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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 $220,000 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 eam 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 present value table.) (Click the icon to view the future value annuity table.) (Click the icon to view the future value table.) To make your plan work answer the following questions: (Click the icon to view the questions.) 1. How much money must you accumulate by retirement? (Hint: Find the present value of the $220,000 withdrawals.) Calculate the present value to find out how much money must be acumulated by retirement. (Round your answer to the nearest whole dollar.) The present value is 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? Over the course of your retirement you will be withdrawing. However, by age 40 you only need to have invested Reference Present Value of Annuity of $1 Periods 1% 14% 16% 18% 20% Period 1 0.990 0.847 0.833 Period 2 1.970 1.528 Period 3 2.941 2.106 Period 4 3.902 2.589 Period 5 4.853 2.991 Period 6 3.326 5.795 6.728 Period 7 3.605 Period 8 7.652 4.344 4.078 3.837 Period 9 8.566 4.031 2% 3% 4% 5% 6% 8% 10% 12% 0.980 0.971 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.862 1.942 1.913 1.886 1.859 1.833 1.783 1.736 1.690 1.647 1.605 1.566 2.884 2.829 2.775 2.723 2.673 2.577 2.487 2.402 2.322 2.246 2.174 3.808 3.717 3.630 3.546 3.465 3.312 3.170 3.037 2.914 2.798 2.690 4.713 4.580 4.452 4.329 4.212 3.993 3.791 3.605 3.433 3.274 3.127 5.601 5.417 5.242 5.076 4.917 4.623 4.355 4.111 3.889 3.685 3.498 6.472 6.230 6.002 5.786 5.582 5.206 4.868 4.564 4.288 4.039 3.812 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.968 4.639 8.162 7.786 7.435 7.108 6.802 6.247 5.759 5.328 4.946 4.607 4.303 8.983 8.530 8.111 7.722 7.360 6.710 6.145 5.650 5.216 4.833 4.494 9.787 9.253 8.760 8.306 7.887 7.139 6.495 5.938 5.453 5.029 4.656 10.575 9.954 9.385 8.863 8.384 7.536 6.814 6.194 5.660 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 5.842 12.106 11.296 10.563 9.899 9.295 8.244 7.367 6.628 6.002 12.849 11.938 11.118 10.380 9.712 8.559 7.606 6.811 6.142 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.469 6.623 19.523 17.413 15.622 14.094 12.783 10.675 9.077 7.843 6.873 22.396 19.600 17.292 15.372 13.765 11.258 9.427 8.055 7.003 27.355 23.115 19.793 17.159 15.046 11.925 9.779 8.244 7.105 Period 10 9.471 4.192 Period 11 10.368 4.327 Period 12 11.255 5.197 4.793 4.439 Period 13 5.342 4.910 4.533 12.134 13.004 Period 14 5.468 5.008 4.611 Period 15 13.865 5.575 5.092 4.675 5.929 5.353 4.870 Period 20 18.046 Period 25 22.023 Period 30 25.808 Period 40 32.835 6.097 5.467 4.948 6.177 5.517 4.979 6.233 5.548 4.997 Print Done - X 3 Reference Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 20% Period 1 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.833 0.909 0.893 0.877 0.862 0.847 0.769 0.743 0.718 Period 2 0.980 0.961 0.890 0.857 0.826 0.694 0.943 0.925 0.907 0.797 0.915 0.889 0.864 0.840 0.794 0.751 0.712 Period 3 0.971 0.942 0.675 0.641 0.609 0.579 Period 4 0.961 0.924 0.888 0.482 Period 5 0.951 0.906 0.863 Period 6 0.942 0.888 0.837 0.790 Period 7 0.933 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.552 0.516 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.476 0.437 0.402 0.746 0.705 0.630 0.564 0.507 0.456 0.410 0.370 0.335 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.354 0.314 0.279 0.731 0.677 0.627 0.540 0.467 0.404 0.351 0.305 0.266 0.233 0.837 0.766 0.703 0.645 0.592 0.500 0.424 0.361 0.308 0.263 0.225 0.194 0.820 0.744 0.676 0.614 0.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 0.871 0.813 Period 8 0.923 0.853 0.789 Period 9 0.914 Period 10 0.905 Period 11 0.195 0.162 0.135 0.896 0.887 0.804 0.722 0.650 0.788 0.701 0.625 Period 12 0.208 0.168 0.137 0.112 0.182 0.145 0.116 0.093 Period 13 0.879 0.773 0.681 0.601 Period 14 0.870 0.758 0.661 0.160 0.125 0.099 0.078 Period 15 0.861 0.743 0.642 0.555 0.481 0.585 0.527 0.429 0.350 0.287 0.237 0.557 0.497 0.397 0.319 0.257 0.530 0.469 0.368 0.290 0.229 0.577 0.505 0.442 0.340 0.263 0.205 0.417 0.315 0.239 0.183 0.377 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 0.295 0.233 0.146 0.092 0.059 0.231 0.174 0.099 0.057 0.033 0.020 0.012 0.007 0.004 0.142 0.097 0.046 0.022 0.011 0.005 0.003 0.001 0.001 0.140 0.108 0.084 0.065 Period 20 0.820 0.673 0.554 0.456 Period 25 0.780 0.610 0.478 0.375 0.038 0.024 0.016 0.010 Period 30 0.742 0.552 0.412 0.308 Period 40 0.672 0.453 0.307 0.208 Print Done Present Value of $1 Reference 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 Period 20 Period 25 Period 30 Period 40 Future Value $1 14% 16% 20% 18% 1.140 1.160 1.180 1.200 1% 2% 3% 1.010 1.020 1.030 1.020 1.040 1.061 1.030 1.061 1.300 1.346 1.392 1.440 1.482 1.561 1.643 1.728 1.041 1.082 1.689 1.811 1.939 2.074 1.051 1.104 1.925 2.100 2.288 2.488 2.700 2.986 4% 5% 6% 8% 10% 12% 1.040 1.050 1.060 1.080 1.100 1.120 1.082 1.103 1.124 1.166 1.210 1.254 1.093 1.125 1.158 1.191 1.260 1.331 1.405 1.126 1.170 1.216 1.262 1.360 1.464 1.574 1.159 1.217 1.276 1.338 1.469 1.611 1.762 1.772 1.974 1.949 2.211 2.502 2.144 2476 2.853 1.999 2.358 2.773 3.252 3.803 2.159 2.594 3.106 2.332 2.853 3.479 3.138 3.896 4.818 3.452 4.363 5.492 1.062 1.126 1.194 1.265 1.340 1.419 1.587 1.072 1.149 1.230 1.316 1.407 1.504 1.714 1.083 1.172 1.267 1.369 1.477 1.594 1.851 1.094 1.195 1.305 1.423 1.551 1.689 1.105 1.219 1.344 1.480 1.629 1.791 2.195 2.436 2.826 3.278 3.759 3.185. 3.583 4.300 4.435 5.160 3.707 4.411 5.234 6.192 1.116 1.243 1.384 4.226 5.117 6.176 7.430 1.539 1.601 8.916 1.710 1.898 1.796 2.012 2.518 1.886 2.133 2.720 1.980 2.261 2.937 1.294 1.469 1.665 1.127 1.268 1.426 1.138 1.149 1.161 5.936 7.288 6.886 7.988 8.599 10.699 1.319 1.513 1.732 10.147 12.839 3.797 4.887 6.261 4.177 5.474 7.138 1.346 1.558 1.801 2.079 2.397 3.172 9.266 11.974 15.407 1.220 1.486 1.806 2.191 2.653 3.207 13.743 19.461 27.393 38.338 4.661 6.727 9.646 6.848 10.835 17.000 26.462 40.874 62.669 1.282 1.641 2.094 2.666 3.386 4.292 95.396 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 7.040 10.286 21.725 45.259 93.051 188.884 378.721 750.378 1,469.772 1.489 2.208 3.262 4.801 Print Done I X 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? Over the course of your retirement you will be withdrawing However, by age 40 you only need to have invested These numbers are different because: OA. You need to have the same accumulated as you will withdraw because you will not earn further interest on your investment when you reach retirement. OB. You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every year-the balance remains invested where it continues to earn 12% interest. OC. You need to have far less accumulated than what you will withdraw because you only withdraw a portion of the investment every year the balance remains invested where it continues to earn 12% interest. OD. None of the above. 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.) (Round your answer to the nearest whole dollar) For the first fifteen years, the amount you must pay into the investment each year is 4. How does the total out-of-pocket savings compare to the investment's value at the end of the 15-year savings period and the withdrawals you will make during retirement? (Use the investment rounded to the nearest whole number that you calculated above, then round your final answer to the nearest whole dollar.) The total out-of-pocket savings amounts to This is far than the amount of money you will than the investment's worth at the end of fifteen years and remarkably eventually withdraw from the investment