4. Your grandmother would like to share some of her fortune with you. She offers to give you money under one of the following scenarios (you get to choose): 1. $7,250 a year at the end of each of the next eight years 2. $49,950 (lump sum) now 3. $98,650 (lump sum) eight years from now Calculate the present value of each scenario using an 8% interest rate. Which scenario yields the highest present value? Would your preference change if you used a 10% interest rate? (Click the icon to view the present value annuity factor table.) 2(Click the icon to view the present value factor table.) 3(Click the icon to view the future value annuity factor table.) 4(Click the icon to view the future value factor table.) Using an 8% interest rate, calculate the present values for each scenario. (Round the amounts to the nearest dollar.) Present value 40470 = Scenario 1 Scenario 2 Scenario 3 = = Which scenario yields the highest present value? (1) appears to be the best option. Based on an 8% interest rate, its present value is the (2) Using a 10% interest rate, calculate the present values for each scenario. (Round the amounts to the nearest dollar.) Present value Scenario 1 Scenario 2 Scenario 3 = = = (3) - appears to be the best option. Based on a 10% interest rate, its present value is the (4) - 1: Present Value of Annuity of $1 Periods 18% 0.847 1.566 2.174 2.690 3.127 20% 0.833 1.528 2.106 2.589 2.991 4.580 16% 0.862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 4.833 1% 2% 3% 0.990 0.980 0.971 1.970 1.942 1.913 2.9412.884 2.829 3.902 3.808 3.717 4.853 4.713 5.795 5.601 5.417 6.728 6.472 6.230 7.652 7.325 7.020 8.566 8.162 7.786 9.471 8.983 8.530 10.368 9.787 9.253 11.255 10.575 9.954 12.134 11.348 10.635 13.004 12.106 11.296 13.865 12.849 11.938 16.351 14.877 22.023 19.523 17.413 25.808 22.396 19.600 32.835 27.355 23.115 4.639 Present Value of Annuity of $1 4% 5% 6% 8% 10% 12% 14% 0.962 0.952 0.943 0.926 0.909 0.893 0.877 1.886 1.859 1.833 1.783 1.736 1.6901.647 2.775 2.723 2.673 2.577 2.487 2.402 2.322 3.630 3.546 3.465 3.312 3.170 3.037 2.914 4.452 4.329 4.212 3.993 3.791 3.605 3.433 5.242 5.076 4.917 4.623 4.355 4.111 3.889 6.002 5.786 5.582 5.206 4.868 4.564 4.288 6.733 6.463 6.210 5.747 5.335 4.968 7.435 7.108 6.802 6.247 5.759 5.328 4.946 8.111 7.722 7.360 6.710 6.145 5.650 5.216 8.760 8.306 7.887 7.139 6.495 5.938 5.453 9.3858.863 8.384 7.536 6.814 6.194 5.660 9.986 9.394 8.853 7.904 7.103 6.424 5.842 10.563 9.899 9.295 8.244 7.367 6.6286.002 11.118 10.380 9.712 8.559 7.606 6.811 6.142 13.590 12.462 11.470 9.818 8.514 7.4696.623 15.622 14.094 12.783 10.675 9.077 7.8436.873 17.292 15.372 13.765 11.258 9.4278.055 7.003 19.793 17.159 15.046 11.925 9.779 8.244 7.105 3.498 3.812 4.078 4.303 4.494 3.326 3.605 3.837 4.031 4.192 5.029 5.197 5.342 5.468 5.575 4.656 4.793 4.910 5.008 5.092 5.353 5.467 5.517 5.548 4.327 4.439 4.533 4.611 4.675 4.870 4.948 4.979 4.997 18.046 5.929 6.097 6.177 6.233 2: Present Value of $1 Periods 3% 0.971 0.943 0.915 0.888 0.863 0.837 0.410 0.813 0.583 1% 2% 0.990 0.980 0.980 0.961 0.971 0.942 0.961 0.924 0.951 0.906 0.942 0.888 0.933 0.871 0.923 0.853 0.914 0.837 0.905 0.820 0.896 0.804 0.788 0.879 0.773 0.870 0.758 0.861 0.743 0.820 0.673 0.780 0.610 0.742 0.552 0.672 0.453 0.789 Present Value of $1 4% 5% 6% 8% 10% 0.962 0.952 0.943 0.926 0.909 0.925 0.907 0.890 0.857 0.826 0.889 0.864 0.840 0.794 0.751 0.855 0.823 0.792 0.735 0.683 0.822 0.784 0.747 0.681 0.621 0.790 | 0.746 0.705 0.630 0.564 0.760 0.711 0.665 0.513 0.731 0.677 0.627 0.540 0.467 0.703 0.645 0.592 0.500 0.424 0.676 0.614 0.558 0.463 0.386 0.650 0.585 0.527 0.429 0.350 0.625 0.557 0.497 0.397 0.319 0.601 0.530 0.469 0.368 0.290 0.577 0.505 0.442 0.340 0.263 0.555 0.481 0.417 0.315 0.239 0.456 0.377 0.312 0.215 0.149 0.375 0.295 0.233 0.146 0.092 0.308 0.231 0.174 0.099 0.057 0.208 0.142 0.097 0.046 0.022 18% 20% 0.847 0.833 0.7180.694 0.609 0.579 0.516 0.482 0.437 0.402 0.370 0.335 0.314 0.279 0.266 0.233 0.225 0.194 0.191 0.162 0.162 0.135 0.137 0.112 0.116 0.093 0.099 0.078 0.084 0.065 12% 14% 16% 0.893 0.877 0.862 0.797 0.769 0.743 0.712 0.675 0.641 0.636 0.592 0.552 0.567 0.519 | 0.476 0.507 0.456 0.452 0.400 0.354 0.404 0.351 0.305 0.361 0.308 0.263 0.322 0.270 0.227 0.287 0.237 0.195 0.257 0.208 0.168 0.229 0.182 0.145 0.205 0.160 0.125 0.183 0.140 | 0.108 0.104 0.073 | 0.051 0.059 0.038 0.024 0.033 0.020 0.012 0.0110.005 0.003 0.766 0.744 0.722 0.701 0.681 0.661 0.642 0.554 0.478 0.412 0.307 0.887 0.037 0.026 0.0160.010 0.007 0.004 0.001 0.001 3: Future Value of Annuity of $1 Future Value of Annuity of $1 Periods 8% 1% 1.000 2.010 3.030 4.060 5.101 2% 1.000 2.020 3.060 4.122 3% 1.000 2.030 3.091 4.184 5.309 4% 1.000 2.040 3.122 4.246 5.416 5% 1.000 2.050 3.153 4.310 5.526 10% 1.000 2.100 3.310 12% 1.000 2.120 3.374 4.779 6.353 4.641 5.204 6.105 6.468 7.662 8.892 10.159 11.464 6.633 7.898 9.214 10.583 12.006 6.802 8.142 9.549 11.027 12.578 6.152 7.214 8.286 9.369 10.462 11.567 12.683 13.809 14.947 16.097 22.019 28.243 34.785 48.886 6.308 7.434 8.583 9.755 10.950 12.169 13.412 14.680 15.974 17.293 24.297 32.030 40.568 60.402 6% 1.000 2.060 3.184 4.375 5.637 6.975 8.394 9.897 11.491 13.181 14.972 16.870 18.882 21.015 23.276 36.786 54.865 | 79.058 154.762 1.000 2.080 3.246 4.506 5.867 7.336 8.923 10.637 12.488 14.487 16.645 18.977 21.495 24.215 27.152 45.762 73.106 113.283 259.057 8.115 10.089 12.300 14.776 17.549 20.655 24.133 28.029 32.393 37.280 14% 16% 18% 20% 1.000 1.000 1.000 1.000 2.140 2. 160 2.180 2.200 3.440 3.506 3.572 3.640 4.921 5.066 5.215 5.368 6.610 6.877 7.154 7.442 8.536 8.977 9.442 9.930 10.730 11.414 12.142 12.916 13.233 14.240 15.327 16.499 16.085 17.519 19.086 20.799 19.337 21.321 23.521 25.959 23.045 25.733 28.755 32.150 27.271 30.850 34.931 39.581 32.089 36.786 42.219 48.497 37.581 43.672 50.818 59.196 43.842 51.660 60.965 72.035 91.025 115.380 146.628 186.688 181.871 249.214 342.603 471.981 356.787 530.312790.948 1,181.882 1,342.025 2,360.757 4,163.213 7,343.858 12.808 14.192 15.618 17.086 18.599 26.870 7.716 9.487 11.436 13.579 15.937 18.531 21.384 24.523 27.975 31.772 57.275 13.486 15.026 16.627 18.292 20.024 14.207 15.917 17.713 19.599 21.579 33.066 47.727 66.439 120.800 36.459 98.347 29.778 41.646 56.085 95.026 72.052 133.334 241.333 767.091 47.575 75.401 164.494 | 442.593 4: Future Value of $1 Future Value of $1 Periods 1% 1.010 1.020 1.030 1.041 1.051 3% 1.030 1.061 1.093 1.126 1.159 4% 1.040 1.082 1.125 1.170 1.217 5% 1.050 1.103 1.158 1.216 1.276 1.340 1.407 1.477 1.551 1.629 1.060 1.124 1.191 1.262 1.338 10% 1.100 1.210 1.331 1.464 1.611 12% 1.120 1.254 1.405 1.574 1.762 14% 1.140 1.300 1.482 1.689 1.925 2.195 16% 1.160 1.346 1.561 1.811 2.100 2.436 18% 1.180 1.392 1.643 1.939 2.288 20% 1.200 1.440 1.728 2.074 2.488 1.974 2.211 2.826 2% 1.020 1.040 1.061 1.082 1.104 1.126 1.149 1.172 1.195 1.219 1.243 1.268 1.294 1.319 1.346 1.486 1.641 1.811 2208 1.194 1.230 1.267 1.305 1.344 1 265 1.316 1.369 1.423 1.480 1.419 1.504 1.594 1.689 1.791 8% 1.080 1.166 1.260 1.360 1.469 1.587 1.714 1.851 1.999 2.159 2.332 2.518 2.720 2.937 3.172 1.772 1.949 2.144 2.358 2.594 2.476 1.062 1.072 1.083 1.094 1.105 1.116 1.127 1.138 1.149 1.161 1.220 1.282 1.348 1.489 2.773 3.106 3.278 3.803 4.411 2.700 3.185 3.759 4.435 5.234 6.176 7.288 8.599 10.147 11.974 1.384 1.426 1.469 1.513 1.558 1.539 1.601 1.665 1.732 1.801 2.191 2.666 3.243 4.801 1.710 1.796 1.886 1.980 2.079 1.898 2.012 2.133 2.261 2.397 3.207 4.292 5.743 10.286 2.853 3.138 3.452 3.797 4.177 6.727 10.835 17.449 45.259 3.707 4.226 4.818 5.492 6.261 7.138 3.479 3.896 4.363 4.887 5.474 9.646 5.117 5.936 6.886 7.988 9.266 2.986 3.583 4.300 5.160 6.192 7.430 8.916 10.699 12.839 15.407 38.338 95.396 237.376 1,469.772 17.000 1.806 2.094 2.427 3.262 2.653 3.386 4.322 7.040 4.661 6.848 10.063 21.725 13.743 26.462 50.950 188.884 29.960 93.051 19.461 40.874 85.850 378.721 27.393 62.669 143.371 750.378 (1) O O O (3) O Scenario 1 Scenario 2 Scenario 3 (2) O highest O lowest Scenario 1 Scenario 2 Scenario 3 (4) O highest O lowest O