Assume you make the following investments: a. You invest a lump sum of $8,250 for four years at 14% interest. What is the investment's value at the end of four years? b. . In a different account earning 14% interest, you invest $2,063 at the end of each year for four years. What is the investment's value at the end of four years? c. What general rule of thumb explains the difference in the investments' future values? (Click the icon to view the future value factor table.) (Click the icon to view the future value annuity factor table.) (Click the icon to view the present value factor table.) (Click the icon to view the present value annuity factor table.) a. You invest a lump sum of $8,250 for four years at 14% interest. What is the investment's value at the end of fou Investment's value = Reference Reference Future Value of $1 Periods 1% 2% 3% 1 %. 3 4% % 5% 6% 8% 10% 12% 14% 16% 18% 20% 8 % % Period 1 1.010 1.020 1.030 1.040 1.050 1.060 1.080 1.100 1.120 1.140 1.160 1.180 1.200 Period 2 1.020 1.040 1061 1.087 1.103 1.124 1.166 1.210 1.254 1.300 1.348 1.392 1.440 Period 3 1.030 1.061 1.093 1.125 1.158 1.191 1.260 1.331 1.405 1.492 1.561 1.643 1.728 Period 4 1.041 1.0821.126 1.170 | 1216 1.262 1.360 1464 1.574 1.689 1811 1.939 2.074 Period 5 1.051 1.104 1.159 1.217 1278 1.338 1.469 1.811 1.782 1.925 2.100 2.208 2.488 Period 6 1.062 1.126 1.194 1.260 1.340 1.419 1.587 1.772 1.974 2.195 2.438 2.700 2.986 Perlod 7 1.072 1.149 1.230 1.316 1.407 1.504 1.714 1.949 2.211 2.502 2.828 3.185 3.583 Period & 1,083 1.1721.287 1.369 1.477 1.592 1.851 2.144 2478 2853 31.278 3.759 4,300 Period 9 1.094 1.195 1.305 1.423 1.551 1.689 1.999 2.358 2773 3.252 3.803 4.436 5.160 Period 10 1.105 1.219 1.344 1.480 1629 1.791 2.159 2.594 3.106 3.707 4.411 5.234 6.192 Period 11 1.11 1.243 1.384 1.539 1.710 1.899 2.332 2.853 3.479 4.226 5.117 6.178 7.430 Period 12 1.127 1.268 1.42 1.601 1.796 2.012 2.518 3.138 3.896 4.818 5.938 7.288 8.916 Period 13 1.139 1.294 1489 1.665 1.886 2.133 2.720 3.452 4333 5.492 5.883 8.599 10.699 Period 14 1.149 1.319 1513 1.732 1.980 2.261 2.937 3.797 4.837 6.261 7.989 10.147 12.839 Period 15 1.161 1.346 1.558 1.801 2.079 2.397 3.172 4.177 5.474 7.138 9.268 11.974 15.407 Period 20 1.220 1.4861.806 2.191 2653 3.207 4.661 6.727 9.648 13.743 19.451 27.393 27.395 39.338 Period 25 1.282 1.6412094 2.666 3396 4.292 6.848 10.935 17.000 26.462 40.874 62.669 95.398 Period 30 1.348 1.811 2427 3.243 | 4322 4.3225.743 10.063 17.449 20.960 50.950 85.850 143.371 237.376 Period 40 1.489 2.208 3.282 4.001 7.040 10.288 21.725 45.25993.051 188.064 378.721 750.378 1.489.772 Future Value of Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 189 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 Period 2 2.010 2.020 2.030 2.040 2.060 2.050 2.080 2.100 2.120 2.140 2.180 2.180 2.200 Period 3 3.000 3.00 3.091 3.122 3.153 3.1843.248 3.310 3.374 3.440 3.506 3.572 3.640 Perlod 4 4.060 4,122 4.184 4.246 4.310 4.375 4.508 4.641 4.779 4.921 5.066 5215 5.368 Period 5 5.101 5.204 5.309 5.416 5.523 56375.667 6.105 3.353 8.610 6,077 7.154 7.442 Period 6 6.152 6.308 6.469 6.633 6.802 6.975 7.338 7.716 8.115 8.536 8.977 9.442 9.900 Period 7 7.214 7.434 7.662 7.898 8.142 8.394 8.923 9.487 10.088 10.730 11.414 12.142 12.916 Period 8 0.283 8.583 8.892 9.214 9.549 9897 10.637 11.436 12.300 13233 14.240 15 327 15.499 Period 9 9.369 9.755 10.159 10.583 11.027 11.491 12.489 13.579 14.776 16.085 17.519 19.086 20.799 Period 10 10.462 10.950 11.464 12.005 12.578 13.181 14.487 15.937 17.549 19.337 21.321 23.521 25.959 Period 11 11.567 12.169 12.89 13.403 14.207 14.972 18.645 18.531 20.655 23.045 25.733 28.755 32.150 Period 12 12.683 13.412 14.192 15.025 15.917 16.870 18.977 21.384 24.133 27.271 30.450 34.931 39.581 Period 13 13.809 14.680 15618 15.627 17.713 18.882 21.495 24.523 28.029 32039 38.786 42219 48.497 Period 14 14.347 15.974 17.09G 19.292 19.599 21.015 24.215 27.975 32.393 37.591 43.672 50.818 59.198 Period 15 16.097 17.29 18.599 20.024 21.579 23.276 27.152 31.772 37.280 43.842 51.660 60.965 Period 20 22.019 24.297 26.870 29.778 33.068 36.786 45.762 57.275 72.052 91.025 115.380 146.828 186.688 Period 25 28.243 32.030 36.459 41.645 | 47.727 54.965 73.103 58.347 133.334 181.871 249.214 342.503 471.991 Perlod 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 40 46.888 60.402 75.401 95.023 120.800 154.762 255.057 442.550 787 091 1,342.025 2330.757 4 163.213 7.343 856 72.035 Print Dana 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 200.820 Period 25 0.780 Period 30 0.742 Period 400.672 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 Present Value of Annuity of $1 Periods Period 1 Period 2 Period 3 Period 4 Period 5 1% 0.990 1.970 2.941 3.902 4.853 2% 3% 4% 0.980 0.971 0.962 1.942 1.913 1.886 2.884 2.829 2.775 3.808 3.717 3.630 4.713 4.580 4.452 5% 6% 8% 10% 12% 0.952 0.943 0.926 0.909 0.893 1.859 1.833 1.783 1.736 1.690 2.723 2.673 2.577 2.487 2.402 3.546 3.465 3.312 3.170 3.037 4.329 4.212 3.993 3.791 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 3.127 20% 0.833 1.528 2.106 2.589 2.991 Period 6 Period 7 Period 8 Period 9 Period 10 5.795 6.728 7.652 8.566 9.471 5.601 5.417 5.242 5.076 4.917 4.623 4.355 4.111 6.472 6.230 6.002 5.786 5.5825.206 4.8684.564 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.968 8.162 7.786 7.435 7.108 6.8026.247 5.759 5.328 8.983 8.530 8.111 7.722 7.360 6.710 6.145 5.650 3.889 4.288 4.639 4.946 5.216 3.685 4.039 4.344 4.607 4.833 3.498 3.812 4.078 4.303 4.494 3.326 3.605 3.837 4.031 4.192 Period 11 | 10.368 9.787 9.2538.760 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 9.986 9.394 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 9.712 8.559 7.6066.811 5.453 5.660 5.842 6.002 6.142 5.029 5.197 5.342 5.468 5.575 4.656 4.793 4.910 5.008 5.092 4.327 4.439 4.533 4.611 4.675 Period 2018.046 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.469 Period 25 22.023 19.523 17.413 15.622 14.094 12.783 10.675 9.077 7.843 Period 30 25.808 22.396 19.600 17.292 15.372 13.765 11.258 9.4278.055 Period 40 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.7798.244 6.623 6.873 7.003 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