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. you plan to save by making 15 equal annual installments into a fairly risky investment fund that you expect will earn 8% per year.

bu reparing for a very satynowe 40 and money wis be ble to win 122.000 per year for the rest 40 years family story you there you will ge you to ve by mag 15 (tromage 2516 womentul you spect wil camery. You were many discoved when you Ce the wwwPre very Arty) Cho the hour VOA 11) Requirements 41. How much money at you accums by trement to make your plan work out od represent van de 328,000 wound you to mower w rewood butte cour) Requirement 2. How to mount to be amount you will win honest ang wewe unterste oor Over the course of your retirement you will be we drawing However, by age 40 you only need to have invested These numbers are truth OA. You need to have tw more score than what you will with bene you wil www tage portion of the investment every year-te balance and insted where it continues to me interest. O You need to have for less wed than what you will withdraw because you only withdra portion of every year the bar romana ested when it continues to come OC Youred to have the same amour accumulated as you will draw because you will not an art on your investment when you reach retirement OD. None of the above d of $il of 51 t you hol nulate compa ou will have Present Value of $1 Periods 1% 2% 3% 4% 5% 6% 7% 9% 10% 12% 14% 15% 16% 18% 20% Period 1 0.990 0.980 0.971 0962 0.952 0943 0.935 0.926 0.917 0.909 0893 0.877 0.870 0.862 0 847 0.833 Period 2 0.980 0.961 0.9430925 0.907 0.890 0.873 08570.842 0.826 0.797 0.769 0.750 0.743 0.7180.694 Period 3 0.971 0.942 0915 0.889 0.854 0.840 0.816 0.794 0.772 0.751 0.712 0.675 0.658 0.641 0.609 0.579 Period 4 0.96109240.888 0.855 0.823 0.792 0.7630.735 0.7080.683 0.638 0.592 0.572 0.552 0.516 0.482 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 04370402 Period 6 0.942 0.888 0.837 0.790 0746 0.705 0.666 0.630 0.596 0.564 0.507 0.456 0432 0410 0.370 0.335 Period 7 0933 0871 0.813 0.750 0.71 0.665 0.623 0.58305470513 0.452 0.400 0.376 0.354 0.3140.279 Period & 0.923 0.853 0.789 0.731 0.6770627 05820.540 0.502 046704040.3510.327 0.3060 266 0.233 Period 9 0.914 0.837 0.786 0.703 0.645 0.592 0.544 0.500 0.400 0.424 0.361 0.308 0.284 0.263 0.225 0.194 Period 10 0.905 0.820 0.7440676 0.614 0.558 0.508 0.46304220.386 0.322 0.270 0.247 0.227 0.19 0.162 Period 11 0.896 0.8040.722 0.650 0.585 0527 0.475 0.429 0.3880350 0.287 0.237 0.215 0.195 0.162 0.135 Period 12 0.887 0.788 0.701 0.625 0.557 0497 0.444 0.397 0.356 0.319 0257 0.208 0.187 0.168 0.1370.112 Period 13 0.579 0.773 0681 0.601 0.530 0.4690415 0.368 0.3260290 0229 0.1820.163 0.145 0.116 0.093 Period 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0 263 0.205 0.1600.141 0.125 0.099 0.078 Period 15 0861 0.743 0542 0.555 0.4810417 0.362 0.315 0.2750 239 0.183 0.140 0.123 0.1080.084 0.066 Period 16 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.2920 252 0218 0.163 0.123 0.1070.093 0.071 0.054 Period 17 0.844 0.714 0.005 0.513 0.436 0.371 0.3170270 0.2310.198 0.146 0.108 0.093 0.080 0.060 0.045 Period 18 0.856 0.700 0.587 0.4940416 0.350 0.296 0.250 0.212 0.10 0.1300.095 0.081 0.069 0.051 0.038 Period 19 0828 0.886 0.5700475 0.39 0331 0.277 0232 0.194 0.164 0.116 0.083 0.070 0.000 0.043 0.031 Period 20 0.820 0.673 05540456 0.377 0.3120258 0.215 0.178 0.149 0.104 0.073 0.061 0.051 0.037 0.020 Period 21 0.811 0.660 05380439 0.359 0294 0242 0.1990.1640.135 0.000 0.064 0.0530.044 0.031 0.022 Period 22 0.809 0.647 0.522 0422 0.342 0.278 0.226 0.154 0.150 0.123 0.003 0.056 0.046 0.038 0.0200018 Period 23 0.795 0.634 0.507 0.4060.3260262 0.211 0.1700.138 0.112 0.074 0.049 0.040 0.033 0.0220015 Period 24 0.788 0.622 0.492 0.360 0.310 0247 0.197 0.158 0.126 0.102 0.066 0.043 0.035 0.028 0.0198013 Period 25 0.780 0.6100478 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.0590.038 0.030 0.024 0.0160.010 Period 26 0.772059804540361 0281 0220 0.172 0.135 0.106 0.084 0.053 0.033 0.025 0.021 0.014 0.009 Period 27 0.754 05860450034702680207 0.161 0.125 0.098 0.076 0.047 0.029 0.023 0.0180.0110.007 ARE ALA umulate Joel mulated 18% ount ac ARE bf $1 T% 15% you ulate pompa u will have Present Value of Ordinary Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 8% 9% 10% 12% 14% 16% 18% 20% Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0917 0.909 0.893 0.877 0.870 0.862 0.847 0.833 Period 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.73616901.647 1.626 1.605 1.566 1528 Period 3 2941 28842829 2.775 2.723 2.673 2.624 2577 2 531 2487 24022 322 2.283 2246 2174 2.106 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 2856 2798 2.690 2.589 Period 5 4853 4.713 45804452 4.329 4.212 4.100 3.993 3.890 3.791 3.605 3433 3.352 3.274 3.127 2.991 Period 6 5.795 5.601 5.417 5.242 5.078 4.917 4.767 4.623 4486 4355 4.111 3.8893.784 3685 3.498 3.326 Period 7 6.728 6.472 6230 6.002 5.786 5582 5.389 5.206 5033 4.86845644 288 4.160 4.039 3.812 3.605 Period & 7.652 7.325 7.020 6.733 6.463 6210 5.971 5.747 5.535 5.335 4.968 4,639 4.487 4.344 4.078 3.837 Period 9 8,566 8.1627.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.328 4.946 4.772 4.607 4.303 4.031 Period 10 9.471 8.9838.530 8.111 7.722 7.360 7.0246.710 6.418 6.145 5.650 5216 5.019 4833 4494 4.192 Period 11 10368 9.787 9.253 8.760 8.306 7.8877499 7.139 6.8056.495 5.938 5.453 5234 5.0294656 4.327 Period 12 11.255 10.575 9.8549.385 8863 8.384 7.9437.536 7.1616.814 6.194 5.660 5421 5.197 4.793 4439 Period 13 12.134 11.348 10.6359.986 9.394 8.853 8 358 7.904 7.487 7.103 6.4246.8425.583 5342 4910 4533 Period 14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.628 6.0025.724 5.468 5,008 4.611 Period 15 13.865 12 849 11.938 11.118 10.3809712 9.108 8.559 80617.606 6.811 6.142 5.847 5.575 5.092 4.675 Period 16 14.718 13.57812561 11652 10.838 10.106 9.447 8.851 8.3137824 6.9746.265 5.954 5669 5.1624.730 Period 17 15.562 14 292 13.166 12 166 11 274 10.477 9.763 9.122 8.5448.022 7.1206.3736,047 5.749 5222 4.775 Period 18 16,398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.2017.250 6.467 6.128 5.818 5.2734.812 Period 19 17.220 15678 1432413.134 12.085 11.158 10336 9.604 8950 8.3657.366 6.550 6.198 5.877 5.3164844 Period 20 18.046 16351 14.877 13.590 12462 11.470 10.5949.818 9.129 8.5147469 6.623 6.250 5.9296,353 4.870 Period 21 18.857 17.011 15.415 14.029 12.821 11.764 10.836 10.0179.292 8.6497.562 6.687 6.312 5.973 5.384 4.891 Period 22 19.660 17.658 15.93714451 13.163 12.042 11.061 10.2019.442 8.7727.645 6.743 6.359 6.01154104909 Period 23 20.456 18 292 16.444 14.857 13.489 12 303 11.272 10.371 9.580 8.8837.718 6.792 6.399 6.044 5432 4.925 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 6.4346.073 5451 4937 Period 25 22.023 19523 17.413 15.622 14.094 12.783 11,654 10.675 9.8239.077 7.843 6.873 6.464 6.097 5.467 4.948 Period 26 22795 20.121 17 877 15.983 14.375 13.003 11.826 10.8109.929 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 1321111.987 10.935 10.027 9.237 7.943 6.935 6.514 6.136 5492 4.964 LAI ulate ulated unt ac ARE LA AR AFA FRA bm of $1 table.) $1 table) ou accumulat ear ate this amou mpare to the will be with live invested Periods Period 1 Period 2 Period 3 Period 4 Perlod 5 Perlod 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 Period 16 Period 17 Period 18 Period 19 Period 20 Period 21 Period 22 Period 23 Period 24 Period 25 Future Value of $1 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 1.010 1020 1030 1040 1050 1060 1070 1.000 1.090 1.100 1.120 1.140 1.150 1.020 1.040 1.061 1.0821.103 1.1241.145 1.166 1.1881210 1.254 1.300 1.323 1030 1.061 1.093 1.125 1.158 1.1911.225 1.260 1.295 1.331 | 1405 1482 1.521 1.041 1.0821.126 1.170 1.216 1.2621.311 1.360 14121464 1574 1.689 1.749 1.051 1.104 1.159 121712761338 1403 1.469 1.539 1.611 1.762 1.925 2.011 1.062 1.126 1.194 1.265 1.340 1419 1.501 1.587 1.6771.772 1.9742.195 2313 1.072 1.149 1.230 1.316 1407 1.5041.606 1.714182819492211 2.502 2.660 1.013 1.1721.267 1.369 1477 1,5941.718 1.851 1.993 2.144 2.476 2853 3.059 1,094 1.195 1305 1423 1.551 1.689 1.838 1.999 2.172 2.358 27733.2523.518 1.105 1219 1344 1.480 1.629 1.7911.967 2159 2.367 2.594 3.106 3.7074046 1.116 1243 1.384 1.539 1710 1.898 2.105 2332 2.580 28533.479 4226 4652 1.127 1.268 1426 1601 1796 2012 2252 2518 2813 3.138 3.896 4.818 5.350 1.138 1.294 1469 1665 1666 2.133 2410 2720 3.066 3.452 4363 5492 6.153 1.149 1.319 1.513 1732 1.980 2261 2.579 2.937 3.342 3.7984.887 6.2617.076 1.161 1.346 1.558 1.801 2079 2.3972.759 3.172 3.642 4.177 5.47471388.137 1.173 1.373 1.605 1.873 2.183 2540 2.9523426 3.970 4.595 6.130 8.1379.358 1.184 1.400 1.653 1.948 2292 2.6933.159 3.700 4328 5.0546,866 9.276 10.76 1.196 1428 1.702 2026 2.407 2.8543.380 3.996 4.717 5.5607.690 10.58 1238 1.208 1457 1.754 2.107 2.527 3.026 3.617 4 316 5.142 6.116 8.613 12.06 14.23 1220 1.488 1.806 2.191 2653 3.207 3.870 4661 5.604 6.727 9.646 13.74 16.37 1.232 1.516 1.860 2.279 2.786 3.400 4.141 5.034 6.1097.400 10.80 15.67 18,82 1.245 1.546 1.916 2370 2.925 3.604 4.430 5.4376.659 8.140 12.10 17.86 21.64 1 2571.5771.974 2465 3.072 3.820 4.741 5,871 | 72588.954 13.55 20.36 24 89 1.270 1.608 2033 2.563 3.225 4.049 5.072 6.341 7.911 9.850 15.18 23.2128.63 1.282 1641 2094 2666 3.386 4 292 5427 6.848 8.623 10.83 17.00 26.46 32.92 1 295 1.673 2.157 2772 3.556 45495.807 7.396 9.399 1192 19.04 30.1737 86 1 308 1.707 2 221 2883 3.733 482262147.988 10.25 13.11 2132 34.39 43.54 stated than wil pntin ated than why les to hit accumulate Period 26 Period 27 A. F PPT AAN WY: age .) bmpletely Periods Period 1 Period 2 Period 3 Period 4 Period 5 mula earest w mod the vithd Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 sted Future Value of Ordinary Annuity of $1 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2.010 2.020 2030 2040 2050 2.060 2.070 2.080 2090 2.100 2.120 2.140 2.150 3,030 3.060 3.091 3.122 3.153 3.1843.215 3246 3.278 3.310 3.374 3.440 3.473 4,0604.122 4.1844246 4.310 4.375 4440 4.506 4.573 4641 4.779 4.921 4.993 5.101 5.2045.309 5.416 5.526 5.637 5.751 5.867 5.9856.105 6.353 6.610 6.742 6.152 6.308 6.468 6.633 6.8026.975 7.153 7336 7523 7.716 8.115 8.536 8.754 7.214743476627898 8.142 8.394 8.654 8.923 9.2009.487 10.09 10.73 11.07 8.286 8.5838.8929.2149.5499.897 10 260 10.64 11.03 11.441230 13 23 13.73 9.369 9.755 10.16 10.58 11.03 11:49 11.98 12.49 13.02 13.58 14.78 16.09 16.79 10.46 10.95 11.48 12.01 12.58 13.18 13.82 1449 15.1915.94 17.55 19.34 20.30 11.57 12.17 12.8113.49 14 21 14.97 15.78 16,65 17.56 1853 20.65 23.0424 35 12.68 13.41 14.19 15.03 15.9216.87 17.8918.98 20.14 21.38 24.13 27 27 29.00 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 14.95 15.97 17.0918.29 19.60 21.02 22.55 2421 26.02 27.98 32.39 37.58 40,50 16.10 17.29 18.60 20.02 21.58 23.28 25.13 27.15 29.36 31.77 3728 43.84 47.58 17.25 18.64 20.16 21.82 23.56 25.67 27.89 30.32 33.00 35.95 42.75 50.98 55.72 18.43 20.01 21.76 23.70 25.84 28.21 30.84 33.75 36.97 40.54 48.88 59.12 65.08 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 20.81 2284 25.12 27.67 30,54 33.76 37 38 41.45 46.02 51.16 63.44 78.97 88.21 22.02 24 30 26.87 29.7833.07 36.79 41.00 45.76 51.16572872.05 91,02 1024 23.24 25.78 28.68 31.97 35.72 39.99 44.87 50.42 56.76 64.00 81.70 104.8 118.8 24.47 27 30 30.5434.25 38.51 43.3949.01 55.4662.87 71.40 92.50 120.4 137.6 25.72 28.8532.45 36.62 4143 47.00 53.4460.89 69.53 79.54 1046 1383 1593 26.97 30.42 34.43 39.08 445050.82 58.18 66.76 76.7988.50 118.2158.71842 28.24 32.03 36.46 41.65 47.73 54.86 63.25 73.11 84.70 98.35 1333 181.9 2128 29.53 33.6738,55 44.31 51.1159.16 68.68 79.95 93.32 1092 150.3 2083 245.7 30.82 35 34 40.7147,08 54.6763.71 74 48 87.35 102.7 121.1 169.4 238.5 283.6 In w ntinues to h whl es to earn ulate Period 16 Period 17 Period 18 Period 19 Period 20 Period 21 Period 22 Period 23 Period 24 Period 25 Period 26 Period 27 LAR ARA TAA BAR AN Requirements 1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the $225,000 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? sa