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 5230,000 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 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 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 this amount 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 50 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 year--the balance ramane in what am intrat 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 this amount 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 OA You need to have for less accumulated than what you will withdraw because you only withdraw a portion of the investment every year--the balance remains invested where it continues to eam 10% interest OB. 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 OC. You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every year--the balance remains invested where it continues to earn 10% interest OD. None of the above 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 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 0.877 0.8700 862 0.847 0.833 Period 20.9800 961 0.943 0.925 0.907 0.890 0.873 0.857 08420 826 0797 0.769 0.756 0.743 0.7180.694 Period 30.971 0.942 0.915 0.8890.864 0840 0.816 0.794 0.772 0.751 0.712 0.675 0.658 0.641 0.609 0.579 Period 4 0.961 0.924 0.888 0.855 0.823 0.792 0763 0.735 0.708 0.683 0.636 0.592 0.572 0.552 0:516 0.482 Period 5 0 951 0.906 0 863 0.822 0784 0.747 0713 0.6810650 0.621 0.567 0.519 0.497 0.476 0.437 0.402 Period 6 10.9420 888 0.837 0 7900 746 0.705 0666 0.630 0.596 0,564 0.5070.456 0.432 0.410 0.370 0.335 Period 70.933 0.871 0.813 0.750 0.711 0.665 0.623 0.5830.54710 513 0.452 0.400 0 376 0.354 0.314 0.279 Period 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.404 0.351 0.327 0.305 0.266 0.233 Period 90.914 0.837 0.766 0.703 0.6450.5920 544 0.500 10.460 0.424 0.361 0.308 0.284 0.263 0.225 0.194 Period 0.9050 820 0.744 0.6760 614 0.558 0.503 0.463 0.422 0.386 0.322 0.270 0.247 0.227 0.191 0.162 10 Period 110.8960 8040.7220 6500585 0.527 0.475 0.4290 3880 350 0.28710.237 0.215 0 195 0.162 0.135 Period 10.887 0788 0.701 0.625 0.557 0 497 0.4440.3970356 0.319 0.267 0.208 0.1870.168 0 137 0.112 12 Period 10.879 0 7730 68110 601 0.530 0.4591 0 41510 368 10 3260 2900 22910.18210 16310 1450,116 10.093 bad equil Round Period 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.229 0.182 0.1630.145 0.116 0.093 13 Period 0.870 0.758 0.661 0577 0.505 0.442 0.388 0.3400 2990 263 0.205 0.160 0.141 0.125 0.099 0.078 14 Period 0.8610 743 0,64210.555 0.481 0.417 0.362 0.315 0275 0 239 0.183 0.140 0.123 0.108 0.084 0.065 15 Period 0.853 0.728 0.62310 534 0.458 0.394 0339 0.292 0.2520 218 0.163 0.1230 107 0.093 0071 0.054 16 Period 0844 0.71406050.513 0.436 0.371 0.317 0.270 0.231/0.1980.146 0.108 0.093 0.080 0.060 0.045 17 Period 0.836 0.700 0.587 0.4940416 0 350 0.296 0.250 0.212 0.180) 0.1300095 0.081 0.069 0.051 0.038 18 Period 0.828 0 686 0.570 0 475 0 396 0331 0 277 0.232 0.1940 164 0.116 0.063/0.0701006000430 031 19 Period 0 820 0.673 05540456 0 3770 312 0.258 0215 0 1780 1490 1040073 0.0610.0510037 0.026 20 Period 0.81106600.5380 4390.359 0.294 0242 0.1990.1640135 0.093 0.06400530 044 0.031 0,022 oma Requid fore Overt Howe These Period 0.811 0.660 0.538 0.439 0.359 0 294 0242 0.199 0.164 0.135 0.093 0.064 0.053 0.044 0.031 0.022 21 Period 0.803 0.647 0.522 0.422 0.342 0.278 0.226 0.184 0.150 0.123 0.083 0.056 0.046 0.038 0.026/0.018 22 Period 0.795 0.634 0.5070 406 0.326 0.262 0.211 0.170.0.138 0.112 0.074 0.049 0.040 0.033 0.022 0.015 23 Period 0.788 0.622 0.492 0.390 0.310 0.247 0.197 0.158 0.1260.102 0.066 0.043 0.035 0.028 0.0190.013 24 Period 0.780 0.610 0.478 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.059 0.038 0.030 0.024 0.016 0.010 25 Period 0.772 0.598 0 4640 361 0.281 0220 0.172 0.135 0.106 0.084 0.053 0.033 0.026 0.021 0.014 0.009 26 Period 0.764 0.586 0.450 0.347 0 268 0.207 0.161 0 125 0.098 0.076 0.0470 029 0,023 0.0180.0110.007 27 Period 0.757 0.574 0.437 0.333 0.255 0.1960.150 0.116 0.090 0.069 0.042 0.026 0.020 0.0160.0100006 28 Period 0749 0 563 0.4240 321 0.243 0.185 01410.1070.08200630037 0.022 0.017 0014 0.008 0.005 29 Period 0.780 0.610 0.478 0.375 0.295 0 233 0.184 0.146 0.116 0.092 0.059 0.038 0.030 0.024 0.016 0.010 25 Period 0.7720598 0.464 0.3610 281 0.220 0.172 0.135 0.106 0.084 0.053 0.033 0.026 0.021 0.014 0.009 26 Period 0.764 0.586 0 450 0.347 0.268 0207 0 161 0.125 0.098 0.076 0.047 0.029 0.023 0.0180.0110.007 27 Period 0.757 0.574 0.4370333 0 255 0.196 0.150 0.116 0.090 0.069 0,0420 026 0.0200016 0.0100.006 28 Period 0 749 0563 0424 0.321 0243 0.185 0.1410.1070 0820063 0.037 0.022 0.017 0.014 0.008 0.005 29 Period 07420 5520.412 0 3080 231 0.1740131 0.0990.0750 0570033 0.020 0,015 0,012 0.007 0.004 30 Period 0.672 0.4530 307 0.208 0 142 0.097 0.057 0.046 0.0320.02200110005 0.004 0.003 0.001 0.001 40 Period 10.608 0.372 0 2280 141 0.087 0.054 0.034 0.021 001310.009 0.003 0.001 0.001 0.001 50 ve se 6% 7% 8% 23 Future Value of $1 Periods 1% 2% 3% 4% 5% 9% 10% 12% 14% 15% Period 1 1010 1.020 1.030 1.040 1.050 1.060 1.070 1080 1.090 1.100 1.120 1.140 1.150 Period 2 1.020 1.040 1061 1.082 1.103 1.124 1.145 1.166 1.188 1.210 1.254 1.300 1.323 Period 3 1.030 1061 1.093 1.125 1.158 1.1911 225 1260 1.295 1331 1.405 1.482 1.521 Period 4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.574 1689 1749 Period 5 1.051 1.104 1.159 1.217 1.276 1.338 1403 1.469 1.539 1.611 1.762 1.925 2.011 Period 6 1.062 1 126 1.194 1265 1.340 1.419 1.501 1.587 1.677 1.772 1.9742.195 2313 Period 7 1072 1 149 1230 1.316 1.407 1504 1.606 1.7141.828 1.949 2.211 2502 2.660 Period 8 1.083 1 172 1267 1.369 1.477 1.594 1718 1 851 1.993 2.144 2.476 2 853 3.059 Period 9 1.094 1.195 1.305 1.423 1551 1689 1.838 1999 2.172 2.358 2.7733.252 3.518 Period 10 1 105 1 219 1 344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 3.106 3.707 4.046 Period 11 1 116 12431384 1.539 1.710 1.898 2.105 2.332258028533 4794.226 4.652 Period 12 1.127 1268 1 426 1.601 1.796 2.012 2 252 2.518 2.813 3.138 3.896 4818 5.350 Period 13 1138 1294 1.469 1665 1 886 2133 2.4102.720 3.066 3.452 4.363 5.492 6.153 Period 14 1.149 1319 15131732 1 980 2261 2.579 2.937 3.342 3.798 4.8876 261 7076 Period 15 116111 346 15581180112079 2.397 275913 17213.642 417715.47417 1388 137 Period 16 1.173 1373 1605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 6.130 8.137 9.358 Period 17 1.184 1.400 1.653 1.948 2292 2.693 3.159 3.700 4.328 5.054 6.866 9.276 10.76 Period 18 1.196 1.428 1.702 2.026 2.407 2 854 3.380 3.996 4.717 5.560 7.690 10.58 12.38 Period 19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 8.613 12.06 14.23 Period 20 1.2201 486 1.806 2 191 2.653 3 2073.870 4.661 5.604 6.727 9.646 13.74 16:37 Period 21 1.232 1.516 1.860 2.279 2.786 3.400 4 1415.0346. 1097.400 10.80 15.67 1882 Period 22 1.245 1.546 1.916 2.370 2.925 3.604 4.430 5.4376.659 8.140 12 10 17 86 21.64 Period 23 1.2571.577 1.974 2.465 3.0723.820 4.741 5.871 7.258 8.954 13.55 20:36 24.89 Period 24 1.270 1.608 2.033 2.563 3.225 4049 5.0726.341 7 911 9.850 15.18 23 21 28.63 Period 25 1282 1.641 2.094 2.666 3.386 4 292 5.4276.848 8.623 10.83 17.00 26.46 3292 Period 26 1.295 1.673 2.157 2.772 3.556 4.549 5.807 7 3969.399 11.92 19.04 30.1737 86 Period 27 1308 1.707 2.221 28833.733 4.822 6.21417988 10.25 13.11 21.32 34.39 43.54 Period 28 1321 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 1776 2.357 3.1194. 1165.418 7:1149.317 12 17 15 86 26.75 44 69 57 58 Period 30 1.348 1.811 2 427 3.243 4.322 5.743 7612 10.06 13.27 17.45 29.96 50.95 66.21 Period 40 1.489 2.208 3.262 4.801 7.040 10.29 14.97 21.72 31.41 45 26 93 05 188.92679 v id nd Present Value of Ordinary Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% Period 10.990 0.980 0.971 0.962 0.952 0.943 0935 0.926 0.917 0.909 0.893 0.877 0.870 0.862 0.847 0.833 Period 2 1970 1942 1913 1.886 1.859 1833 1.808 1783 1759 1736 1.6901.647 1626 1.605 1.566 1.528 Period 3 2941 2 884 2 8292.775 2.7232 673 2.624 2577 2.531 2487 2.402 2322 2283 2246 2.174 2. 106 Period 4 3.902 3 8083.717 3.630 3.5463 465 3.3873,312 3.240 3.1703.037 2.914 2.855 2.798 2690 2.589 Period 5 4.853 4.713 4580 4.452 432942124 100 3 9933.890 3.791 3.605 3.433 3.352 3274/3127 2.9944 Period 6 5.795 5.601 5.417 5242 50764.917 4 767 4.623 4.486 4355 4 111 3.8893.784 3.685 3.498 3.326 Period 76.728 6 472 6.230 6.002 5.7865.5825 3895 206 5,033 4.868/4.5644 288 4160 4.039 3.812 3.605 Period 8 76527325 70206.733 6.4636210159715.7475.535 5335 496846394 487 4 344 4.078 3.837 Period 9 8 566 8. 162 7 786 7 4357 108 6.802 6.515 6 247 5.9955.759 5328/4.9464.7724.607 4.303/4031 Period 10 9 471 8.983 8.530 8 1117 722 7 360 70246.710 6.418 6.145 5.6505.216 5 019 4.833 4.494 4.192 Period 11 10 3689 787 9 263 8.760 8.3067 8877 499 7 139 6.805 6.495 5938 5.453 5.23450294.656 4.327 Period 12 11 255 10.575 9.95493858.863 6,384 79437.53671616.814 6.1945.660 5.421 5 1974.793 4.439 Period 131213411.348 10.635 9 986 9 394 8.653 8 358 7 904 7.487 7 1036 424 5 842 5.583 5.342 4.910 4533 Period 1413.00412 106 11 296 10 5639 899 9.295 8.7458244 778673676 628 6.002 57245.468 5.0084611 Period 1513.86512 849 11 93811.118110 380 9 7129 1088 559 18 06112 60616 811 6 142 58475575 5.092 4 675 al 1011 T ve . se Period 1614.71813.578 12.561 11652 10.83810 1069.447 8. 851 8 313 7.824 6.9746.265 5.954 5.669 5.162 4.730 Period 171556214 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 5222 4.775 Period 1816,39814.992 13.754 12 659 11.690 10.828 10.05993728.756 8.2017.250 6.467 6.128 5.818 5.273 4,812 Period 19 17 22615 678 14 324 13.13412 08511.15810.336 9.604 8.950 8.3657366 6.550 6.198 5.8775 316 4 844 Period 2018.04616.351 14.877 13.590 12 462 11.470 10.594 9.818 9.129 8.5147469 6.623 6.259 5.929 5353 4.870 Period 2118 85717.01115.415 14.029 12 82111.764 10.836 10.017 9.292 86497562 6.687 6.3125 973 5384 4 891 Period 22 19.660 17 658 15 937 14.451 13 163 12.042 11.06110 2019.442 8.772 7645 67436.359 6 011 5.410 4 909 Period 23 20.45618 292 16.444 14857 13.48912.303 11 27210 371 9.5808.883 7718 6792 6.399 6.044 5432 4.925 Period 2421 24318.914 16.936 15 247 13.79912 550 11.469 10.529 9707 8.985 7784 6.835 6.4346.073 5 451 4937 Period 2522 02319,523 17 41315.622 14.09412.783 11 654 10.6769.8239.07778436.873 6.464 6.097 5.467 4.948 Period 2622.795 20 121 17 877 15.98314 37513.00311.826 10 810 9.929 9.1617 896 6.906 6 491 6 118 5 480 4956 Period 2723.56020 707 18.327 16.3301464313 211 11.98710 935 10.027 92377 943 6.935 6.514 6.136 5.492 4964 Period 2824 3162128118.764 16.66314 89813.40612.13711.051 10. 116 9.307 79846.961 6,534 6.1525 5024970 Period 292506621.844 19 188 16 98415 1411359112 278 11 158 10.198 93708.022 6 983 6.551 6.166 5.510 4.975 Period 30 25 80822 396 19 60017 292 15 37213 76512.40911 258 10 274 9 4278.055 7.003 6.566 6.177 5.517 4.979 Period 40 32 83527 355 23 115 19 793 17 159 15.04613 332 11 925/10.757 9.779 8 244 7 105 6.642 6.233 5.548 4 997 Period 5039 1931 47425730121 482182561576711381122331 962 9915184 7131 6.66116246 5.5544999 Future Value of Ordinary Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% Period 1 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 Period 2 2010 2020 2030 2040 2050 2060 2070 2.080 2090 2.100 2.120 2140 2.150 Period 3 3.030 3.060 3.091 3.122 3.153 3.1843.215 3.246 3.278 3 310 3.374 3.440 3.473 Period 4 4060 4.122 4 184 4.246 4.310 4.375 4.440 4.506 4.573 4.641 4.779 4.921 4.993 Period 5 5.101 5.204 5.309 5.416 5.526 5.6375.751 5 867 5.985 6.105 6 353 6.610 6.742 Period 6 6 1526.308 6.468 6.633 6.802 6.975 7.153 7336 7523 7.7168.115 8 536 8.754 Period 7 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487 10.09 10.73 11.07 Period 8 8 286 8.5838 892 9.214 9.5499 897 10.260 10.64 11.03 11.4412.30 13.23 13.73 Period 9 9.369 9.755 10.16 10.58 11.03 11 49 11.98 12.49 13.02 13.5814.78 16.09 16.79 Period 10 10.46 10.95 11.46 12.01 1258 13.18 13.82 14.49 15 19 15.94 1755 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 Period 12 12.68 13 41 14 19 15.03 15.92 16.87 17 89 18.98 20.14 21 38 24 13 27 2729.00 Period 13 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 Period 14 14.95 15.97 17.09 18 29 19.602102 22 55 24 21 26.02 27 98 32 39 37 58 40 50 Period 15 16 10 17 29 18 60 20.02 21.58 23 28 25 13 27 15 29 36 31 7737 28 43 84 47.58 Period 16 17 26 18.64 20.16 21.82 23.66 25.67 27 89 30 32 33.00 35.95 42.75 50.98 55.72 Period 17 18.43 20.0121.76 23.70 25.84 28.21 30.84 33.75 36.97 40.54 48.88 59.12 65.08 Period 18 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 Period 19 20.81 22.84 25.12 27.67 30.54 33.76 37 38 41.45 46.02 51 16 63.44 78.97 88.21 Period 20 22.02 24.30 26.87 29.78 33.07 36.79 41.00 45.76 51.165728 72.05 91.02 102.4 Period 21 23 24 25.78 28.68 31.97 35.72 39.99 44.87 50,42 56.76 64.00 81.70 1048 118.8 Period 22 24.47 27 30 30.54 34.25 38.51 43.39 49.01 55.46 62.87 71.40 92.50 120.4 1376 Period 23 25.72 28.85 32.45 36.62 41.4347.00 53 44 60.89 69.53 79.54 104.6 138.3 1593 Period 24 26.97 30.42 34.43 39.08 44 50 50.82 58.18 66.76 76 79 88.50 118.2 158.7 1842 Period 25 28 24 32.03 36.46 41.65 47.73 54.86 63.25 73 11 84.70 98.35 133.3 181.9 212.8 Period 26 29.53 33.67 38.55 44 31 51.11 59.16 68.68 79.95 93.32 109.2 150.3 208 3 245.7 Period 27 30.82 35 34 40.71 47.08 54.6763.71 74.48 87.35 102.7 121.1 169.4 238.5 283.6 Period 28 32. 133705 42.93 49.97 58.40 68.53 80.70 95 34 113.0 134.2 190 7 272.9 3271 Period 29 33.45 38 79 45.22 52.97 62.32 73.6487.35 1040 1241 148.6 214,6 3121 3772 Period 30 34.78 40 57 47 58 56.08 66 44 79.06 94.46 113.31363 1645 241.3 356 8 434 7 Period 40 48.8960.40 75 40 95 03 1208 154 8 199 6 259.1 337.9 44267671 1,342 1779 Darind IGAARAA 111 112715001 2002 201611162on on 1721 a re