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 $225,000 per year for the next 30 years (based on family history, you think you'll live to age 70). You plan to save for retirement by making 10 equal annual installments (from age 30 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 70 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: (Click the icon to view the questions.) 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: O A. You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every yearthe balance remains invested where it continues to earn 12% interest. O B. You need to have far less accumulated than what you will withdraw because you only withdraw a portion of the investment every yearthe balance remains invested where it continues to earn 12% interest. O C. 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. D. None of the above. 3. How much must you pay into the investment each year for the first ten 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 ten 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 10-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 than the amount of money you will eventually withdraw This is far than the investment's worth at the end of ten years and remarkably from the investment. 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 ten 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 10-year savings period and the withdrawals you will make during retirement? Present Value of Annuity of $1 Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 0.990 0.980 0.971 0.962 0.9520.943 0.926 0.909 0.893 0.877 0.862 1.970 1.942 1.9131.886 1.859 1.833 1.783 1.736 1.690 1.647 1.605 2.941 2.884 2.829 2.775 2.723 2.673 2.577 2.487 2.4022.322 2.246 3.902 3.808 3.717 3.630 3.546 3.465 3.312 3.170 3.037 2.914 2.798 4.853 4.713 4.580 4.452 4.329 4.2123.993 3.791 3.605 3.433 3.274 18% 0.847 1.566 2.174 2.690 3.127 20% 0.833 1.528 2.106 2.589 2.991 Period 6 5.795 5.601 5.417 5.242 5.076 4.917 4.623 4.355 4.111 3.889 Period 7 6.728 6.472 6.230 6.002 5.786 5.582 5.206 4.868 4.564 4.288 Period 8 7.652 7.3257.020 6.733 6.463 6.210 5.747 5.335 4.9684.639 Period 9 8.566 8.1627.786 7.4357.108 6.8026.247 5.759 5.328 4.946 Period 10 9.471 8.983 8.530 8.111 7.722 7.360 6.710 6.145 5.6505.216 3.685 3.498 4.039 3.812 4.344 4.078 4.607 4.303 4.833 4.494 3.326 3.605 3.837 4.031 4.192 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 9.9869.394 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 9.7128.559 7.606 6.811 5.453 5.660 5.842 6.002 6.142 5.029 4.656 5.197 4.793 5.342 4.910 5.468 5.008 5.575 5.092 4.327 4.439 4.533 4.611 4.675 Period 20 18.046 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.469 6.623 Period 25 22.023 19.523 17.413 15.622 14.094 12.783 10.675 9.077 7.843 6.873 Period 30 25.808 22.396 19.600 17.292 | 15.372 13.765 11.258 9.427 8.055 7.003 Period 40 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.779 8.244 7.105 5.929 6.097 6.177 6.233 5.353 5.467 5.517 5.548 4.870 4.948 4.979 4.997 Present Value of $1 Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 0.990 0.980 0.971 0.961 0.951 2% 0.980 0.961 0.942 0.924 0.906 3% 0.971 0.943 0.915 0.888 0.863 4% 0.962 0.925 0.889 0.855 0.822 5% 0.952 0.907 0.864 0.823 0.784 6% 0.943 0.890 0.840 0.792 0.747 8% 0.926 0.857 0.794 0.735 0.681 10% 0.909 0.826 0.751 0.683 0.621 12% 0.893 0.797 0.712 0.636 0.567 14% 0.877 0.769 0.675 0.592 0.519 16% 0.862 0.743 0.641 0.552 0.476 18% 0.847 0.718 0.609 0.516 0.437 20% 0.833 0.694 0.579 0.482 0.402 Period 6 0.942 Period 7 0.933 Period 8 0.923 Period 9 0.914 Period 10 0.905 0.888 0.871 0.853 0.837 0.820 0.837 0.813 0.789 0.766 0.744 0.790 0.760 0.731 0.703 0.676 0.746 0.711 0.677 0.645 0.614 0.705 0.665 0.627 0.592 0.558 0.630 0.583 0.540 0.500 0.463 0.564 0.513 0.467 0.424 0.386 0.507 0.452 0.404 0.361 0.322 0.456 0.400 0.351 0.308 0.270 0.410 0.354 0.305 0.263 0.227 0.370 0.314 0.266 0.225 0.191 0.335 0.279 0.233 0.194 0.162 Period 110.896 Period 12 0.887 Period 13 0.879 Period 14 0.870 Period 15 0.861 0.804 0.788 0.773 0.758 0.743 0.722 0.701 0.681 0.661 0.642 0.650 0.625 0.601 0.577 0.555 0.585 0.557 0.530 0.505 0.481 0.527 0.497 0.469 0.442 0.417 0.429 0.397 0.368 0.340 0.315 0.350 0.319 0.290 0.263 0.239 0.287 0.257 0.229 0.205 0.183 0.237 0.208 0.182 0.160 0.140 0.195 0.168 0.145 0.125 0.108 0.162 0.137 0.116 0.099 0.084 0.135 0.112 0.093 0.078 0.065 Period 20 0.820 Period 25 0.780 Period 30 0.742 Period 40 0.672 0.673 0.610 0.552 0.453 0.554 0.478 0.412 0.307 0.456 0.375 0.308 0.208 0.377 0.295 0.231 0.142 0.312 0.233 0.174 0.097 0.215 0.146 0.099 0.046 0.149 0.092 0.057 0.022 0.104 0.059 0.033 0.011 0.073 0.038 0.020 0.005 0.051 0.024 0.012 0.003 0.037 0.016 0.007 0.001 0.026 0.010 0.004 0.001 Future Value of $1 2% 3% 4% 5% Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 1.010 1.020 1.030 1.041 1.051 1.020 1.040 1.061 1.082 1.104 1.030 1.061 1.093 1.126 1.159 1.040 1.082 1.125 1.170 1.217 1.050 1.103 1.158 1.216 1.276 6% 1.060 1.124 1.191 1.262 1.338 8% 1.080 1.166 1.260 1.360 1.469 10% 1.100 1.210 1.331 1.464 1.611 12% 1.120 1.254 1.405 1.574 1.762 14% 1.140 1.300 1.482 1.689 1.925 16% 1.160 1.346 1.561 1.811 2.100 18% 1.180 1.392 1.643 1.939 2.288 20% 1.200 1.440 1.728 2.074 2.488 Period 6 Period 7 Period 8 Period 9 Period 10 1.062 1.072 1.083 1.094 1.105 1.126 1.149 1.172 1.195 1.219 1.194 1.230 1.267 1.305 1.344 1.265 1.316 1.369 1.423 1.480 1.340 1.407 1.477 1.551 1.629 1.419 1.504 1.594 1.689 1.791 1.587 1.714 1.851 1.999 2.159 1.772 1.949 2.144 2.358 2.594 1.974 2.211 2.476 2.773 3.106 2.195 2.502 2.853 3.252 3.707 2.436 2.826 3.278 3.803 4.411 2.700 3.185 3.759 4.435 5.234 2.986 3.583 4.300 5.160 6.192 Period 11 Period 12 Period 13 Period 14 Period 15 1.116 1.127 1.138 1.149 1.161 1.243 1.268 1.294 1.319 1.346 1.384 1.426 1.469 1.513 1.558 1.539 1.601 1.665 1.732 1.801 1.710 1.796 1.886 1.980 2.079 1.898 2.012 2.133 2.261 2.397 2.332 2.518 2.720 2.937 3.172 2.853 3.138 3.452 3.797 4.177 3.479 3.896 4.363 4.887 5.474 4.226 4.818 5.492 6.261 7.138 5.117 5.936 6.886 7.988 9.266 6.176 7.288 8.599 10.147 11.974 7.430 8.916 10.699 12.839 15.407 Period 20 Period 25 Period 30 Period 40 1.220 1.282 1.348 1.489 1.486 1.641 1.811 2.208 1.806 2.094 2.427 3.262 2.191 2.666 3.243 4.801 2.653 3.386 4.322 7.040 3.207 4.292 5.743 10.286 4.661 6.727 9.646 13.743 19.461 27.393 38.338 6.848 10.835 17.000 26.462 40.874 62.669 95.396 10.063 17.449 29.960 50.950 85.850 143.371 237.376 21.725 45.259 93.051 188.884 378.721 750.378|1,469.772