 | 17.413 15.622 14.094 12.783 11.654 10.675 9.8239.077 6.312 6.359 6.399 6.434 6.464 5.973 6.011 6.044 6.073 6.097 5.384 4.891 5.410 4.909 5.432 4.925 5.451 4.937 5.467 4.948 Damiad 24 22 705121 47 077 15002 41 276 112nnel 11 O 100101000 0101 7 On Ona 101 110 con 100 Future Value of Ordinary Annuity of $1 Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 2% 3% 4% 5% 1.000 1.000 1.000 1.000 1.000 2.010 2.020 2.030 2.040 2.050 3.030 3.060 3.091 3.122 3.153 4.060 4.122 4.184 4.246 4.310 5.101 5.204 5.309 5.416 5.526 6% 1.000 2.060 3.184 4.375 5.637 7% 8% 9% 10% 12% 14% 15% 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.070 2.080 2.090 2.100 2.120 2.140 2.150 3.215 3.246 3.278 3.310 3.374 | 3.440 3.473 4.440 4.506 4.573 4.641 4.779 4.921 4.993 5.751 5.867 5.985 6.105 6.353 6.610 6.742 Period 6 Period 7 Period 8 Period 9 Period 10 6.152 6.308 6.468 6.633 6.802 7.214 7.434 7.6627.898 8.142 8.286 8.583 8.8929.214 9.549 9.369 9.755 10.16 10.58 | 11.03 10.46 10.95 | 11.46 12.01 12.58 6.975 8.394 9.897 11.49 13.18 7.153 7.336 7.523 7.716 8.654 8.923 9.200 | 9.487 10.260 10.64 11.03 11.44 11.98 12.49 | 13.02 13.58 13.82 14.49 15.1915.94 8.115 8.536 8.754 10.09 10.73 11.07 12.30 13.23 13.73 14.78 16.09 16.79 17.55 19.34 20.30 Period 11 Period 12 Period 13 Period 14 Period 15 11.57 12.17 12.81 13.49 14.21 12.68 13.41 14.19 15.03 15.92 13.81 14.68 15.62 16.63 17.71 14.95 15.97 17.09 | 18.29 19.60 16.10 17.29 18.60 20.02 21.58 14.97 16.87 18.88 21.02 23.28 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 Period 16 Period 17 Period 18 Period 19 Period 20 17.26 18.64 20.16 21.8223.66 18.43 20.01 21.76 23.70 25.84 19.61 21.41 23.41 25.65 28.13 20.81 22.84 25.12 27.67 30.54 22.02 24.30 26.87 29.78 33.07 25.67 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 Period 21 Period 22 Period 23 Period 24 Period 25 23.24 25.78 28.68 31.97 35.72 24.47 27.30 30.54 34.25 38.51 25.72 28.85 32.45 36.62 41.43 26.97 30.42 34.43 39.08 44.50 28.24 32.03 36.46 41.65 47.73 39.99 43.39 47.00 50.82 54.86 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 79.54 104.6 138.3 159.3 58.18 66.76 76.79 | 88.50 118.2 158.7 184.2 63.25 73.11 84.70 98.35 133.3 | 181.9 212.8 Dorind 20 20.52 2207 2055 11 21 51 11 50 10 9898 70 05 0222 1002 1503 208 2 2157