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 draw $210,000 per year for the next 40 years (based on family history, you think you'll live to age 80 ). You plan to save for retirement by making 15 equal annual installments (from age 25 to age 40 ) into a fairly risky investment fund that you expect will earn 12% per year. You will leave the money in this fund until it is completely depleten are 80 years old. (Click the icon to view the present value annuity table.) (Click the icon to view the future value annuity table.) (Click the icon to view the present value table.) (Click the icon to view the future value table.) To make your plan work answer the following questions: \begin{tabular}{l} \hline \multicolumn{10}{|c|}{ Present Value of Annuity of \$1 } \\ \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 \\ \hline \end{tabular} \end{tabular} \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|} 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 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Period 11 & 10.368 & y.181 & y.253 & 8.160 & 8.306 & 1.881 & 1.139 & 6.495 & 5.938 & 5.453 & 5.029 & 4.656 & 4.321 \\ 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 & 4.979 \\ 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} Present Value of $1 \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l||} \hline 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 \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline Period 11 & 0.896 & 0.804 & 0.122 & 0.650 & 0.585 & 0.521 & 0.429 & 0.350 & 0.281 & 0.231 & 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} Future Value of $1 \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 & 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 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Period 11 & 1.116 & 1.243 & 1.384 & 1.539 & 1.110 & 1.898 & 2.332 & 2.853 & 3.4/4 & 4.226 & 5.117 & 6.1/6 & 1.430 \\ 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} 1. How much money must you accumulate by retirement? (Hint: Find the present value of the $210,000 withdrawals.) 2. How does this amount compare to the total amount you will draw out of the investment during retirement? How can these numbers be so different? 3. How much must you pay into the investment each year for the first fifteen years? (Hint: Your answer from Requirement 1 becomes the future value of this annuity.) 4. How does the total out-of-pocket savings compare to the investment's value at the end of the 15-year savings perioc and the withdrawals you will make during retirement