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Assume you want to retire early at age 54. You plan to save using one of the following two strategies: (1) save $4,500 a year in an IRA beginning when you are 24 and ending when you are 54 (30 years) or (2) wait until you are 44 to start saving and then save $13,500 per year for the next 10 years. Assume you will earn the historic stock market average of 12% per year. (Click the icon to view the future value annuity factor table.) (Click the icon to view the future value factor table.) (Click the icon to view the present value annuity factor table.) (Click the icon to view the present value factor table.) Read the requirements Requirement 1. How much out-of-pocket cash will you invest under the two options? Reference - X i Reference X Calculate how much out-of-pocket cash you will invest under the two options. Option 1: Future Value of Annuity of $1 Future Value of $1 Option 2: Periods 1% 2% 3% 4% 5% 5% 6% 8% 10% 12% 14% 16% 18% 20% Period 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 2.010 2.020 2.030 2.040 1.100 2.050 2.120 2.140 Period 1 1.010 1.020 1.030 1.040 1.050 1.060 1.080 1.120 1.200 Requirement 2. How much savings will you have accumulated at age 54 under the two options? Period 2 2.060 2.080 2.100 2.160 2.180 2.200 1.140 1.160 3.122 3.440 1.020 1.040 1.061 1.082 1.103 1.124 1.166 3.246 3.310 3.374 1.210 1.254 1.300 1.346 1.392 1.440 Period 3 3.030 3.153 3.184 3.506 3.572 3.640 Period 2 1.405 1.561 Calculate the total amount of savings that you will have accumulated at age 54 under the two options. (Round the savings to the nearest dollar amount.) 4.060 4.122 4.184 4.246 1.191 1.331 1.482 Period 4 4.310 4.375 4.506 4.641 4.779 4 921 5.066 5.215 Period 3 1.030 1.061 1.093 1.728 5 368 1.260 5.101 5.204 5.309 5.526 5.637 5.867 6.353 6.877 7 642 Period 4 1.041 1.082 1.170 1.216 1.262 1.360 1.464 1.574 1.689 1.811 1.939 2.074 Period 5 6.105 6.610 7.154 Period 5 1.051 1.104 1.159 1.217 1.276 1.338 1.469 1.611 1.762 1.926 2.100 2.288 2.488 Option 1: Period 6 6.152 6.308 6.468 6.633 6.802 6.975 7.336 7.716 8.115 8.536 8.977 9.442 9.930 Period 6 1.062 1.126 1.194 1.265 1.419 1.587 1.772 1.974 2.195 2.436 2.700 2.986 Option 2: Period 7 7.214 7.662 8.394 8.923 9.487 10.089 10.730 11.414 12.142 12.916 Period 7 1.072 1.149 1.316 2.826 3.185 11.436 12.300 15.327 1.714 2.211 3.583 Period 8 9.214 10.637 13.233 14.240 16.499 Period 9 Period 8 3.759 4.300 Requirement 3. Explain the results 9.369 9.755 10.159 10.583 11.0 11.491 188 13.579 14.776 16.085 17.019 19.086 20.799 1.094 1.689 3.803 4.435 5.160 Period 10 10.462 10.950 11.464 12. 12.006 12.5 13.181 14.487 15.937 17.5 17.549 19.337 21.321 Period 9 1.195 2.773 3.252 25.959 Period 10 1.105 1.219 1.480 1.791 3.106 3.707 4.411 5.234 6.192 The strategy involving grows substantially larger over time. This is due to the fact that the savings are invested V, so time does the work. Period 11 11.567 12.169 12.808 13.486 14.2 14 972 16.645 18.531 20.655 23.045 25.733 28.755 32.150 7.430 Period 12 13.412 14.192 15 . 16.870 18.977 21.384 2 27.271 39.581 Period 11 .116 1.243 1.384 1.539 1.710 30.850 34.931 2.853 3.479 4.226 5.117 6.176 48.497 Period 12 1.426 1.601 7.288 Period 13 32.089 3.896 8.916 Requirement 4. If you were to let the savings continue to grow for eight more years (with no further out-of-pocket investments), under each scenario, what will the investment be worth when you are age 62? 36.786 42.219 Period 13 10.699 Period 14 14.947 15.974 17.086 18. 21.015 215 27.975 32.393 37.581 43.672 50.818 59.196 Period 15 16.097 17 293 18.599 20.024 21.579 23 276 27.152 31.772 37.280 43.842 12.839 Calculate the total amount of savings at age 62, with no further out-of-pocket investments, under each scenario. (Round the savings to the nearest dollar amount.) 51 660 72.035 Period 14 1.149 1.319 60.965 6.261 10.147 Period 15 1 161 1.346 2.397 5.474 9.266 11.974 15.407 Period 20 20 22.019 24.297 26.870 29.778 33.066 36.786 45.762 57 275 72.052 91.025 115.380 146.628 186.688 Period 25 28.243 32.030 36.459 41.646 4 46 47.727 54.865 6 98.347 133.334 181.871 249.214 342.603 Period 20 1.220 1.486 1.806 2.191 2.653 3.207 8.727 13.743 19.461 27.393 38.338 Option 1: 471.981 Period 30 34.785 40.568 47.575 56.085 66.439 79.058 113.283 164.494 241.333 356.787 530.312 790.948 1,181.882 Period 25 1.282 2.094 2.666 4.292 17.000 26.462 40.874 62.669 95.396 Option 2: Period 40 48.896 60.402 75.401 95.026 120.800 154.762 259.057 442.593 767.091 1,342.025 2,360.757 4,163.213 7,343.858 Period 30 1.348 1.811 3.243 50.950 237.376 Period 40 1.489 2 208 4.801 45.259 93.051 188.884 378.721 750.378 1,469.772 i Reference - X Reference - X Done Print Done Present Value of Annuity of $1 Periods 1% 2% 3% 4% 10% 12% 14% 16% 18% 20% Period 1 0.990 0.980 0.971 0.893 0.847 0.833 Present Value of $1 Period 2 1.970 1.913 1 1.859 1.736 1.690 1.605 1.566 1.528 Periods 1% 2% 3% 4% 10% 12% 14% 16% 18% 20% Period 3 2.941 2.884 2.829 2.775 2.6732 2.322 2.246 2174 2.106 Period 1 0.990 0.980 0.971 0.962 09 0.909 0.893 0.877 0.862 0.847 0.833 Period 4 3.902 3.808 3.717 3.630 3.546 53.312 3.170 3.037 2.914 2.798 2.690 2.589 4.452 4.329 3.993 3.274 Period 2 0.980 0.961 0.943 0.797 0.743 0.718 0.694 Period 5 4.853 3.127 2.991 Period 3 0.971 0.942 0.609 0.579 Period 6 5.795 5.601 5.417 5.242 3.326 Period 4 0.961 Period 7 6.728 6. 6.472 6.230 6.002 4.039 3.812 3.605 Period 5 0.951 0.906 0.476 0.437 0.402 Period 8 7.652 7.020 6.733 5.335 4.344 4.078 3.837 Period 6 0.888 0.790 10 0.370 0.335 Period 9 8.566 8.162 7.786 7.435 7.108 8.802 6.247 5.328 4.607 4.303 4.031 Period 7 0.933 0.871 0.813 0.760 0.314 0.279 Period 10 9.471 4.833 4.192 Period 8 0.923 0.233 Period 11 10.368 9.787 5.453 4.327 Period 9 0.914 0. 0.194 Period 12 11. 10.575 9.9 4.793 4.439 Period 10 0.905 0.820 0.7 0.191 0 Period 13 12.134 11.348 10.635 9.986 7.103 5.842 5.342 4.910 4.583 Period 11 0.896 0.804 0.162 0.135 Period 14 13.004 12.106 11 296 10.563 9.899 4.611 Period 12 0.887 0.788 0.137 0.112 Period 15 13.865 12.849 1 11.118 10.380 5.092 4.675 Period 13 0.093 eriod 20 16.351 14.87 7.469 Period 14 0.870 0.7 0.661 0.577 50.099 0.078 Period 25 22.023 19.523 17.413 15.622 14.094 12 783 10.675 9.077 7.84 6.873 6.097 5.467 4.948 Period 15 0.861 0.7 0.642 0.555 0.481 0.108 0.084 0.065 Period 30 25.808 22 396 19.600 17 292 15.372 13.765 11.258 8.065 7.003 6.177 5.517 4.979 Period 20 0.820 0.673 0. 0.073 0.051 0.037 0.026 Period 40 32 835 27.355 23.115 19.793 17 25 9.779 4.997 0.456 0.377 0.312 Period 25 0.780 0.610 0.478 0.375 0.295 0.233 0.146 50.092 .059 0.038 0.024 0.016 0.010 eriod 30 0.742 0.552 0.412 0.308 0 0.231 0.174 0.099 0.057 0.033 0.020 0.012 0. 0.007 0.004 eriod 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