You are planning for an early retirement. You would like to retire at age 40 and have enough money saved to be able to draw $225,000 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 20 equal annual installments (from age 20 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 depleted when you are 80 years old. (Click the icon to view the present value annuity table.) (Click the icon to view the future value annuity table.) Present Value of Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 8% 10% Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.909 Period 2 1.970 1.942 1.913 1.886 1.859 1.833 1.783 1.736 Period 3 2.941 2.884 2.829 2.775 2.723 2.673 2.577 2.487 2.402 Period 4 3.902 3.808 3.717 3.630 3.546 3.465 3.170 3.037 Period 5 4.853 4.713 4.580 4.452 4.329 4.212 3.312 3.993 3.791 3.605 12% 14% 16% 18% 20% 0.893 0.877 0.862 0.847 0.833 1.690 1.647 1.605 1.566 1.528 2.322 2.246 2.914 2.798 2.690 2.589 3.433 3.274 3.127 2.991 2.174 2.106 Period 6 5 705 5.601 5417 5.242 5076 4 017 4623 4 355 A 111 3 889 3.685 3498 3326 Period 6 5.795 Period 7 6.728 Period 8 7.652 Period 9 8.566 Period 10 9.471 5.601 5.417 5.242 6.472 6.230 6.002 7.325 7.020 6.733 5.076 4.917 5.076 4.917 4.623 4.623 4.355 4.111 3.889 3.685 3.498 3.326 5.786 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 6.463 6.210 5.747 6.210 5.747 5.335 4.968 4.639 4.344 4.078 3.837 8.162 7.786 7.435 7.108 6.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 8.983 8.530 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 6.495 5.938 5.453 Period 12 11.255 10.575 9.954 9.385 8.863 8.384 8.384 7.536 7.536 6.814 6.194 6.814 6.194 5.660 5.029 5.197 4.793 4.656 4.327 4.439 Period 13 12.134 11.348 10.635 9.986 9.394 8.853 7.904 7.904 7.103 6.424 5.842 5.342 4.910 4.533 Period 11 12.001 12 106 11 206|10.562 0.900 0205 7.267 6.608 6002 5 168 5.008 1.611 Period 12 11.255 Period 13 12.134 Period 14 13.004 Period 15 13.865 Period 20 18.046 10.575 9.954 9.385 8.863 8.384 7.536 6.814 6.194 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 12.106 11.296 10.563 9.899 9.295 8.244 7.367 6.628 12.849 11.938 11.118 10.380 9.712 8.559 7.606 6.811 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.469 Period 25 22.023 19.523 17.413 15.622 14.094 12.783 10.675 9.077 7.843 Period 30 25.808 22.396 19.600 17.292 15.372 13.765 11.258 9.427 8.055 Period 40 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.779 8.244 5.660 5.197 4.793 4.439 5.842 5.342 4.910 4.533 6.002 5.468 5.008 4.611 6.142 5.575 5.092 4.675 6.623 5.929 5.353 4.870 6.873 6.097 6.177 5.467 4.948 5.517 4.979 5.548 4.997 7.003 7.105 6.233 Future Value of Annuity of $1 Periods Period 1 Period 2 1% 2% 3% 4% 2.010 1.000 1.000 1.000 2.020 2.030 Period 3 3.030 3.060 3.091 3.122 3.153 5% 6% 1.000 1.000 1.000 2.040 2.050 2.060 3.184 8% 1.000 10% 12% 14% 16% 18% 20% 1.000 1.000 1.000 1.000 1.000 1.000 2.080 2.100 2.120 2.140 2.160 2.180 2.200 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 5 5.101 5.204 5.309 5.416 5.526 5.637 Period 6 Period 7 Period 8 Period 9 6.152 6.308 6.468 6.633 6.802 7.214 7.434 7.662 7.898 8.142 5.867 6.975 7.336 7.716 8.115 8.536 8.394 8.923 9.487 10.089 10.730 6.105 6.353 6.610 6.877 7.154 7.442 8.977 9.442 9.930 11.414 12.142 12.916 8.286 8.583 8.892 9.214 9.549 9.369 9.755 10.159 10.583 11.027 Period 10 10.462 10.950 11.464 12.006 Period 11 Period 12 12.578 11.567 12.169 12.808 13.486 14.207 14.972 12.683 13.412 14.192 15.026 15.917 16.870 9.897 10.637 11.436 12.300 11.491 12.488 13.579 14.776 13.181 14.487 15.937 17.549 16.645 18.531 20.655 18.977 21.384 24.133 13.233 14.240 15.327 16.085 19.337 16.499 17.519 19.086 21.321 23.521 20.799 25.959 23.045 25.733 28.755 32.150 27.271 30.850 34.931 39.581 Period 12 12.683 13.412 14.192 15.026 15.917 16.870 18.977 21.384 24.133 Period 13 13.809 14.680 15.618 16.627 17.713 18.882 21.495 24.523 28.029 Period 14 14.947 15.974 17.086 18.292 19.599 21.015 24.215 27.975 32.393 Period 15 16.097 17.293 18.599 20.024 21.579 23.276 27.152 31.772 37.280 27.271 30.850 32.089 37.581 34.931 39.581 36.786 42.219 48.497 43.672 50.818 59.196 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 $1 Periods 1% 2% 3% 4% Period 1 0.990 0.980 Period 2 0.980 0.961 Period 3 0.971 0.971 0.962 0.943 0.925 0.942 0.915 0.889 0.907 0.864 0.840 Period 4 0.961 Period 5 0.951 0.924 0.906 0.863 0.888 0.855 0.823 0.792 0.822 0.784 0.747 5% 6% 8% 10% 12% 14% 16% 18% 20% 0.952 0.943 0.926 0.909 0.893 0.890 0.857 0.826 0.797 0.794 0.751 0.712 0.735 0.683 0.636 0.681 0.621 0.567 0.519 0.476 0.437 0.877 0.862 0.847 0.833 0.769 0.743 0.718 0.694 0.675 0.641 0.609 0.579 0.592 0.552 0.516 0.482 0.402 Period 6 0942 0888 0.837 0790 0746 0.705 0.630 0.564 0.507 0456 0410 0.370 0.335 Period 6 0.942 Period 7 0.933 Period 8 0.923 0.888 0.837 0.790 0.746 0.871 0.813 0.760 0.711 0.853 0.789 0.731 0.677 Period 9 0.914 0.837 0.766 0.703 0.645 Period 10 0.905 0.820 0.744 0.676 Period 11 0.896 0.804 0.722 0.650 Period 12 0.887 0.788 0.701 0.625 Period 13 0.879 0.773 0.681 0.601 0.540 0.467 0.404 0.351 0.305 0.266 0.233 0.500 0.424 0.361 0.308 0.263 0.225 0.194 0.463 0.386 0.322 0.270 0.227 0.191 0.162 0.585 0.527 0.429 0.350 0.287 0.237 0.557 0.497 0.397 0.319 0.257 0.208 0.530 0.469 0.368 0.290 0.229 0.182 0.705 0.630 0.564 0.507 0.456 0.410 0.370 0.335 0.665 0.583 0.513 0.452 0.400 0.354 0.314 0.279 0.627 0.592 0.614 0.558 0.195 0.162 0.135 0.168 0.137 0.112 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 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 Period 14 0.870 0.758 0.661 Period 15 0.861 0.743 0.577 0.642 0.555 0.481 0.505 0.442 0.340 0.417 0.315 0.263 0.239 0.229 0.182 0.145 0.205 0.160 0.125 0.099 0.078 0.183 0.140 0.108 0.084 0.065 0.116 0.093 Period 20 0.820 0.673 0.554 Period 25 0.780 0.610 Period 30 0.742 0.552 0.412 0.308 Period 40 0.672 0.453 0.307 0.208 0.456 0.377 0.478 0.375 0.295 0.231 0.142 0.312 0.215 0.149 0.233 0.146 0.092 0.174 0.099 0.057 0.097 0.046 0.022 0.104 0.073 0.051 0.037 0.026 0.059 0.038 0.024 0.016 0.010 0.033 0.020 0.012 0.007 0.004 0.011 0.005 0.003 0.001 0.001 Future Value of $1 Periods 1% 2% 3% 4% 5% 6% Period 1 1.010 1.020 1.030 1.040 1.050 Period 2 1.020 1.040 1.061 1.082 1.103 1.124 1.166 8% 10% 12% 14% 1.060 1.080 1.100 1.120 1.140 1.160 1.210 1.254 1.300 1.346 16% 18% 20% 1.180 1.200 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 Period 5 1.051 1.104 1.159 1.217 1.276 1.338 1.360 1.464 1.574 1.689 1.469 1.611 1.762 1.925 1.811 1.939 2.074 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 2195 2436 2 700 2986 renou 1.002 1.120 1.134 1.203 1.340 1.419 Period 7 1.072 1.149 1.230 Period 8 1.083 1.172 1.267 Period 9 1.094 1.195 1.305 1.423 Period 10 1.105 1.219 1.344 1.480 1.629 1.791 1.914 1.316 1.407 1.504 1.714 1.949 2.211 1.369 1.477 1.594 1.851 2.144 2.476 1.551 1.689 1.999 2.358 2.773 2.159 2.594 3.106 1.307 1.112 2.199 2.430 2.700 2.900 2.502 2.826 3.185 2.853 3.278 3.759 3.252 3.803 4.435 3.707 4.411 5.234 6.192 3.583 4.300 5.160 Period 11 1.116 1.243 1.384 1.539 Period 12 1.127 1.268 1.426 1.601 1.710 1.898 1.796 2.012 2.332 2.853 3.479 4.226 5.117 6.176 7.430 Period 13 1.138 1.294 1.469 1.665 Period 14 1.149 1.319 1.513 1.732 2.518 3.138 3.896 4.818 1.886 2.133 2.720 3.452 4.363 1.980 2.261 2.937 3.797 4.887 5.936 7.288 8.916 5.492 6.886 8.599 10.699 6.261 7.988 10.147 12.839 Period 12 1.127 1.268 1.426 Period 13 1.138 1.294 1.469 1.665 Period 14 1.149 1.319 1.513 1.732 Period 15 1.161 1.346 1.558 1.801 1.601 1.796 2.012 2.518 3.138 3.896 4.818 1.886 2.133 2.720 3.452 4.363 5.492 1.980 2.261 2.937 3.797 4.887 6.261 2.079 2.397 3.172 4.177 5.474 7.138 5.936 7.288 8.916 6.886 8.599 7.988 10.147 12.839 9.266 11.974 15.407 10.699 Period 20 1.220 1.486 1.806 2.191 Period 25 1.282 1.641 2.094 2.666 Period 30 1.348 1.811 2.427 3.243 Period 40 1.489 2.208 3.262 4.801 2.653 3.207 4.661 6.727 9.646 13.743 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 93.051 188.884 378.721 750.378 1,469.772 1. How much money must you accumulate by retirement? (Hint: Find the present value of the $225,000 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 twenty 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 twenty-year savings period and the withdrawals you will make during retirement