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 $215,000 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 14% 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.) To make your plan work answer the following questions: (Click the icon to view the questions.) (Click the icon to view the future value annuity table.) (Click the icon to view the future value table.) Reference Reference Present Value of Annuity of $1 Future Value of $1 Periods 1% 2% 3% 4% Period 1 0.990 0.980 0.971 0.962 Period 2 1.970 1.942 1.913 1.886 Period 3 2.941 2.884 2.829 2.775 Period 4 3.902 3.808 3.717 3.630 Period 5 4.853 4.713 4.580 4.452 Period 6 5.795 Period 7 6.728 5% 6% 8% 10% 12% 14% 0.952 0.943 0.926 0.909 0.893 0.877 1.859 1.833 1.783 1.736 1.690 1.647 2.723 2.673 2.577 2.487 2.402 2.322 3.546 3.465 3.312 3.170 3.037 2.914 4.329 4.212 3.993 3.791 3.605 3.433 16% 18% 20% 0.862 0.847 0.833 1.605 1.566 Periods 1% 2% 5% 1.528 Period 1 Period 2 2.246 2.174 2.106 2.798 Period 3 2.690 2.589 Period 4 3.274 3.127 2.991 Period 5 5.601 5.417 5.242 5.076 4.917 4.623 4.355 4.111 6.472 6.230 6.002 5.786 5.582 5.206 4.868 4.564 Period 8 7.652 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.968 Period 9 8.566 8.162 7.786 7.435 7.108 6.802 6.247 5.759 5.328 Period 10 9.471 8.983 8.530 8.111 7.722 7.360 6.710 6.145 5.650 Period 11 10.368 9.787 9.253 8.760 8.306 7.887 7.139 6.495 5.938 Period 12 11.255 10.575 9.954 9.385 8.863 8.384 7.536 6.814 6.194 Period 13 12.134 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 Period 14 13.004 12.106 11.296 10.563 9.899 9.295 8.244 7.367 6.628 Period 15 13.865 12.849 11.938 11.118 10.380 9.712 8.559 7.606 6.811 Period 20 18.046 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 3.889 3.685 3.498 3.326 Period 6 4.288 4.039 3.812 3.605 Period 7 4.639 4.344 4.078 3.837 Period 8 4.946 4.607 4.303 4.031 Period 9 5.216 4.833 4.494 4.192 Period 10 5.453 5.029 4.656 4.327 Period 11 5.660 5.197 4.793 4.439 Period 12 5.842 5.342 4.910 4.533 6.002 6.142 5.468 5.008 4.611 5.575 5.092 4.675 6.623 6.873 7.003 7.105 5.929 5.353 4.870 6.097 5.467 4.948 6.177 5.517 4.979 6.233 5.548 4.997 3% 4% 6% 8% 10% 12% 14% 16% 18% 20% 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 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 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 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 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 1.062 1.126 1.194 1.265 1.340 1.419 1.587 1.772 1.974 2.195 2.436 2.700 1.072 1.149 1.230 1.316 1.407 1.504 1.714 1.949 2.211 2.502 2.826 3.185 1.083 1.172 1.267 1.369 1.477 1.594 1.851 2.144 2.476 2.853 3.278 3.759 1.094 1.195 1.305 1.423 1.551 1.689 1.999 2.358 2.773 3.252 3.803 4.435 1.105 1.219 1.344 1.480 1.629 1.791 2.159 2.594 3.106 3.707 4.411 5.234 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 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 2.986 3.583 4.300 5.160 6.192 Present Value of $1 Periods 1% 2% 3% Period 1 0.990 0.980 0.971 0.961 0.943 5% 0.952 Period 7 0.933 4% 0.962 0.877 0.862 0.847 0.833 Period 2 0.980 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 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 Period 30 0.742 0.552 0.412 0.308 0.231 0.174 0.099 0.057 0.033 0.020 0.012 Period 40 0.672 0.453 0.307 0.208 6% 8% 0.943 0.926 10% 12% 0.909 0.893 14% 16% 18% 20% erent? 0.016 0.010 0.142 0.097 0.046 0.022 0.011 0.005 0.003 0.007 0.004 0.001 0.001 More info 1. How much money must you accumulate by retirement? (Hint: Find the present value of the $215,000 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 period and the withdrawals you will make during retirement? Print Done - 1. How much money must you accumulate by retirement? (Hint: Find the present value of the $215,000 withdrawals.) Calculate the present value to find out how much money must be accumulated 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 These numbers are different because: A. 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 14% interest. B. 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. C. 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 14% interest. D. 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 investment's worth at the end of fifteen years and remarkably than the amount of money you will eventually withdraw from the investment