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Print 5. Assume you make the following investments: a. You invest a lump sum of $7,750 for four years at 12% interest. What is the investment's value at the end of four years? b. In a different account earning 12% interest, you invest $1,938 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? 1(Click the icon to view the future value factor table.) 2 (Click the icon to view the future value annuity factor table.) (Click the icon to view the present value factor table.) 4(Click the icon to view the present value annuity factor table.) a. You invest a lump sum of $7,750 for four years at 12% interest. What is the investment's value at the end of four years? (Round your answer to the nearest whole dollar.) Investment's value = b. In a different account earning 12% interest, you invest $1,938 at the end of each year for four years. What is the investment's value at the end of four years? (Round your answer to the nearest whole dollar.) Investment's value = c. What general rule of thumb explains the difference in the investments' future values? The future value of the annuity is (1) - than the future value of the lump sum investment. The (2) - earned interest over the full four years. However, the (3) - _ earned interest only as the installments were received over the course of four years. The (4) - the cash is invested, the (5) interest is earned. The investor lets time do the work. Print 1: Reference Future Value of $1 Periods 4% 12% 16% 18% 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 1.040 1.082 1.125 1.170 1.217 5% 1.050 1.103 1.158 1.216 1.276 6% 1.060 1.124 1.191 1.262 8% 1.080 1.166 1.260 1.360 1.469 10% 1.100 1.210 1.331 1.464 1.611 1.120 1.254 1.405 1.574 1.762 14% 1.140 1.300 1.482 1.689 1.160 1.346 1.561 1.811 2.100 1.180 1.392 1.643 1.939 2.288 20% 1.200 1.440 1.728 2.074 2.488 1.338 1.925 1.194 1.974 1.062 1.072 2.195 2.502 1.230 2.211 1.126 1.149 1.172 1.195 1.219 1.083 1.265 1.316 1.369 1.423 1.480 1.772 1.949 2.144 1.340 1.407 1.477 1.551 1.629 1.419 1.504 1.594 1.689 1.791 1.267 1.305 1.344 1.587 1.714 1.851 1.999 2.159 2.476 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 2.853 3.252 3.707 2.358 1.094 1.105 2.773 3.106 1.116 2.594 2.853 3.138 1.127 1.243 1.268 1.294 1.319 1.346 1.384 1.426 1.469 1.513 1.558 1.138 1.539 1.601 1.665 1.732 1.801 1.710 1.796 1.886 1.980 2.079 2.332 2.518 2.720 1.898 2.012 2.133 2.261 2.397 3.479 3.896 4.363 3.452 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 2.937 4.887 1.149 1.161 3.797 4.177 3.172 5.474 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 7.040 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 62.669 143.371 750.378 38.338 95.396 237.376 1,469.772 Print 2: Reference Periods 3% 1% 1.000 2.010 2% 1.000 2.020 3.060 4.122 5.204 1.000 2.030 3.091 4% 1.000 2.040 3.122 12% 1.000 2.120 3.374 14% 1.000 2.140 3.440 4.921 6.610 16% 1.000 2.160 3.506 5.066 18% 1.000 2.180 3.572 5.215 7.154 20% 1.000 2.200 3.640 5.368 7.442 3.030 4.184 4.246 4.641 4.779 4.060 5.101 5.309 5.416 6.353 6.877 6.308 7.434 6.152 7.214 8.286 9.369 10.462 6.468 7.662 8.892 10.159 11.464 8.583 6.633 7.898 9.214 10.583 12.006 Future Value of Annuity of $1 5% 6% 8% 10% 1.000 1.000 1.000 1.000 2.050 2.060 2.080 2.100 3.153 3.184 3.246 3.310 4.310 4.375 4.506 5.526 5.637 5.867 6.105 6.802 6.975 7.336 7.716 8.142 8.394 8.923 9.487 9.549 9.897 10.637 11.436 11.027 11.491 12.488 13.579 12.578 13.181 14.487 15.937 14.207 14.972 16.645 18.531 15.917 16.870 18.977 21.384 17.713 18.882 21.495 24.523 19.599 21.015 24.215 27.975 21.579 23.276 27.152 31.772 33.066 36.786 45.762 57.275 47.727 54.865 73.106 98.347 66.439 79.058 113.283 164.494 | 120.800 154.762 259.057 442.593 8.115 10.089 12.300 14.776 17.549 8.536 10.730 13.233 16.085 8.977 11.414 14.240 17.519 21.321 9.930 12.916 16.499 20.799 25.959 19.337 9.755 10.950 12.169 13.412 14.680 15.974 9.442 12.142 15.327 19.086 23.521 28.755 34.931 42.219 50.818 60.965 11.567 12.683 13.809 14.947 16.097 12.808 13.486 14.192 15.026 15.618 16.627 17.086 18.292 18.599 20.024 26.870 29.778 36.459 41.646 47.575 56.085 75.401 | 95.026 20.655 24.133 28.029 32.393 37.280 23.045 27.271 32.089 37.581 43.842 91.025 181.871 356.787 1,342.025 25.733 30.850 36.786 43.672 51.660 17.293 32.150 39.581 48.497 59.196 72.035 22.019 28.243 34.785 48.886 24.297 32.030 40.568 | 60.402 72.052 133.334 241.333 767.091 115.380 146.628 249.214 342.603 530.312 790.948 2,360.757 4,163.213 186.688 471.981 1,181.882 7,343.858 3: Reference Periods 14% 0.877 1.647 2.322 2.914 3.433 18% 0.847 1.566 2.174 2.690 3.127 20% 0.833 1.528 2.106 3.170 2.589 2.991 5.795 3.326 3.605 Present Value of Annuity of $1 2% 3% 4% 5% 6% 8% 10% 12% 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.909 0.893 1.970 1.942 1.913 1.886 1.859 1.833 1.783 1.736 1.690 2.941 2.884 2.829 2.775 2.723 2.673 2.577 2.487 2.402 3.902 3.808 3.717 3.630 3.546 3.465 3.312 3.037 4.853 4.713 4.580 4.452 4.329 4.212 3.993 3.791 3.605 5.601 5.417 5.242 5.076 4.917 4.623 4.355 4.111 6.728 6.472 6.230 6.002 5.786 5.582 5.206 4.868 4.564 7.652 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.968 8.566 8.162 7.786 7.435 7.108 6.802 6.247 5.759 5.328 9.471 8.983 8.530 8.111 7.722 7.360 6.710 6.145 5.650 10.368 9.787 9.253 8.760 8.306 7.887 7.139 6.495 5.938 11.255 10.575 9.385 8.863 8.384 7.536 6.814 6.194 12.134 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 13.004 12.106 11.296 10.563 9.899 9.295 8.244 7.367 13.865 12.849 11.938 11.118 10.380 9.712 8.559 7.606 18.046 16.351 14.877 13.590 12.462 11.470 9.818 8.514 7.469 22.023 | 19.523 | 17.413 | 15.622 14.094 | 12.783 | 10.675 9.077 7.843 25.808 22.396 19.600 17.292 15.372 13.765 11.258 9.427 8.055 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.7798.244 3.889 4.288 4.639 4.946 5.216 3.837 16% 0.862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 4.833 5.029 5.197 5.342 5.468 5.575 5.929 6.097 6.177 6.233 3.498 3.812 4.078 4.303 4.494 5.453 5.660 5.842 9.954 4.031 4.192 4.327 4.439 4.533 4.656 4.793 4.910 5.008 5.092 6.628 6.811 6.002 4.611 6.142 6.623 6.873 7.003 7.105 5.353 5.467 5.517 5.548 4.675 4.870 4.948 4.979 4.997 40 4: Reference Present Value of Annuity of $1 Periods 0.990 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 2.941 2.402 20% 0.833 1.528 2.106 2.589 2.991 3.326 3.605 | 2% 3% 4% 5% 6% 0.980 0.971 0.962 0.952 0.943 1.970 1.942 1.913 1.886 1.859 1.833 2.884 2.829 2.775 2.723 2.673 3.902 3.808 3.717 3.630 3.546 3.465 4.853 4.713 4.580 4.452 4.329 4.212 5.795 5.601 5.417 5.242 5.076 4.917 6.728 6.472 6.230 6.002 5.786 5.582 7.652 7.325 7.020 6.733 6.463 6.210 8.566 8.162 7.786 7.435 7.108 6.802 9.471 8.983 8.530 8.111 7.722 7.360 10.368 9.787 9.253 8.760 8.306 7.887 11.255 10.575 9.954 9.385 8.863 8.384 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 18.046 16.351 14.877 | 13.590 12.462 | 11.470 22.023 19.523 17.413 15.622 14.094 | 12.783 22.396 19.600 17.292 15.372 | 13.765 32.835 27.355 23.115 19.793 17.159 15.046 8% 10% 12% 0.926 0.909 0.893 1.783 1.736 1.690 2.577 2.487 3.312 3.170 3.037 3.993 3.791 3.605 4.623 4.355 4.111 5.206 4.868 4.564 5.747 5.335 4.968 6.247 5.759 5.328 6.710 6.145 5.650 7.139 6.495 5.938 7.536 6.814 6.194 7.904 7.103 6.424 8.244 7.367 6.628 8.559 7.606 6.811 9.818 8.514 7.469 10.675 9.077 11.258 | 9.427 | 8.055 11.925 9.779 8.244 3.889 4.288 4.639 4.946 5.216 3.837 4.031 3.498 3.812 4.078 4.303 4.494 5.453 5.660 3.685 4.039 4.344 4.607 4.833 5.029 5.197 5.342 5.468 5.575 5.929 6.097 6.177 6.233 5.842 6.002 6.142 4.656 4.793 4.910 5.008 5.092 7.843 6.623 6.873 7.003 7.105 5.353 5.467 5.517 5.548 4.675 4.870 4.948 4.979 4.997 25.808 22.396 (1) O O higher lower (2) O O annuity lump-sum investment (3) O O annuity lump-sum investment (4) O O later sooner (5) O less more