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 $235,000 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 10 % per year. You will leave the money in this fund until it is completely depleted when you are 80 years old.

1. How much money must you accumulate by retirement? (Hint: Find the present value of the 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 less accumulated than what you will withdraw because you only withdraw a portion of the investment every yearlong dashthe balance remains invested where it continues to earn 10 % interest.

B. You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every yearlong dashthe balance remains invested where it continues to earn 10 % interest.

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 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.

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 $______. 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.

Reference Present Value of Annuity of $1 Periods1% 2% 3% 4% 5% 696 8% 10%12% 14%16% 18% 20 0.990 0.980 0.9710.9620.9520.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 1.9701.9421.913 1.8861.859 1.833 1.783 1.736 1.690 1.647 1.6051.5661.528 2.941 2.8842.8292.775 2.723 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.106 4 3.902 3.8083.717 3.630 3.546 3.465 3.312 3.170 3.0372.914 2.798 2.690 2.589 4.853 4.7134.580 | 4.452 4.329 4.212 3.993 3.7913.605 3.433 3.274 3.1272.991 6 5.795 5.601 5.4175.242 5.076 4.9174.623 4.355 4.111 3.889 3.685 3.4983.326 7 6.728 6.4726.2306.002 5.7865.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 8 7.6527.3257.020 6.733 6.463 6.210 5.747 5.335 4.9684.639 4.3444.078 3.837 8.566 8.1627.7867.4357.108 6.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 10 9.471 8.983 8.530 8.1117.7227.3606.7106.145 5.6505.216 4.833 4.494 4.192 11 10.368 9.7879.253 8.760 8.3067.8877.1396.495 5.938 5.453 5.029 4.656 4.327 12 11.255 10.5759.9549.385 8.863 8.384 7.536 6.814 6.1945.660 5.197 4.7934.439 13 12.134 11.348 10.6359.9869.394 8.853 7.904 7.103 6.424 5.842 5.342 4.910 4.533 14 13.004 12.106 11.296 10.5639.8999.2958.2447.3676.628 6.002 5.468 5.008 4.611 15 13.865 12.849 11.938| 11.118 10.3809.712 8.559 7.606 6.811 6.142 5.5755.0924.675 20 18.046 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.4696.623 5.929 5.3534.870 25 22.023 19.523 17.41315.622 14.094 12.783 10.675 9.0777.843 6.873 6.097 5.467 4.948 30 25.808 22.39619.60017.292 15.372 13.765 11.258 9.427 8.055 7.003 6.1775.5174.979 40 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.779 8.244 7.105 6.233 5.548 4.997 Print Done Reference Present Value of $1 Periods l 196 | 296 | 3% | 4% | 5% | 6% | 896 | 1096 | 1296 | 1496 | 1696 | 1896 | 2096 1 0.990 0.980 0.971 0.9620.9520.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 2 0.980 0.961 0.943 0.9250.9070.890 0.857 0.826 0.797 0.769 0.743 0.718 0.694 3 0.971 0.942 0.915 0.889 0.8640.8400.7940.751 0.712 0.675 0.641 0.609 0.579 4 0.961 0.924 0.888 0.855 0.8230.7920.735 0.683 0.636 0.592 0.552 0.516 0.482 5 0.951 0.906 0.863 0.822 0.7840.7470.6810.621 0.567 0.519 0.476 0.437 0.402 6 0.942 0.888 0.8370.790 0.746 0.705 0.630 0.564 0.507 0.456 0.4100.3700.335 7 0.933 0.871 0.813 0.7600.711 0.665 0.583 0.513 0.452 0.400 0.354 0.314 0.279 8 0.923 0.853 0.7890.7310.6770.627 0.540 0.467 0.404 0.351 0.305 0.266 0.233 9 0.914 0.837 0.766 0.703 0.6450.5920.500 0.424 0.361 0.308 0.263 0.225 0.194 10 0.905 0.820 0.744 0.6760.6140.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 11 0.896 |0.8040.722 0.650 0.585 0.527 0.429 0.350 0.287 0.237 0.1950.162 0.135 12 0.887 |0.7880.7010.625 0.557 0.497 0.397 0.319 0.257 0.208 0.1680.1370.112 13 0.879 0.7730.6810.6010.530 0.469 0.368 0.290 0.229 0.182 0.145 0.116 0.093 14 0.870 0.7580.6610.5770.505 0.442 0.340 0.263 0.205 0.160 0.125 0.099 0.078 15 0.861 0.743 0.642 0.5550.4810.4170.315 0.239 0.183 0.140 0.108 0.084 0.065 20 0.820 0.6730.554 0.456 0.377 0.312 0.215 0.149 0.104 0.073 0.0510.0370.026 25 0.780 |0.6100.4780.375 0.295 0.233 0.146 0.092 0.059 0.038 0.0240.016 0.010 30 0.742 0.5520.412 0.308 0.231 0.174 0.099 0.057 0.033 0.020 0.0120.0070.00 40 0.672 0.453 0.307 0.208 0.142 0.097 0.046 0.022 0.011 0.005 0.003 0.001 0.001 1 7 0 68 5311 49 3456 78 76 211122 74 39 26 5 1-91 39 66 3 742 3345 11 26 4 6 2 581 482 4 19 1-1 1 1 1 2 22334 55679 908 2 2 2 2842 2233 44567 542 4163 76 717 57 924 23 334 0% 1 2 3 4 1 29185 7 27 ass ess 7599 3827 535 178 5 9 741 072 237 1 35791 1 5 123 317 723 369 094 0123 227 123 4 2 345 2 01122 90 6 456 7 3 3 112 2334 1369 3 693 2a 69259 3 4791 4 1112 22 6 611 2 00011 123 5 67891 0 0 12346 2 223 rio- 1 12345 20 25 30 40 12345 6789