Assume you want to retire early at age 52. You plan to save using one of the following two strategies: (1) save $4,800 a year in an IRA beginning when you are 22 and ends when you are 52 (30 years) or (2) wait until you are 42 to start saving and then save $14,400 per year for the next 10 years. Assume you will earn the historic stock market average of 12% per year.

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.

Requirement 2:

How much savings will you have accumulated at age 52 under the two options?

Requirement 3:

Explain the results.

Requirement 4:

If you let the savings continue to grow for ten more years (with no further out-of-pocket investments), under each scenario, what will the investment be worth when you are age 62?

Periods 12% 1% 1.000 2.010 3.030 4.060 5.101 4% 1.000 2.040 3.122 4.246 5.416 16% 1.000 2.160 3.506 5.066 6.877 6.152 6.975 7.214 8.286 9.369 10.462 11.567 12.683 13.809 14.947 16.097 22.019 28.243 34.785 48.886 2% 1.000 2.020 3.060 4.122 5.204 6.308 7.434 8.583 9.755 10.950 12.169 13.412 14.680 15.974 17.293 24.297 32.030 40.568 60.402 3% 1.000 2.030 3.091 4.184 5.309 6.468 7.662 8.892 10.159 11.464 12.808 14.192 15.618 17.086 18.599 26.870 36.459 47.575 75.401 6.633 7.898 9.214 10.583 12.006 13.486 15.026 16.627 18.292 20.024 29.778 41.646 56.085 95.026 Future Value of Annuity of $1 5% 6% 8% 10% 1.000 1.000 1.000 1.000 2.050 2.060 2.080 2.100 3.153 3.184 3.246 3.310 4.310 4.375 4.506 4.641 5.526 5.637 5.867 6.105 6.802 7.336 7.716 8.142 8.394 8.923 9.487 9.549 9.897 10.637 11.436 11.027 11.491 12.488 13.579 12.578 13.181 14.487 15.937 14.207 14.972 16.645 18.531 15.917 16.870 18.977 21.384 17.713 18.882 21.495 24.523 19.599 21.015 24.215 27.975 21.579 23.276 27.152 31.772 33.066 36.786 45.762 57.275 47.727 54.865 73.106 98.347 66.439 79.058 113.283 164.494 120.800 154.762 259.057 442.593 14% 1.000 1.000 2.120 2.140 3.374 3.440 4.779 4.921 6.353 6.610 8.115 8.536 10.089 10.730 12.300 13.233 14.776 16.085 17.549 19.337 20.655 23.045 24.133 27.271 28.029 32.089 32.393 37.581 37.280 43.842 72.052 91.025 133.334 181.871 241.333356.787 767.091 1,342.025 8.977 11.414 14.240 17.519 21.321 25.733 30.850 36.786 43.672 51.660 115.380 249.214 530.312 2,360.757 18% 20% 1.000 1.000 2.180 2.200 3.572 3.640 5.215 5.368 7.154 7.442 9.442 9.930 12.142 12.916 15.327 16.499 19.086 20.799 23.521 25.959 28.755 32.150 34.931 39.581 42.219 48.497 50.818 59.196 60.965 72.035 146.628 186.688 342.603 471.981 790.948 1,181.882 4,163.213 7,343.858 Future Value of $1 Periods 14% 1% 1.010 1.020 1.030 2% 1.020 1.040 1.061 1.082 1.104 1.041 3% 1.030 1.061 1.093 1.126 1.159 1.194 1.230 1.267 1.305 1.344 1.051 1.062 1.072 1.083 1.094 1.105 5% 1.050 1.103 1.158 1.216 1.276 1.340 1.407 1.477 1.551 1.629 1.140 1.300 1.482 1.689 1.925 4% 1.040 1.082 1.125 1.170 1.217 1.265 1.316 1.369 1.423 1.480 1.539 1.601 1.665 1.732 1.801 2.191 2.666 3.243 4.801 6% 1.060 1.124 1.191 1.262 1.338 1.419 1.504 1.594 1.689 1.791 1.898 2.012 2.133 2.261 2.397 3.207 4.292 5.743 10.286 10% 1.100 1.210 1.331 1.464 1.611 1.772 1.949 2.144 2.358 2.594 8% 1.080 1.166 1.260 1.360 1.469 1.587 1.714 1.851 1.999 2.159 2.332 2.518 2.720 2.937 3.172 4.661 6.848 10.063 21.725 12% 1.120 1.254 1.405 1.574 1.762 1.974 2.211 2.476 2.773 3.106 1.126 1.149 1.172 1.195 1.219 18% 1.180 1.392 1.643 1.939 2.288 2.700 3.185 3.759 4.435 5.234 16% 1.160 1.346 1.561 1.811 2.100 2.436 2.826 3.278 3.803 4.411 5.117 5.936 6.886 7.988 9.266 19.461 40.874 85.850 378.721 2.195 2.502 2.853 3.252 3.707 20% 1.200 1.440 1.728 2.074 2.488 2.986 3.583 4.300 5.160 6.192 7.430 8.916 10.699 12.839 15.407 4.226 1.710 1.796 1.886 1.116 1.127 1.138 1.149 1.161 1.220 1.282 1.348 1.489 1.243 1.268 1.294 1.319 1.346 1.486 1.641 1.811 2.208 1.384 1.426 1.469 1.513 1.558 1.806 2.094 1.980 2.079 2.853 3.138 3.452 3.797 4.177 6.727 10.835 17.449 45.259 3.479 3.896 4.363 4.887 5.474 9.646 17.000 29.960 93.051 4.818 5.492 6.261 7.138 13.743 26.462 50.950 188.884 6.176 7.288 8.599 10.147 11.974 27.393 62.669 143.371 750.378 2.653 3.386 4.322 7.040 38.338 95.396 237.376 1,469.772 2.427 3.262 Periods 16% 0.862 1.605 2.246 2.798 3.274 18% 0.847 1.566 2.174 2.690 3.127 Present Value of Annuity of $1 1% 2% 3% 4% 5% 6% 8% 10% 12% 0.990 0.980 | 0.971 0.962 0.952 0.943 0.926 | 0.909 0.893 1.970 1.942 1.913 1.886 1.859 1.833 1.783 1.736 1.690 2.9412.884 2.829 2.775 2.723 2.673 2.577 2.487 | 2.402 3.902 3.808 3.717 3.630 | 3.546 3.465 3.312 3.170 | 3.037 4.853 4.713 4.580 4.452 | 4.329 4.212 3.993 3.791 3.605 5.795 5.601 5.417 5.242 5.076 4.917 4.623 4.355 4.111 6.728 6.472 6.230 6.002 5.786 5.582 5.206 4.868 4.564 7.652 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.968 8.566 8.162 7.786 7.435 7.108 6.802 6.247 5.759 5.328 9.471 8.530 8.111 7.722 7.360 6.710 6.145 5.650 10.368 9.787 9.253 8.760 8.306 7.887 7.139 6.495 5.938 11.255 10.575 9.954 9.385 8.863 8.384 7.536 6.814 6.194 12.134 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 13.004 12.106 11.296 10.563 9.899 9.295 8.244 7.367 6.628 13.865 12.849 11.938 11.118 10.380 9.712 8.559 7.606 6.811 18.046 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.469 22.023 19.523 17.413 | 15.622 14.094 | 12.783 | 10.675 9.077 25.808 22.396 19.600 17.292 15.372 13.765 11.258 9.427 8.055 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.7798.244 14% 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.623 6.873 7.003 7.105 3.685 4.039 4.344 4.607 4.833 5.029 5.197 5.342 5.468 5.575 3.498 3.812 4.078 4.303 4.494 4.656 4.793 4.910 5.008 5.092 5.353 5.467 5.517 5.548 20% 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.870 4.948 5.929 6.097 6.177 6.233 4.979 4.997 Periods 1% 0.990 0.980 0.971 0.961 0.951 0.942 0.933 2% 0.980 0.961 0.942 0.924 0.906 0.888 0.871 0.853 0.837 0.820 0.804 0.788 0.773 0.758 0.743 0.673 0.610 0.552 0.453 0.923 0.914 0.905 0.896 0.887 0.879 0.870 0.861 0.820 0.780 742 0.672 3% 4% 0.971 0.962 0.943 0.925 0.915 0.889 0.888 0.855 0.863 0.822 0.837 0.790 0.813 0.760 0.789 0.731 0.766 0.703 0.744 0.676 0.722 | 0.650 0.701 0.625 0.601 0.661 0.577 0.642 0.555 0.554 0.456 0.478 0.375 0.412 0.308 0.307 0.208 Present Value of $1 5% 6% 8% 10% 12% 14% 16% 0.952 0.943 0.926 0.909 0.893 0.877 0.862 0.907 0.890 0.857 0.826 0.797 0.769 0.743 0.864 0.840 0.794 0.751 0.712 0.675 0.641 0.823 0.792 0.735 0.683 0.636 0.592 0.552 0.784 0.747 0.681 0.621 0.567 | 0.519 0.476 | 0.746 0.705 0.630 0.564 0.507 0.456 0.410 0.711 0.665 0.583 0.513 0.452 0.400 0.354 | 0.677 0.627 0.540 0.467 | 0.404 0.351 0.305 0.645 0.592 0.500 0.424 0.361 0.308 0.263 0.614 0.558 0.463 0.386 0.322 | 0.270 0.227 0.585 0.527 0.429 0.350 0.287 | 0.237 0.195 0.557 0.497 0.397 0.319 0.257 0.208 | 0.168 0.530 0.469 0.368 0.290 0.229 0.182 0.145 0.505 0.442 0.340 0.263 0.205 0.125 0.481 0.417 0.315 0.239 0.183 0.140 | 0.108 0.377 0.312 0.215 0.149 0.104 0.073 0.051 0.295 0.233 0.146 0.092 0.059 0.038 0.024 0.231 0.174 0,099 0.057 0.033 0.020 0,012 0.142 0.097 0.046 0.022 0.011 0.005 0.003 18% 20% 0.847 0.833 0.7180.694 0.609 0.579 0.516 0.482 0.437 0.402 0.370 0.335 0.314 0.279 0.266 0.233 0.225 0.194 0.162 | 0.162 0.135 0.137 0.112 0.116 0.093 0.099 0.078 0.084 0.065 0.037 0.026 0.016 0.007 0.004 0.001 0.001 0.681 40