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 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 future value annuity table) in the present value annuity table) Future Value of $1 Periods 1 2 3 1% 1.010 1.020 1.030 1.041 1.051 2% 1.020 1.040 1.061 1.082 1.104 3% 1.030 1.061 1.093 1.126 1.159 49 1.040 1.082 1.125 1.170 1.217 5% 1.050 1.103 1.158 1.216 1.276 69 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 4 5 6 7 8 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 9 10 11 12 13 14 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 20 25 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 3.207 4.292 5.743 10.286 4.661 6.848 10.063 21.725 6.727 10.835 17.449 45.259 9.646 17.000 29.960 93.051 13.743 26.462 50.950 188.884 19.461 40.874 85.850 378.721 27.393 38.338 62.669 95.396 143.371 237.376 750.378 1,469.772 30 40 7.040 Periods 4% 20% 1 2 3 1% 0.990 1.970 2.941 3.902 4.853 2% 0.980 1.942 2.884 3.808 4.713 3% 0.971 1.913 2.829 3.717 4.580 0.962 1.886 2.775 3.630 4.452 Present Value of Annuity of $1 5% 6% 8% 10% 0.952 0.943 0.926 0.909 1.859 1.833 1.783 1.736 2.723 2.673 2.577 2.487 3.546 3.465 3.312 3.170 4.329 4.212 3.993 3.791 12% 0.893 1.690 2.402 3.037 3.605 14% 0.877 1.647 2.322 2.914 3.433 16% 0.862 1.605 2.246 2.798 3.274 18% 0.847 1.566 2.174 2.690 0.833 1.528 2.106 2.589 2.991 4 3.127 6 3.685 7 5.417 6.230 7.020 7.786 3.889 4.288 3.326 3.605 5.795 6.728 7.652 8.566 9.471 4.039 5.601 6.472 7.325 8.162 8.983 8 5.242 6.002 6.733 7.435 8.111 5.076 5.786 6.463 7.108 7.722 4.111 4.564 4.968 4.917 5.582 6.210 6.802 7.360 4.623 5.206 5.747 6.247 6.710 4.355 4.868 5.335 5.759 6.145 4.639 3.498 3.812 4.078 4.303 4.494 3.837 9 5.328 4.344 4.607 4.833 4.946 5.216 10 8.530 4.031 4.192 5.650 5.938 4.327 5.029 5.197 6.194 11 12 13 14 10.368 9.787 9.253 8.760 8.306 7.887 11.255 10.575 9.954 9.385 8.863 8.384 12.134 11.348 10.635 9.986 9.394 8.853 13.004 12.106 11.296 10.563 9.899 9.295 13.865 12.849 11.938 11.118 10.380 9.712 7.139 7.536 7.904 8.244 8.559 6.495 6.814 7.103 7.367 7.606 5.453 5.660 5.842 6.002 6.142 6.424 6.628 6.811 5.342 4.656 4.793 4.910 5.008 5.092 4.439 4.533 4.611 4.675 5.468 5.575 15 20 7.469 5.929 6.097 25 18.046 16.351 14.877 13.590 12.462 | 11.470 9.818 8.514 22.023 19.52317.413 | 15.622 14.094 12.783 10.675 9.077 25.80822.396 19.600 17.292 15.372 13.765 11.258 9.427 32.835 27.355 23.115 19.793 17.159 | 15.046 11.925 9.779 6.623 6.873 7.003 7.105 7.843 8.055 8.244 5.353 5.467 5.517 5.548 4.870 4.948 4.979 4.997 30 6.177 40 6.233 Periods 1 2 3 4 1% 0.990 0.980 0.971 0.961 0.951 29 0.980 0.961 0.942 0.924 0.906 3% 0.971 0.943 0.915 0.888 0.863 Present Value of $1 496 5% 6% 896 10% 12% 0.962 0.952 0.943 0.926 0.909 0.893 0.925 0.907 0.890 0.857 0.826 0.797 0.889 0.864 0.840 0.794 0.751 0.712 0.855 0.823 0.792 0.735 0.683 0.636 0.822 0.784 0.747 0.681 0.621 0.567 14% 16% 18% 0.877 0.862 0.847 0.769 0.743 0.718 0.675 0.641 0.609 0.592 0.552 0.516 0.519 0.476 0.437 20% 0.833 0.694 0.579 0.482 0.402 5 6 7 8 9 10 0.942 0.933 0.923 0.914 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 0.370 0.354 0.314 0.305 0.266 0.263 0.225 0.227 0.191 0.335 0.279 0.233 0.194 0.162 11 12 13 14 15 0.896 0.887 0.879 0.870 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 20 25 30 40 0.820 0.780 0.742 0.672 0.673 0.610 0.552 0.453 0.554 0.478 0.412 0.307 0.456 0.377 0.375 0.295 0.308 0.231 0.208 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 0.037 0.024 0.016 0.012 0.007 0.003 0.001 0.026 0.010 0.004 0.001 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? 1. How much money must you accumulate by retirement? (Hint Find the present value of the $225,000 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 $ $225,000 However, by age 40 you only need to have invested These numbers are different because O A. 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 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 the same accumulated as you will withdraw because you will not earn further interest on your investment when you reach retirement None of the above. 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) (Round your answer to the neam whole dollar) You must pay $ into the investment each year for the first twenty years. 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? (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 S This is far less than the investment's worth at the end of twenty years and remarkably higher than the amount of money you will eventually withdraw from the investment