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 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 $225,000 withdrawals.) (Round your final answer to the nearest whole dollar.) To make the plan work, you must accumulate $ 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: A. 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 14% interest. B. 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 14% interest. 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. D. None of the above Present Value of $1 Periods 1 2 3 4 5 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% 0.952 0.907 0.864 0.823 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% 0.917 0.842 0.772 0.708 0.650 10% 0.909 0.826 0.751 0.683 0.621 12% 0.893 0.797 0.712 0.636 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 18% 0.847 0.718 0.609 0.516 0.437 20% 0.833 0.694 0.579 0.482 0.402 0.942 0.933 0.923 0.914 0.905 0.888 0.871 0.853 0.837 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 0.370 0.314 0.266 0.225 0.191 0.335 0.279 0.233 0.194 0.162 9 10 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 0.475 0.444 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 0.137 0.116 0.099 0.084 0.135 0.112 0.093 0.078 0.065 16 17 18 19 20 0.853 0.844 0.836 0.828 0.820 0.728 0.714 0.700 0.686 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 0.198 0.180 0.164 0.149 0.163 0.146 0.130 0.116 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 0.060 0.051 0.043 0.037 0.054 0.045 0.038 0.031 0.026 21 22 23 0.811 0.803 0.795 0.660 0.647 0.634 0.538 0.522 0.507 0.439 0.422 0.406 0.359 0.342 0.326 0.294 0.278 0.262 0.242 0.226 0.211 0.199 0.184 0.170 0.164 0.150 0.138 0.135 0.123 0.112 0.093 0.083 0.074 0.064 0.056 0.049 0.053 0.046 0.040 0.044 0.038 0.033 0.031 0.026 0.022 0.022 0.018 0.015 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% 1.070 1.145 1.225 1.311 1.403 8% 1.080 1.166 1.260 1.360 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 8 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 1.974 2.211 2.476 2.773 3.106 2.195 2.502 2.853 3.252 3.707 2.313 2.660 3.059 3.518 4.046 0 10 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 3.798 4.177 3.479 3.896 4.363 4.887 5.474 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 6.130 6.866 7.690 88.613 9.646 8.137 9.276 10.58 12.06 13.74 9.358 10.76 12.38 14.23 16.37 21 22 23 1.232 1.245 1.257 1.516 1.546 1.577 1.860 1.916 1.974 2.279 2.370 2.465 2.786 2.925 3.072 3.400 3.604 3.820 4.141 4.430 4.741 5.034 5.437 5.871 6.109 6.659 7.258 7.400 88.140 8.954 10.80 12.10 13.55 15.67 17.86 20.36 18.82 21.64 24.89 Present Value of Ordinary Annuity of $1 Periods 2 3 4 5 1% 0.990 1.970 2.941 3.902 4.853 2% 0.980 1.942 2.884 3.808 4.713 3% 0.971 1.913 2.829 3.717 4.580 4% 0.962 1.886 2.775 3.630 4.452 5% 0.952 1.859 2.723 3.546 4.329 6% 0.943 1.833 2.673 3.465 4.212 7% 0.935 1.808 2.624 3.387 4.100 8% 0.926 1.783 2.577 3.312 3.993 9% 0.917 1.759 2.531 3.240 3.890 10% 0.909 1.736 2.487 3.170 3.791 12% 0.893 1.690 2.402 3.037 3.605 14% 0.877 1.647 2.322 2.914 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% 0.847 1.566 2.174 2.690 3.127 20% 0.833 1.528 2.106 2.589 2.991 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 4.111 4.564 4.968 5.328 5.650 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 11 12 13 14 15 10.368 9.787 9.253 11.255 10.575 9.954 12.134 11.348 10.635 13.004 | 12.106 11.296 13.865 12.849 11.938 8.760 9.385 9.986 10.563 11.118 8.306 8.863 9.394 9.899 10.380 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 5.938 6.194 6.424 6.628 6.811 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 16 17 18 19 20 14.718 13.578 12.561 | 11.652 10.838 10.106 9.447 15.562 14.292 13.166 12.166 | 11.274 10.477 9.763 16.398 14.992 13.754 12.659 11.690 10.828 10.059 17.226 15.678 14.324 13.134 12.085 11.158 10.336 18.046 16.351 14.877 13.590 12.462 11.470 10.594 8.851 9.122 9.372 9.604 9.818 8.313 8.544 8.756 8.950 9.129 7.824 8.022 8.201 8.365 8.514 6.974 7.120 7.250 7.366 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 21 22 23 18.857 17.011 15.415 14.029 12.821 11.764 10.836 10.017 19.660 17.658 15.937 14.451 13.163 12.042 11.061 10.201 20.456 18.292 | 16.444 14.857 | 13.489 12.303 11.272 | 10.371 9.292 9.442 9.580 8.649 8.772 8.883 7.562 7.645 7.718 6.687 6.743 6.792 6.312 6.359 6.399 5.973 6.011 6.044 5.384 5.410 5.432 4.891 4.909 4.925 Future Value of Ordinary Annuity of $1 Periods -- 2 3 4 5 1% 1.000 2010 3.030 4.060 5.101 2% 1.000 2.020 3.060 4.122 5.204 3% 1.000 2.030 3.091 4.184 5.309 4% 1.000 2.040 3.122 4.246 5.416 5% 1.000 2.050 3.153 4.310 5.526 6% 1.000 2.060 3.184 4.375 5.637 7% 1.000 2.070 3.215 4.440 5.751 8% 1.000 2.080 3.246 4.506 5.867 9% 1.000 2.090 3.278 4.573 5.985 10% 1.000 2.100 3.310 4.641 6.105 12% 1.000 2.120 3.374 4.779 6.353 14% 1.000 2.140 3.440 4.921 6.610 15% 1.000 2.150 3.473 4.993 6.742 6 7 8 9 10 6.152 7.214 88.286 9.369 10.46 6.308 7.434 8.583 9.755 10.95 6.468 7.662 8.892 10.16 11.46 6.633 7.898 9.214 10.58 12.01 6.802 8.142 9.549 11.03 12.58 6.975 8.394 9.897 11.49 13.18 7.153 8.654 10.260 11.98 13.82 7.336 8.923 10.64 12.49 14.49 7.523 9.200 11.03 13.02 15.19 7.716 9.487 11.44 13.58 15.94 88.115 10.09 12.30 14.78 17.55 8.536 10.73 13.23 16.09 19.34 8.754 11.07 13.73 16.79 20.30 11 12 13 14 15 11.57 12.68 13.81 14.95 16.10 12.17 13.41 14.68 15.97 17.29 12.81 14.19 15.62 17.09 18.60 13.49 15.03 16.63 18.29 20.02 14.21 15.92 17.71 19.60 21.58 14.97 16.87 18.88 21.02 23.28 15.78 17.89 20.14 22.55 25.13 16.65 18.98 21.50 24.21 27.15 17.56 20.14 22.95 26.02 29.36 18.53 21.38 24.52 27.98 31.77 20.65 24.13 28.03 32.39 37.28 23.04 27.27 32.09 37.58 43.84 24.35 29.00 34.35 40.50 47.58 16 17 18 19 20 17.26 18.43 19.61 20.81 22.02 18.64 20.01 21.41 22.84 24.30 20.16 21.76 23.41 25.12 26.87 21.82 23.70 25.65 27.67 29.78 23.66 25.84 28.13 30.54 33.07 25.67 28.21 30.91 33.76 36.79 27.89 30.84 34.00 37.38 41.00 30.32 33.75 37.45 41.45 45.76 33.00 36.97 41.30 46.02 51.16 35.95 40.54 45.60 51.16 57.28 42.75 48.88 55.75 63.44 72.05 50.98 59.12 68.39 78.97 91.02 55.72 65.08 75.84 88.21 102.4 21 22 23 23.24 24.47 25.72 25.78 27.30 28.85 28.68 30.54 32.45 31.97 34.25 36.62 35.72 38.51 41.43 39.99 43.39 47.00 44.87 49.01 53.44 50.42 55.46 60.89 56.76 62.87 69.53 64.00 71.40 79.54 81.70 92.50 104.6 104.8 120.4 138.3 118.8 137.6 159.3