Your younger sister, Linda, will start college in five years. She has just informed your parents that she wants to go to Hampton University, which will cost $42,000 per year for four years (cost assumed to come at the end of each year). Anticipating Linda's ambitions, your parents started investing $6,200 per year five years ago and will continue to do so for five more years. Use 12 percent as the appropriate interest rate throughout this problem (for discounting or compounding). How much will your parents have to save each year (A?) for the next five years in addition to the $6,200 they are currently saving to have the necessary funds for Linda's education? Use Appendix C and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) FVA = $2? PVA = $17? A? A? A? A? A? 2 2 2 2 2 2 2 2 2 2 -17 -17 - 17 - 17 -5 - 4 -3 -2 - 1 0 1 2 3 4 5 6 7 8 9 Additional annual savings required Appendix C Future value of an annuity of $1, FVFA Ps =A104/ Percent Period 1% 5% % 8% 10% 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 2.010 2.020 2.030 2.050 2.060 2.080 2.100 2.110 3 3.060 3.153 3.030 4.060 3.310 3.342 2.040 3.122 4.246 5.416 3.091 4.184 5.309 4 1.000 2.070 3.215 4.440 5.751 7.153 4.122 3.184 4.375 5.637 4.310 4.641 4.710 5 5.101 2.090 3.278 4.573 5.985 7.523 9.200 5.204 3.246 4.506 5.867 7.336 8.923 5.526 6.105 6.228 6 6.468 6.152 7.214 8.286 6.308 7.434 6.633 7.898 6.802 8.142 6.975 8.394 7.716 9.487 7 7.662 8.654 8 8.583 8.892 9 9.369 9.755 9.214 10.583 12.006 10.159 9.549 11.027 12.578 7.913 9.783 11.859 14.164 16.722 9.897 11.491 13.181 10.260 11.978 13.816 10.637 12.488 14.487 11.436 13.579 15.937 10 10.462 10.950 11.464 11.567 14.972 15.784 12.169 13.412 12.808 14.192 13.486 15.026 14.207 15.917 16.645 18.977 18.531 21:384 19.561 22.713 12 12.683 17.888 11.028 13.021 15.193 17.560 20.141 22.953 26.019 29.361 33.003 36.974 13 15.618 16.627 17.713 16.870 18.882 21.015 13.809 14.947 20.141 22.550 26.212 30.095 17.086 18.292 19.599 21.495 24.215 27.152 30.324 14.680 15.974 17.293 18.639 20.012 24.523 27.975 31.772 35.950 15 16.097 18.599 20.024 23.276 25.129 27.888 34.405 39.190 16 17.258 18.430 21.579 23.657 25.840 20.157 21.762 21.825 23.698 25.673 28.213 17 30.840 33.750 40.545 44.501 21.412 23.414 30.906 45.599 50.396 18 19 19.615 20.811 25.645 27.671 28.132 30.539 33.999 37.379 41.301 46.018 22.841 25.117 51.159 37450 41.446 45.762 73.106 24.297 33.066 40.995 20 51.160 33.760 36.786 54.865 57.275 56.939 64.203 114.41 26.870 36.459 22.019 28.243 29.778 41.646 47.727 63,249 84.701 25 98.347 32.030 40.588 30 34.785 66.439 94.461 136.31 47.575 75.401 56.085 95.026 152.67 40 60.402 48.886 120.80 79.058 154.76 290.34 113.28 259.06 573.77 164.49 442.59 1.163.9 199.64 406.53 199.02 581.83 1.668.8 337.89 815.08 64.463 84.579 112.80 209.85 Appendix C (concluded) Future value of an annuity of $1 Percent Period % % % 6% 6% T8 B% 19 20% 25% % 1000 1000 1000 2.130 1000 1000 1.000 1000 1000 2160 1000 320 1000 2.150 3473 492 2.180 2.190 2200 2250 200 3374 200 2.170 3.539 5.141 3.640 4779 2.1 3.440 4929 6.610 8.536 10730 3.213 5766 5.368 3.407 4.350 6.480 8823 10.405 63553 85 31506 5.066 6877 88977 7.014 16.742 8.754 3572 5.215 7154 9.442 12.142 15.327 1442 9930 12.96 8297 259 15.072 101089 9207 11772 4.73 1067 11414 8 27 14240 123 16.685 6.499 15.416 18420 17519 19.086 3606 5291 1297 9.683 2.523 15.902 19.923 24701 30.404 37.180 45244 54841 2727 16.786 20304 24.349 201799 200 1496 59 20 655 24133 8023 3293 18285 22.393 1234se7egot 2 3 Sense B 21.94 27.2009 3990 5.137 9.043 2756 583 858 32.015 42619 5605 34327 9765 279 639 8.4 29.002 19337 23.045 272 2089 37581 43.842 50980 25.650 39985 34.883 21.321 25.733 30.850 36.786 43.677 51660 60925 23.521 28755 34931 42219 50.818 60965 2559 150 39.58 48.497 32.824 39.404 19842 82 3253 47566 5708 60 649 0959 18 4.352 14 47.103 59196 40505 47,580 40.4 46.672 6.61 79850 55.77 2035 442 7299 7286 42753 8884 55750 63.440 59.18 65.07 15 575 70.749 68294 78969 7586 8212 71673 84.149 92.60 : 56.110 66.649 72.979 93.406 29 20.03 221 96222 5.27 138 128.12 434 85.01 48397 20 6542 86.69 115 24931 40204 2052 132 24133 76709 498 37.068 10374 2:41 146.53 3420 7909 4.162.2 220 0947 155.62 29320 1013.7 91025 1024 13187 2279 25679 434.75 1342.0 1791 49945 72177 605 3756 4295 10548 2272 200890 280256.0 54744 50E 260.8 966. 5529.8 40 530 248.80 800 20,393.0 1,559.60 3.124.5 15,0900 1189 73439 45.4970 2000 24595 104360 1515.0 Appendix D Present value of an annuity of $1, PV FA PVA = A 1- (1 + 71 Percent Period 2% 4% 5% 5% 8% 9 10% 11% 12% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 2 1.970 1.942 1.913 1.859 1.808 1.7 13 1.690 3 2.884 1.833 2.673 2.941 3.902 1.886 2.775 3.630 2.723 2.624 2.829 3.717 1.783 2.577 3.312 1.759 2.531 3.240 1.736 2.487 3.170 2444 4 3.808 3.546 3.465 3.387 3.102 2.402 3.037 3.605 5 4.853 4.580 4.452 4.329 4.212 4.713 5.601 3.890 3.696 6 5.795 4.100 4.767 3.993 4.623 5.242 3.791 4.355 5.417 5.076 4.917 4.486 4.231 4.111 7 6.728 6.002 5.786 5.033 4.868 4.712 4.564 6.472 7.325 6.230 7.020 8 5.582 6.210 7.652 5.206 5.747 6.733 5.389 5.971 6.515 6.463 5.535 5.335 5.146 4.968 9 8.162 7.435 6.247 8.566 9.471 5.759 5.328 7.108 7.722 10 5.537 5.889 7.024 6.802 7.360 7.887 8.983 9.787 7.786 8.530 9.253 9.954 6.145 8.111 8.760 5.995 6.418 6.805 6.710 7.139 10.368 8.306 5.650 5.938 7.499 6.495 6.207 12 11.255 10.575 9.385 8.863 8.384 7.943 6.492 6.194 7.536 7.904 7.161 7.487 6.814 7.103 13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 6.750 6.424 14 13.004 12.106 11.296 10.563 9.899 8.745 8.244 7.786 15 12.849 13.865 11.938 6.982 7.191 10.380 6.628 6.811 11. 118 9.295 9.712 10.106 9.108 8.559 8.061 8.313 16 14.718 12.561 10.838 9.447 8.851 11.652 12.166 7.367 7.606 7.824 8.022 8.201 6.974 13.578 14.292 14.992 17 15.562 13.166 11.274 10.477 9.763 10.059 7.120 9.122 9.372 7.379 7.549 7.702 8.544 8.756 18 16.398 13.754 12.659 11.690 10.828 7.250 19 17.226 15.678 13.134 9.604 8.950 8.365 14.324 14.877 12.085 12.462 11.158 11.470 10.336 10.594 7.839 7.963 7.366 7.469 20 18.046 16.351 13.590 9.818 9.129 8.514 25 19523 15.622 14.094 12.783 10.675 9.823 9.077 22.023 25.808 17.413 19.600 11.654 12.409 8.422 8.694 7.843 8.055 30 22.396 17 292 15.372 13.765 11.258 10.274 9.427 40 32.835 19.793 17.159 15.046 13.332 11.925 10.757 8.951 27355 31.424 23.115 25.730 9.779 9.915 8.244 8.304 50 39.196 21.482 18.256 15.762 13.801 12.233 10.962 9.042 Appendix D (concluded) Present value of an annuity of $1 Percent Period 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 35% 40% 50% 1 0.885 0.877 0.855 0.870 1.626 0.847 0.800 0.862 1.605 0.769 2 1.668 1.647 0.840 1.547 0.833 1.528 1.585 1.566 0.741 1.289 0.714 1.224 0.667 1.111 1.440 1.361 3 2.322 2.361 2.974 2.246 2.174 2.283 2.855 2.140 2.106 1.696 1.589 4 2.210 2.743 2.914 1.952 2.362 2.798 1.816 2.166 2.690 2.639 2.589 1.997 1.849 5 3.433 3.517 3.998 3.127 2.689 1.407 1.605 1.737 1.824 3.274 3.685 2.436 3.199 3.589 2.220 6 2.035 3.889 2.991 3.326 3.352 3.784 4.160 4.487 3.498 2.951 2.643 2.385 2.168 7 4.423 3.058 3.410 3.706 3.954 4.039 3.812 3.161 1.883 8 4.799 4.288 4.639 4.946 4.344 3.922 4.207 4.451 4.078 3.605 3.837 4.031 3.329 2.508 2.598 2.665 2.263 2.331 2.379 9 5.132 4.772 4.607 4.303 2.802 2.925 3.019 3.092 3.147 4.163 1.922 1.948 3.463 10 5.426 5.2 16 4.659 4.494 4.192 5.019 5.234 2.715 2.414 1.965 11 4.339 4.486 5.687 4.833 5.029 5.197 5.453 3.571 3.656 4.836 4.656 2.752 2.438 1.977 12 5.660 4.988 3.725 5.918 6.122 5.421 5.583 2.779 2.456 4.611 4.7 15 1.985 4.793 4.910 13 5.842 4.327 4.439 4.533 4.611 3.190 3.223 5.342 5.118 3.780 2.799 2.469 14 6.302 6.002 1.990 1.993 5.008 4.802 3.824 3.249 5.724 5.847 6.462 6.142 5.468 5.575 5.668 5.229 5.324 5.405 5.092 4.876 15 16 4.675 3.859 2.814 2.825 2.834 6.604 6.265 1.995 1.997 5.954 5.162 4.938 4.730 2478 2.484 2.489 2.492 3.887 6.729 6.373 6.047 4.775 2.840 1.998 5.749 5.818 5.222 5.273 4.988 5.033 18 3.268 3.283 3.295 3.304 3.311 3.316 6.840 6.467 6.128 4.812 2.844 2.494 5.475 5.534 5.584 5.628 1.999 3.910 3.928 3.942 3.954 19 6.198 5.877 5.316 2.848 2.496 1.999 6.938 7.025 6.550 6.623 5.070 5.101 4.843 4.870 20 6.259 5.929 5.353 2.850 2.497 1.999 25 6.873 6.097 5.766 5.467 4.948 2.856 2.499 7.330 7.496 7.634 6.464 6.566 30 5.517 4.979 7.003 7.105 2.857 6.177 6.233 2.500 3.985 3.995 3.999 5.195 5.235 5.258 5.262 3.329 3.332 3.333 5.829 5.871 5.880 2.000 2.000 2.000 6.642 5.548 4.997 2.857 2.500 50 7.675 7.133 6.661 6.246 5.554 4.999 4.000 3.333 2.857 2.500 2.000