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 $255,000 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 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 future value annuity table.) Reference x (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.) Periods 14% 16% 1. How much money must you accumulate by retirement? (Hint: Find the present value of the $255,000 withdrawals.) 0.877 1.647 2 3 4 Calculate the present value to find out how much money must be accumulated by retirement. (Round your answer to the nearest whole dollar.) 1% 0.990 1.970 2.941 3.902 4.853 2% 0.980 1.942 2.884 3.808 4.713 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 2.487 3.546 3.465 3.312 3.170 4.329 4.212 3.993 3.791 3% 496 0.971 | 0.962 1.913 1.886 2.829 2.775 3.717 3.630 4.580 4.452 1296 0.893 1.690 2.402 3.037 3.605 18% 20% 0.847 0.833 1.566 1.528 2.174 2.106 2.690 2.589 3.127 | 2.991 2.577 0.862 1.605 2.246 2.798 3.274 2.322 2.914 3.433 The present value is $ 5 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? 3.889 3.498 3.812 Over the course of your retirement you will be withdrawing $ However, by age 40 you only need to have invested 6 7 8 9 10 5.795 6.728 7.652 8.566 9.471 5.601 6.472 7.325 8.162 8.983 5.417 5.2425.076 6.230 6.002 5.786 7.020 6.733 6.463 7.786 7.435 7.108 8.530 8.111 7.722 4.917 5.582 6.210 6.802 7.360 4.622 4.355 5.206 4.868 5.747 5.335 6.247 5.759 6.710 6.145 4.111 4.564 4.968 5.328 4.288 4.639 4.946 5.216 3.685 4.039 4.344 4.607 4.078 4.303 4.494 3.326 3.605 3.837 4.031 4.192 These numbers are different because: 5.650 4.833 11 12 10.368 9.787 9.253 8.760 11.255 10.575 9.954 9.385 8.306 8.863 7.887 7.139 8.384 7.536 6.495 6.814 5.938 6.194 5.453 5.029 4.656 5.660 5.197 4.793 4.327 4.439 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 14% 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 14% interest. OC. You need to have the same accumulated as you will with draw because you will not earn further interest on your investment when you reach retirement. OD. None of the above. Reference x 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 nearest whole dollar.) You must pay $ into the investment each year for the first twenty years. Present Value of $1 1896 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 nur Periods 1 2 0.847 0.890 0.743 0.718 The total out-of-pocket savings amounts to $ This is far than the investment's worth at the end of twenty years and remarkably than the amount of money you will eventually withdraw from the investment. 1% 29 0.990 0.980 0.980 0.961 0.971 0.942 0.961 0.924 0.951 0.906 3% 4% 0.971 0.962 0.943 0.925 0.915 0.889 0.888 0.855 0.863 0.822 5% 6% 0.952 0.943 0.907 0.864 0.840 0.823 0.792 0.784 0.747 896 0.926 0.857 0.794 0.735 0.681 10% 1296 1496 1696 0.909 0.893 0.877 0.862 0.826 0.797 0.769 0.751 0.712 0.675 0.641 0.683 0.636 0.592 0.552 0.621 0.567 0.519 0.476 20% 0.833 0.694 0.579 0.482 0.402 3 4 0.609 0.516 0.437 5 Reference 6 7 0.837 0.813 0.942 0.888 0.933 0.871 0.853 0.914 0.905 0.820 0.923 0.789 0.790 0.760 0.731 0.703 0.676 0.746 0.705 0.711 0.665 0.677 0.645 0.592 0.614 0.558 8 9 0.627 0.630 0.583 0.540 0.500 0.463 0.564 0.507 0.456 0.410 0.513 0.452 0.400 0.354 0.467 0.404 0.424 0.361 0.308 0.263 0.386 0.322 0.270 0.227 0.351 0.305 0.370 0.314 0.266 0.225 0.191 0.335 0.279 0.233 0.194 0.162 0.837 Future Value of $1 0.766 0.744 10 2% 5% 18% Periods 1 2 10% 1.100 1.020 1.050 11 12 1.210 1% 1.010 1.020 1.030 1.041 1.051 3% 1.030 1.061 1.093 1.126 1.159 1.040 1.061 1.082 1.104 4% 1.040 1.082 1.125 1.170 1.217 6% 1.060 1.124 1.191 1.262 1.338 1.103 1.158 1.216 1.276 8% 1.080 1.166 1.260 1.360 1.469 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 2.100 209 1.200 1.440 1.728 2.074 2.488 0.896 0.887 0.879 0.870 1.180 1.392 1.643 1.939 2.288 3 0.722 0.701 0.681 0.661 0.804 0.788 0.773 0.758 0.743 0.650 0.625 0.601 0.577 1.331 1.464 1.611 Choose from any list or enter any number in 0.585 0.527 0.429 0.350 0.287 0.237 0.195 0.162 0.135 0.557 0.497 0.397 0.319 0.257 0.208 0.168 0.137 0.112 0.530 0.469 0.368 46.29090.229 0.182 0.145 0.116 0.093 0.505 0.442 0.340 0.263 0.205 0.160 0.125 0.099.0.078 0.481 0.417 0.315 0.239 0.183 0.140 0.108 0.084 0.065 0.377 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 13 14 15 4 5 0.861 0.642 0.555 1.062 1.126 6 1.194 1.265 1.340 1.419 1.587 1.772 1.974 2.195 2.436 2.700 2.986 20 0.820 0.673 0.554 0.456