Assume you want to retire early at age 52 . You plan to save using one of the following two strategies: (1) save $3,900 a year in an IRA beginning when you are 22 and ending when you are 52 (30 years) or (2) wait until you are 37 to start saving and then save $7,800 per y for the next 15 years. Assume you will earn the historic stock market average of 14% per year. (Click the icon to view the future value annuity factor table.) (Click the icon to view the future value factor table.) (Click the icon to view the present value annuity factor table.) Click the icon to view the present value factor table.) Read the requirements. 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: \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{10}{|c|}{ Future Value of \$1 } \\ \hline Periods & 1% & 2% & 3% & 4% & 5% & 6% & 8% & 10% & 12% & 14% & 16% & 18% & 20% \\ \hline Period 1 & 1.010 & 1.020 & 1.030 & 1.040 & 1.050 & 1.060 & 1.080 & 1.100 & 1.120 & 1.140 & 1.160 & 1.180 & 1.200 \\ Period 2 & 1.020 & 1.040 & 1.061 & 1.082 & 1.103 & 1.124 & 1.166 & 1.210 & 1.254 & 1.300 & 1.346 & 1.392 & 1.440 \\ Period 3 & 1.030 & 1.061 & 1.093 & 1.125 & 1.158 & 1.191 & 1.260 & 1.331 & 1.405 & 1.482 & 1.561 & 1.643 & 1.728 \\ Period 4 & 1.041 & 1.082 & 1.126 & 1.170 & 1.216 & 1.262 & 1.360 & 1.464 & 1.574 & 1.689 & 1.811 & 1.939 & 2.074 \\ Period 5 & 1.051 & 1.104 & 1.159 & 1.217 & 1.276 & 1.338 & 1.469 & 1.611 & 1.762 & 1.925 & 2.100 & 2.288 & 2.488 \\ Period 6 & 1.062 & 1.126 & 1.194 & 1.265 & 1.340 & 1.419 & 1.587 & 1.772 & 1.974 & 2.195 & 2.436 & 2.700 & 2.986 \\ Period 7 & 1.072 & 1.149 & 1.230 & 1.316 & 1.407 & 1.504 & 1.714 & 1.949 & 2.211 & 2.502 & 2.826 & 3.185 & 3.583 \\ Period 8 & 1.083 & 1.172 & 1.267 & 1.369 & 1.477 & 1.594 & 1.851 & 2.144 & 2.476 & 2.853 & 3.278 & 3.759 & 4.300 \\ Period 9 & 1.094 & 1.195 & 1.305 & 1.423 & 1.551 & 1.689 & 1.999 & 2.358 & 2.773 & 3.252 & 3.803 & 4.435 & 5.160 \\ Period 10 & 1.105 & 1.219 & 1.344 & 1.480 & 1.629 & 1.791 & 2.159 & 2.594 & 3.106 & 3.707 & 4.411 & 5.234 & 6.192 \\ Period 11 & 1.116 & 1.243 & 1.384 & 1.539 & 1.710 & 1.898 & 2.332 & 2.853 & 3.479 & 4.226 & 5.117 & 6.176 & 7.430 \\ Period 12 & 1.127 & 1.268 & 1.426 & 1.601 & 1.796 & 2.012 & 2.518 & 3.138 & 3.896 & 4.818 & 5.936 & 7.288 & 8.916 \\ Period 13 & 1.138 & 1.294 & 1.469 & 1.665 & 1.886 & 2.133 & 2.720 & 3.452 & 4.363 & 5.492 & 6.886 & 8.599 & 10.699 \\ Period 14 & 1.149 & 1.319 & 1.513 & 1.732 & 1.980 & 2.261 & 2.937 & 3.797 & 4.887 & 6.261 & 7.988 & 10.147 & 12.839 \\ Period 15 & 1.161 & 1.346 & 1.558 & 1.801 & 2.079 & 2.397 & 3.172 & 4.177 & 5.474 & 7.138 & 9.266 & 11.974 & 15.407 \\ Period 20 & 1.220 & 1.486 & 1.806 & 2.191 & 2.653 & 3.207 & 4.661 & 6.727 & 9.646 & 13.743 & 19.461 & 27.393 & 38.338 \\ Period 25 & 1.282 & 1.641 & 2.094 & 2.666 & 3.386 & 4.292 & 6.848 & 10.835 & 17.000 & 26.462 & 40.874 & 62.669 & 95.396 \\ Period 30 & 1.348 & 1.811 & 2.427 & 3.243 & 4.322 & 5.743 & 10.063 & 17.449 & 29.960 & 50.950 & 85.850 & 143.371 & 237.376 \\ Period 40 & 1.489 & 2.208 & 3.262 & 4.801 & 7.040 & 10.286 & 21.725 & 45.259 & 93.051 & 188.884 & 378.721 & 750.378 & 1.469 .772 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Periods & 1% & 2% & 3% & 4% & 5% & 6% & 8% & 10% & 12% & 14% & 16% & 18% & 20% \\ \hline 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 & 0.833 \\ 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 & 1.528 \\ 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 & 2.106 \\ 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 & 2.589 \\ Period 5 & 4.853 & 4.713 & 4.580 & 4.452 & 4.329 & 4.212 & 3.993 & 3.791 & 3.605 & 3.433 & 3.274 & 3.127 & 2.991 \\ Period 6 & 5.795 & 5.601 & 5.417 & 5.242 & 5.076 & 4.917 & 4.623 & 4.355 & 4.111 & 3.889 & 3.685 & 3.498 & 3.326 \\ Period 7 & 6.728 & 6.472 & 6.230 & 6.002 & 5.786 & 5.582 & 5.206 & 4.868 & 4.564 & 4.288 & 4.039 & 3.812 & 3.605 \\ Period 8 & 7.652 & 7.325 & 7.020 & 6.733 & 6.463 & 6.210 & 5.747 & 5.335 & 4.968 & 4.639 & 4.344 & 4.078 & 3.837 \\ Period 9 & 8.566 & 8.162 & 7.786 & 7.435 & 7.108 & 6.802 & 6.247 & 5.759 & 5.328 & 4.946 & 4.607 & 4.303 & 4.031 \\ Period 10 & 9.471 & 8.983 & 8.530 & 8.111 & 7.722 & 7.360 & 6.710 & 6.145 & 5.650 & 5.216 & 4.833 & 4.494 & 4.192 \\ 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 & 4.327 \\ Period 12 & 11.255 & 10.575 & 9.954 & 9.385 & 8.863 & 8.384 & 7.536 & 6.814 & 6.194 & 5.660 & 5.197 & 4.793 & 4.439 \\ 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 & 4.533 \\ Period 14 & 13.004 & 12.106 & 11.296 & 10.563 & 9.899 & 9.295 & 8.244 & 7.367 & 6.628 & 6.002 & 5.468 & 5.008 & 4.611 \\ 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 & 4.675 \\ Period 20 & 18.046 & 16.351 & 14.877 & 13.590 & 12.462 & 11.470 & 9.818 & 8.514 & 7.469 & 6.623 & 5.929 & 5.353 & 4.870 \\ Period 25 & 22.023 & 19.523 & 17.413 & 15.622 & 14.094 & 12.783 & 10.675 & 9.077 & 7.843 & 6.873 & 6.097 & 5.467 & 4.948 \\ Period 30 & 25.808 & 22.396 & 19.600 & 17.292 & 15.372 & 13.765 & 11.258 & 9.427 & 8.055 & 7.003 & 6.177 & 5.517 \\ Period 40 & 32.835 & 27.355 & 23.115 & 19.793 & 17.159 & 15.046 & 11.925 & 9.779 & 8.244 & 7.105 & 6.233 & 5.548 & 4.997 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{10}{|c|}{ Present Value of \$1 } \\ \hline Periods & 1% & 2% & 3% & 4% & 5% & 6% & 8% & 10% & 12% & 14% & 16% & 18% & 20% \\ \hline 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 & 0.833 \\ Period 2 & 0.980 & 0.961 & 0.943 & 0.925 & 0.907 & 0.890 & 0.857 & 0.826 & 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 & 0.675 & 0.641 & 0.609 & 0.579 \\ Period 4 & 0.961 & 0.924 & 0.888 & 0.855 & 0.823 & 0.792 & 0.735 & 0.683 & 0.636 & 0.592 & 0.552 & 0.516 & 0.482 \\ Period 5 & 0.951 & 0.906 & 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 & 0.456 & 0.410 & 0.370 & 0.335 \\ Period 7 & 0.933 & 0.871 & 0.813 & 0.760 & 0.711 & 0.665 & 0.583 & 0.513 & 0.452 & 0.400 & 0.354 & 0.314 & 0.279 \\ Period 8 & 0.923 & 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 & 0.592 & 0.500 & 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 11 & 0.896 & 0.804 & 0.722 & 0.650 & 0.585 & 0.527 & 0.429 & 0.350 & 0.287 & 0.237 & 0.195 & 0.162 & 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 & 0.108 & 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 & 0.016 & 0.010 \\ 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 & 0.011 & 0.005 & 0.003 & 0.001 & 0.001 \\ \hline \end{tabular} 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 52 under the two options? 3. Explain the results. 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
