Assume you want to retire early at age

54.

You plan to save using one of the following two strategies: (1) save

$4,500

a year in an IRA beginning when you are

29

and ending when you are

54

(25

years) or (2) wait until you are

42

to start saving and then save

$9,375

per year for the next

12

years. Assume you will earn the historic stock market average of

14%

per year.

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Part 1

Requirement 1. How much out-of-pocket cash will you invest under the two options?

Calculate how much out-of-pocket cash you will invest under the two options.

Option 1:

Future Value of Annuity of $1 20% 0.833 1.528 2.106 2.589 2.991 Period 6 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 20% 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 2.010 2.020 2.030 2.040 2.050 2.060 2.080 2.100 2.120 2.140 2.160 2.180 2.200 Period 3 3.030 3.060 3.091 3.122 3.153 3.184 3.246 3.310 3.374 3.440 3.506 3.572 3.640 Period 4 4.060 4.122 4.184 4.246 4.310 4.375 4.506 4.641 4.779 4.921 5.066 5.215 5.368 Period 5 5.101 5.204 5.309 5.416 5.526 5.637 5.867 6.105 6.353 6.610 6.877 7.154 7.442 Period 6 6.152 6.308 6.468 6.633 6.802 6.975 7.336 7.716 8.115 8.536 8.977 9.442 9.930 Period 7 7.214 7.434 7.662 7.898 8.142 8.394 8.923 9.487 10.089 10.730 11.414 12.142 12.916 Period 8 8.286 8.583 8.892 9.214 9.549 9.897 10.637 11.436 12.300 | 13.233 14.240 15.327 16.499 Period 9 9.369 9.755 10.159 10.583 11.027 11.491 12.488 13.579 14.776 16.085 17.519 19.086 20.799 Period 10 10.462 10.950 11.464 12.006 12.578 13.181 14.487 15.937 17.549 | 19.337 21.321 23.521 25.959 Period 11 11.567 12.169 12.808 13.486 14.207 14.972 14.972 16.645 16.645 18.531 20.655 23.045 25.733 28.755 32.150 Period 12 12.683 13.412 14.192 15.026 15.917 | 16.870 18.977 21.384 24.133 27.271 30.850 34.931 39.581 Period 13 13.809 14.680 15.618 16.627 17.713 18.882 21.495 24.523 28.029 | | 32.089 36.786 42.219 48.497 Period 14 14.94715.974 17.086 18.292 19.599 21.015 24 215 27.975 32.393 37.581 43.672 50.818 59.196 Period 15 16.09717.29318.599 20.024 21.579 23.276 27.152 31.772 37.280 43.842 51.660 60.965 72.035 Period 20 22.019 24.297 26.870 29.778 33.066 36.786 45.762 57.275 72.052 91.025 115.380 146.628 186.688 Period 25 28.243 32.030 36.459 41.646 47.727 54.865 73.106 98.347 133.334 181.871 249.214 342.603 471.981 Period 30 34.785 40.568 47.575 56.085 66.439 79.058 113.283 164.494 241.333 356.787 530.312 790.948 1,181.882 Period 40 48.886 60.402 75.401 95.026 120.800 154.762 259.057 442.593 767.091 1,342.025 2,360.757|4,163 213 7,343.858 Present Value of Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.862 0.847 Period 2 1.970 1.942 1.913 1.886 1.859 1.833 1.783 1.736 1.690 1.647 1.605 1.566 Period 3 2.941 2.884 2.829 2.775 2.723 2.673 2.577 2.487 2.402 2.322 2.246 2.174 Period 4 3.902 3.808 3.717 3.630 3.546 3.465 3.312 3.170 3.037 2.914 2.798 2.690 Period 5 4.853 4.713 4.580 4.452 4.329 4.2123.993 3.791 3.605 3.433 3.274 3.127 5.795 5.601 5.417 5.2425.076 4.917 4.623 4.355 4.111 3.8893.685 3.498 Period 7 6.728 6.472 6.230 6.002 5.786 5.5825.206 4.868 4.564 4.288 4.039 3.812 Period 8 7.652 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.9684.639 4.344 4.078 Period 9 8.566 8.162 7.786 7.435 7.108 6.8026.247 5.759 5.328 4.946 4.607 4.303 Period 10 9.471 8.9838.530 8.111 7.722 7.360 6.710 6.145 5.6505.216 4.833 4.494 Period 11 10.368 9.787 9.253 8.760 8.306 7.887 7.139 6.495 5.938 5.453 5.029 4.656 Period 12 11.255 10.575 9.9549.3858.863 8.384 7.536 6.814 6.194 5.660 5.197 4.793 Period 13 12.134 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 5.842 5.342 4.910 Period 14 13.004 12.106 11.296 10.563 9.899 9.295 8.244 7.3676.628 6.002 5.468 5.008 Period 15 13.865 12.849 11.938 11.118 10.380 9.712 8.559 7.606 6.811 6.142 5.575 5.092 Period 2018.046 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.4696.623 5.929 5.353 Period 25 22.023 19.523 17.413 15.622 14.094 12.783 10.675 9.077 7.8436.873 6.097 5.467 Period 30 25.808 22.396 19.600 17.292 15.372 13.765 11.258 9.4278.055 7.003 6.177 5.517 Period 40 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.7798.244 7.105 6.233 5.548 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.870 4.948 4.979 4.997 Future Value of $1 8% 1% 1.010 1.020 1.030 2% 1.020 1.040 1.061 1.082 3% 1.030 1.061 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 10% 1.100 1.210 1.331 1.464 1.611 1.080 1.166 1.260 1.360 12% 1.120 1.254 1.405 1.574 1.762 14% 1.140 1.300 1.482 1.689 1.925 18% 1.180 1.392 1.643 1.939 2.288 16% 1.160 1.346 1.561 1.811 2.100 20% 1.200 1.440 1.728 2.074 1.093 1.126 1.159 1.041 1.051 1.104 1.469 2.488 1.974 2.211 Periods Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 1.062 1.072 1.083 1.094 1.105 1.126 1.149 1.172 1.195 1.219 1.1941.265 1.340 1.230 1.316 1.407 1.267 1.369 1.477 1.305 1.423 1.551 1.344 1.480 1.629 1.419 1.504 1.594 1.689 1.791 1.587 1.772 1.714 1.949 1.851 2.144 1.999 2.358 2.159 2.594 2.195 2.502 2.853 3.252 3.707 2.436 2.826 3.278 3.803 2.476 2.773 3.106 2.700 3.185 3.759 4.435 5.234 2.986 3.583 4.300 5.160 6.192 Present Value of $1 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 20% Period 1 1 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 Period 2 0.980 0.961 0.943 0.925 0.907 0.890 0.8570.826 0.797 0.769 0.743 0.718 0.694 Period 3 0.971 0.942 0.915 0.889 0.864 0.840 0.794 0.751 0.712 0.712 0.675 0.641 0.609 0.579 Period 40.961 0.924 0.888 0.855 0.823 0.792 0.735 0.683 0.683 0.636 0.592 0.552 0.516 0.482 Period 5 0.951 0.906 0.863 0.863 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.476 0.437 0.402 Period 6 0.942 0.888 0.837 0.790 0.746 0.705 0.630 0.564 0.507 0.4560.410 0.370 0.335 Period 70.933 0.871 0.813 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.354 0.3140.279 Period 80.923 0.853 0.789 0.731 0.677 0.627 0.540 0.467 0.404 0.351 0.305 0.266 0.233 Period 9 0.914 0.837 0.766 0.703 0.645 0.6450.592 0.5920.500 0.424 0.361 0.308 0.263 0.225 0.194 Period 10 0.905 0.820 0.744 0.676 0.614 0.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 Period 110.896 0.8040.722 0.650 0.585 0.527 0.429 0.350 0.287 0.237 0.1950.162 0.135 Period 12 0.887 0.788 0.701 0.625 0.557 0.497 0.397 0.319 0.257 0.208 0.168 0.137 0.112 Period 13 0.879 0.773 0.681 0.601 0.530 0.469 0.368 0.290 0.229 0.182 0.145 0.116 0.093 Period 14 0.870 0.758 0.661 0.577 0.505 0.442 0.340 0.263 0.205 0.160 0.125 0.099 0.078 Period 15 0.861 0.743 0.642 0.555 0.481 0.417 0.315 0.239 0.183 0.140 0.315 0.239 0.183 0.140 0.108 0.084 0.065 Period 20 0.820 0.673 0.554 0.456 0.377 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 Period 25 0.780 0.610 0.478 0.375 0.295 0.233 0.146 0.092 0.059 0.038 0.024 0.0160.010 Period 30 0.742 0.552 0.412 0.308 0.231 0.174 0,099 0.057 0.033 0.020 0.012 0.007 0.004 Period 40 0.672 0.453 0.307 0.208 0.142 0.097 0.046 0.022 0.0110.005 0.003 0.001 0.001 4.411 1.116 1.127 1.138 1.243 1.384 1.268 1.426 1.294 1.469 1.319 1.513 1.346 1.558 1.539 1.601 1.665 1.732 1.801 1.710 1.898 1.796 2.012 1.886 2.133 1.980 2.261 2.079 2.397 2.332 2.518 2.720 2.937 3.172 2.853 3.138 3.452 3.797 4177 3.479 3.896 4.363 4.887 5.474 4.226 4.818 5.492 6.261 7.138 5.117 5.936 6.886 7.988 9.266 6.176 7.288 8.599 10.147 11.974 7.430 8.916 10.699 12.839 15.407 1.149 1.161 Period 20 Period 25 Period 30 Period 40 1.220 1.282 1.348 1.489 1.486 1.806 2.191 1.641 2.094 2.666 1.811 2.427 3.243 2.208 3.262 4.801 2.653 3.207 4.661 6.727 9.646 13.743 19.461 19.461 27.393 38.338 3.386 4.292 6.848 10.835 17.000 26.462 40.874 62.669 95.396 | 4.322 5.743 10.063 17.449 29.960 50.950 85.850 143.371 237.376 | 7.040 10.286 21.725 45.259 93.051 188.884 378.721 750.3781,469.772 - Requirements 1. How much out-of-pocket cash will you invest under the two options? 2. How much savings will you have accumulated at age 54 under the two options? 3. Explain the results 4. If you let the savings continue to grow for eight more years with no further out-of-pocket investments), under each scenario, what will the investment be worth when you are age 62? Future Value of Annuity of $1 20% 0.833 1.528 2.106 2.589 2.991 Period 6 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 20% 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 2.010 2.020 2.030 2.040 2.050 2.060 2.080 2.100 2.120 2.140 2.160 2.180 2.200 Period 3 3.030 3.060 3.091 3.122 3.153 3.184 3.246 3.310 3.374 3.440 3.506 3.572 3.640 Period 4 4.060 4.122 4.184 4.246 4.310 4.375 4.506 4.641 4.779 4.921 5.066 5.215 5.368 Period 5 5.101 5.204 5.309 5.416 5.526 5.637 5.867 6.105 6.353 6.610 6.877 7.154 7.442 Period 6 6.152 6.308 6.468 6.633 6.802 6.975 7.336 7.716 8.115 8.536 8.977 9.442 9.930 Period 7 7.214 7.434 7.662 7.898 8.142 8.394 8.923 9.487 10.089 10.730 11.414 12.142 12.916 Period 8 8.286 8.583 8.892 9.214 9.549 9.897 10.637 11.436 12.300 | 13.233 14.240 15.327 16.499 Period 9 9.369 9.755 10.159 10.583 11.027 11.491 12.488 13.579 14.776 16.085 17.519 19.086 20.799 Period 10 10.462 10.950 11.464 12.006 12.578 13.181 14.487 15.937 17.549 | 19.337 21.321 23.521 25.959 Period 11 11.567 12.169 12.808 13.486 14.207 14.972 14.972 16.645 16.645 18.531 20.655 23.045 25.733 28.755 32.150 Period 12 12.683 13.412 14.192 15.026 15.917 | 16.870 18.977 21.384 24.133 27.271 30.850 34.931 39.581 Period 13 13.809 14.680 15.618 16.627 17.713 18.882 21.495 24.523 28.029 | | 32.089 36.786 42.219 48.497 Period 14 14.94715.974 17.086 18.292 19.599 21.015 24 215 27.975 32.393 37.581 43.672 50.818 59.196 Period 15 16.09717.29318.599 20.024 21.579 23.276 27.152 31.772 37.280 43.842 51.660 60.965 72.035 Period 20 22.019 24.297 26.870 29.778 33.066 36.786 45.762 57.275 72.052 91.025 115.380 146.628 186.688 Period 25 28.243 32.030 36.459 41.646 47.727 54.865 73.106 98.347 133.334 181.871 249.214 342.603 471.981 Period 30 34.785 40.568 47.575 56.085 66.439 79.058 113.283 164.494 241.333 356.787 530.312 790.948 1,181.882 Period 40 48.886 60.402 75.401 95.026 120.800 154.762 259.057 442.593 767.091 1,342.025 2,360.757|4,163 213 7,343.858 Present Value of Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.862 0.847 Period 2 1.970 1.942 1.913 1.886 1.859 1.833 1.783 1.736 1.690 1.647 1.605 1.566 Period 3 2.941 2.884 2.829 2.775 2.723 2.673 2.577 2.487 2.402 2.322 2.246 2.174 Period 4 3.902 3.808 3.717 3.630 3.546 3.465 3.312 3.170 3.037 2.914 2.798 2.690 Period 5 4.853 4.713 4.580 4.452 4.329 4.2123.993 3.791 3.605 3.433 3.274 3.127 5.795 5.601 5.417 5.2425.076 4.917 4.623 4.355 4.111 3.8893.685 3.498 Period 7 6.728 6.472 6.230 6.002 5.786 5.5825.206 4.868 4.564 4.288 4.039 3.812 Period 8 7.652 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.9684.639 4.344 4.078 Period 9 8.566 8.162 7.786 7.435 7.108 6.8026.247 5.759 5.328 4.946 4.607 4.303 Period 10 9.471 8.9838.530 8.111 7.722 7.360 6.710 6.145 5.6505.216 4.833 4.494 Period 11 10.368 9.787 9.253 8.760 8.306 7.887 7.139 6.495 5.938 5.453 5.029 4.656 Period 12 11.255 10.575 9.9549.3858.863 8.384 7.536 6.814 6.194 5.660 5.197 4.793 Period 13 12.134 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 5.842 5.342 4.910 Period 14 13.004 12.106 11.296 10.563 9.899 9.295 8.244 7.3676.628 6.002 5.468 5.008 Period 15 13.865 12.849 11.938 11.118 10.380 9.712 8.559 7.606 6.811 6.142 5.575 5.092 Period 2018.046 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.4696.623 5.929 5.353 Period 25 22.023 19.523 17.413 15.622 14.094 12.783 10.675 9.077 7.8436.873 6.097 5.467 Period 30 25.808 22.396 19.600 17.292 15.372 13.765 11.258 9.4278.055 7.003 6.177 5.517 Period 40 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.7798.244 7.105 6.233 5.548 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.870 4.948 4.979 4.997 Future Value of $1 8% 1% 1.010 1.020 1.030 2% 1.020 1.040 1.061 1.082 3% 1.030 1.061 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 10% 1.100 1.210 1.331 1.464 1.611 1.080 1.166 1.260 1.360 12% 1.120 1.254 1.405 1.574 1.762 14% 1.140 1.300 1.482 1.689 1.925 18% 1.180 1.392 1.643 1.939 2.288 16% 1.160 1.346 1.561 1.811 2.100 20% 1.200 1.440 1.728 2.074 1.093 1.126 1.159 1.041 1.051 1.104 1.469 2.488 1.974 2.211 Periods Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 1.062 1.072 1.083 1.094 1.105 1.126 1.149 1.172 1.195 1.219 1.1941.265 1.340 1.230 1.316 1.407 1.267 1.369 1.477 1.305 1.423 1.551 1.344 1.480 1.629 1.419 1.504 1.594 1.689 1.791 1.587 1.772 1.714 1.949 1.851 2.144 1.999 2.358 2.159 2.594 2.195 2.502 2.853 3.252 3.707 2.436 2.826 3.278 3.803 2.476 2.773 3.106 2.700 3.185 3.759 4.435 5.234 2.986 3.583 4.300 5.160 6.192 Present Value of $1 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 20% Period 1 1 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 Period 2 0.980 0.961 0.943 0.925 0.907 0.890 0.8570.826 0.797 0.769 0.743 0.718 0.694 Period 3 0.971 0.942 0.915 0.889 0.864 0.840 0.794 0.751 0.712 0.712 0.675 0.641 0.609 0.579 Period 40.961 0.924 0.888 0.855 0.823 0.792 0.735 0.683 0.683 0.636 0.592 0.552 0.516 0.482 Period 5 0.951 0.906 0.863 0.863 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.476 0.437 0.402 Period 6 0.942 0.888 0.837 0.790 0.746 0.705 0.630 0.564 0.507 0.4560.410 0.370 0.335 Period 70.933 0.871 0.813 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.354 0.3140.279 Period 80.923 0.853 0.789 0.731 0.677 0.627 0.540 0.467 0.404 0.351 0.305 0.266 0.233 Period 9 0.914 0.837 0.766 0.703 0.645 0.6450.592 0.5920.500 0.424 0.361 0.308 0.263 0.225 0.194 Period 10 0.905 0.820 0.744 0.676 0.614 0.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 Period 110.896 0.8040.722 0.650 0.585 0.527 0.429 0.350 0.287 0.237 0.1950.162 0.135 Period 12 0.887 0.788 0.701 0.625 0.557 0.497 0.397 0.319 0.257 0.208 0.168 0.137 0.112 Period 13 0.879 0.773 0.681 0.601 0.530 0.469 0.368 0.290 0.229 0.182 0.145 0.116 0.093 Period 14 0.870 0.758 0.661 0.577 0.505 0.442 0.340 0.263 0.205 0.160 0.125 0.099 0.078 Period 15 0.861 0.743 0.642 0.555 0.481 0.417 0.315 0.239 0.183 0.140 0.315 0.239 0.183 0.140 0.108 0.084 0.065 Period 20 0.820 0.673 0.554 0.456 0.377 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 Period 25 0.780 0.610 0.478 0.375 0.295 0.233 0.146 0.092 0.059 0.038 0.024 0.0160.010 Period 30 0.742 0.552 0.412 0.308 0.231 0.174 0,099 0.057 0.033 0.020 0.012 0.007 0.004 Period 40 0.672 0.453 0.307 0.208 0.142 0.097 0.046 0.022 0.0110.005 0.003 0.001 0.001 4.411 1.116 1.127 1.138 1.243 1.384 1.268 1.426 1.294 1.469 1.319 1.513 1.346 1.558 1.539 1.601 1.665 1.732 1.801 1.710 1.898 1.796 2.012 1.886 2.133 1.980 2.261 2.079 2.397 2.332 2.518 2.720 2.937 3.172 2.853 3.138 3.452 3.797 4177 3.479 3.896 4.363 4.887 5.474 4.226 4.818 5.492 6.261 7.138 5.117 5.936 6.886 7.988 9.266 6.176 7.288 8.599 10.147 11.974 7.430 8.916 10.699 12.839 15.407 1.149 1.161 Period 20 Period 25 Period 30 Period 40 1.220 1.282 1.348 1.489 1.486 1.806 2.191 1.641 2.094 2.666 1.811 2.427 3.243 2.208 3.262 4.801 2.653 3.207 4.661 6.727 9.646 13.743 19.461 19.461 27.393 38.338 3.386 4.292 6.848 10.835 17.000 26.462 40.874 62.669 95.396 | 4.322 5.743 10.063 17.449 29.960 50.950 85.850 143.371 237.376 | 7.040 10.286 21.725 45.259 93.051 188.884 378.721 750.3781,469.772 - Requirements 1. How much out-of-pocket cash will you invest under the two options? 2. How much savings will you have accumulated at age 54 under the two options? 3. Explain the results 4. If you let the savings continue to grow for eight more years with no further out-of-pocket investments), under each scenario, what will the investment be worth when you are age 62