Problem 9-47 Special consideration of annuities and time periods [LO9-4] Your parents have accumulated a $140,000 nest egg. They have been planning to use this money to pay college costs to be incurred by you and your sister, Courtney. However, Courtney has decided to forgo college and start a nail salon. Your parents are giving Courtney $23,000 to help her get started, and they have decided to take year-end vacations costing $9,000 per year for the next four years. Use 9 percent as the appropriate interest rate throughout this problem. Use Appendix A and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a. How much money will your parents have at the end of four years to help you with graduate school, which you will start then? (Round your final answer to 2 decimal places.) Funds available for graduate school b. You plan to work on a master's and perhaps a PhD. If graduate school costs $25,100 per year, approximately how long will you be able to stay in school based on these funds? (Round your final answer to 2 decimal places.) Number of years Appendix A Future value of $1, FVF FV = PV(1 + i)" Percent Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 1 1.010 1.020 1.030 1.040 1.050 1.080 1.090 1.100 1.060 1.124 2 1.040 1.103 1.082 1.125 1.188 1.295 1.210 1.331 1.110 1.232 1.368 3 1.158 1.191 1.020 1.030 1.041 1.051 1.062 1.061 1.082 4 1.170 1.216 1.518 1.061 1.093 1.126 1.159 1.194 1.230 5 1.166 1.260 1.360 1.469 1.587 1.714 1.104 1.276 1.262 1.338 1.419 1.217 1.265 1.070 1.145 1.225 1.311 1.403 1.501 1.606 1.718 1.838 1.412 1.539 1.677 1.464 1.611 1.772 1.949 6 1.126 1.149 1.340 1.407 7 1.072 1.316 1.504 1.828 1.685 1.870 2.076 2.305 2.558 8 1.083 1.172 1.267 1.305 1.369 1.423 1.477 1.551 1.594 1.689 1.851 1.999 1.993 2.172 9 1.094 1.195 10 1.105 1.629 1.791 1.219 1.243 1.344 1.384 2.159 2.332 2.367 2.580 2.144 2.358 2.594 2.853 3.138 2.839 3.152 11 1.898 1.480 1.539 1.601 1.665 1.116 1.127 1.710 1.796 12 1.426 2.012 1.268 1.294 2.518 2.720 13 1.138 1.469 1.886 1.967 2.105 2.252 2.410 2.579 2.759 2.952 2.133 2.813 3.066 3.342 3.452 14 1.513 1.732 1.980 2.937 1.149 1.161 1.319 1.346 2.261 2.397 3.498 3.883 4.310 4.785 5.311 5.895 15 1.558 1.801 2.079 3.642 3.970 16 1.173 1.605 2.183 2.540 1.373 1.400 3.172 3.426 3.700 3.996 17 1.184 1.653 2.292 2.693 1.873 1.948 2.026 2.107 4.328 3.797 4.177 4.595 5.054 5.560 6.116 6.727 10.835 18 1.196 1.428 1.702 3.159 3.380 3.617 19 4.717 5.142 1.208 2.407 2.527 2.653 1.457 2.854 3.026 3.207 1.754 1.806 2.094 20 1.486 2.191 5.604 1.641 2.666 3.386 25 30 1.220 1.282 1.348 1.489 4.316 4.661 6.848 10.063 21.725 46.902 1.811 2.208 2.427 3.262 6.544 7.263 8.062 13.585 22.892 65.001 184.57 4.292 5.743 10.286 18.420 3.870 5.427 7.612 14.974 29.457 3.243 4.801 7.107 4.322 7.040 11.467 8.623 13.268 31.409 74.358 40 17.449 45.259 117.39 50 1.645 2.692 4.384 Appendix A (concluded) Future value of $1 Percent Period 12% 13% 14% 15% 17% 19% 25% 30% 1.130 1.140 1 2 1.250 1.120 1.254 1.300 1.150 1.323 16% 1.160 1.346 1.561 18% 1.180 1.392 1.170 1.369 20% 1.200 1.440 1.190 1.416 1.277 1.690 3 1.443 1.300 1.482 1.689 1.521 1.602 1.643 1.685 2.197 4 1.630 1.749 1.811 2.856 1.728 2.074 2.488 2.986 5 1.874 2.192 2.565 1.925 2.195 1.563 1.953 2.441 3.052 3.815 4.768 2.005 2.386 2.840 1.842 2.082 2.353 2.100 2.436 3.713 4.827 6 1.405 1.574 1.762 1.974 2.211 2.476 2.773 3.106 3.479 7 2.826 3.001 1.939 2.288 2.700 3.185 3.759 4.435 5.234 3.379 3.583 6.276 2.011 2.313 2.660 3.059 3.518 4.046 2.502 2.853 3.252 8 2.658 3.278 5.960 8.157 9 4.300 5.160 3.004 3.511 4.108 4.807 3.803 4.021 4.785 5.696 7.451 10.604 13.786 10 3.395 4.411 6.192 9.313 3.707 4.226 11 3.836 4.652 5.624 6.176 6.777 7.430 17.922 11.642 14.552 12 3.896 5.350 6.580 8.064 8.916 23.298 4.335 4.898 4.818 5.492 7.288 8.599 13 4.363 5.117 5.936 6.886 7.988 9.266 6.153 7.699 9.596 10.699 18.190 30.288 14 4.887 7.076 39.374 5.535 6.254 6.261 7.138 9.007 10.539 10.147 11.974 11.420 13.590 12.839 15.407 22.737 28.422 15 5.474 8.137 9.358 8.137 12.330 16.172 35.527 16 17 7.067 7.986 9.024 51.186 66.542 86.504 112.46 9.276 19.244 6.130 6.866 7.690 8.613 9.646 44.409 10.761 12.375 18 10.748 12.468 14.463 16.777 19.461 40.874 10.575 12.056 13.743 26.462 14.426 16.879 19.748 23.106 19 18.488 22.186 26.623 31.948 38.338 95.396 20 14.129 16.672 19.673 23.214 27.393 62.669 143.37 750.38 3,927.4 22.091 27.252 32.429 77.388 184.68 146.19 190.05 705.64 25 10.197 11.523 21.231 39.116 132.78 450.74 50.658 14.232 16.367 32.919 66.212 267.86 1,083.7 55.511 69.389 86.736 264.70 807.79 7,523.2 70,065.0 17.000 29.960 93.051 289.00 85.850 30 40 50.950 188.88 111.07 533.87 378.72 1,670.7 1,051.7 5,988.9 237.38 1,469.8 9,100.4 2,620.0 36,1 19.0 497,929.0 50 700.23 2,566.2 Appendix D Present value of an annuity of $1, PVIFA PVA=A1- 1 (1 + i)" Percent 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% Period 1 2 3 0.980 1.942 0.935 1.808 0.990 1.970 2.941 3.902 0.971 1.913 2.829 3.717 0.962 1.886 2.775 3.630 0.952 1.859 2.723 3.546 0.943 1.833 2.673 3.465 0.926 1.783 2.577 3.312 0.917 1.759 2.531 3.240 12% 0.893 1.690 2.402 3.037 2.884 2.624 4 3.387 5 11% 0.901 1.713 2.444 3.102 3.696 4.231 4.712 5.146 5.537 4.329 4.100 3.605 4.212 4.917 3.890 4.486 6 4.767 4.111 7 8 4.853 5.795 6.728 7.652 8.566 3.808 4.713 5.601 6.472 7.325 8.162 8.983 9.787 10.575 11.348 4.580 5.417 6.230 7.020 7.786 5.076 5.786 6.463 7.108 5.582 6.210 6.802 3.993 4.623 5.206 5.747 6.247 5.033 5.535 5.995 6.418 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 4.564 4.968 5.328 5.650 9 10 9.471 8.530 7.722 6.710 11 10.368 4.452 5.242 6.002 6.733 7.435 8.111 8.760 9.385 9.986 10.563 11.118 11.652 12.166 8.306 7.360 7.887 8.384 7.139 5.938 9.253 9.954 10.635 6.805 7.161 12 8.863 11.255 12.134 7.536 6.194 6.424 13 9.394 8.853 7.904 7.487 14 6.628 9.899 10.380 11.296 11.938 12.561 7.786 8.061 15 13.004 13.865 14.718 15.562 16.398 12.106 12.849 13.578 14.292 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8.745 9.108 9.447 9.763 10.059 10.336 10.594 11.654 12.409 13.332 6.811 5.889 6.207 6.492 6.750 6.982 7.191 7.379 7.549 7.702 9.295 9.712 10.106 10.477 10.828 8.244 8.559 8.851 9.122 7.367 7.606 7.824 16 10.838 6.974 8.313 8.544 17 13.166 8.022 11.274 11.690 18 14.992 9.372 13.754 14.324 12.659 13.134 8.756 8.950 8.201 8.365 7.120 7.250 7.366 19 17.226 12.085 11.158 8.514 20 25 30 15.678 16.351 19.523 22.396 27.355 14.877 17.413 19.600 13.590 15.622 18.046 22.023 25.808 32.835 39.196 9.129 9.823 7.469 7.843 9.604 9.818 10.675 11.258 11.925 12.462 14.094 15.372 17.159 18.256 11.470 12.783 13.765 15.046 15.762 17.292 7.839 7.963 8.422 8.694 8.951 9.042 9.077 9.427 9.779 9.915 10.274 40 23.115 19.793 10.757 8.055 8.244 8.304 50 ................. 31.424 25.730 21.482 13.801 12.233 10.962 Appendix D (concluded) Present value of an annuity of $1 13% 14% 15% 16% 17% 18% 30% 40% 50% Period 1 2 1 ............ 0.885 1.668 2.361 2.974 Percent 19% 0.840 1.547 2.140 2.639 0.714 1.224 1.589 3 4 1.849 5 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 0.769 1.361 1.816 2.166 2.436 2.643 3.517 3.998 0.667 1.111 1.407 1.605 1.737 1.824 0.862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 4.833 5.029 0.855 1.585 2.210 2.743 3.199 3.589 3.922 4.207 4.451 4.659 4.836 6 0.870 1.626 2.283 2.855 3.352 3.784 4.160 4.487 4.772 5.019 5.234 5.421 0.847 1.566 2.174 2.690 3.127 3.498 3.812 4.078 4.303 4.494 4.656 20% 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 2.035 2.168 3.058 3.410 3.706 3.954 7 4.423 2.802 2.263 1.883 8 25% 0.800 1.440 1.952 2.362 2.689 2.951 3.161 3.329 3.463 3.571 3.656 3.725 3.780 3.824 3.859 3.887 9 2.925 3.019 3.092 3.147 2.331 2.379 2.414 10 11 4.799 5.132 5.426 5.687 5.918 6.122 6.302 6.462 6.604 2.438 35% 0.741 1.289 1.696 1.997 2.220 2.385 2.508 2.598 2.665 2.715 2.752 2.779 2.799 2.814 2.825 2.834 2.840 2.844 2.848 2.850 2.856 2.857 4.163 4.339 4.486 4.611 4.715 4.802 12 5.660 4.793 3.190 2.456 5.197 5.342 4.439 4.533 1.922 1.948 1.965 1.977 1.985 1.990 1.993 1.995 1.997 13 4.910 3.223 2.469 5.842 6.002 5.583 5.724 14 4.988 5.118 5.229 5.324 5.405 5.468 5.008 4.611 3.249 2.478 15 5.847 4.876 3.268 6.142 6.265 6.373 5.575 5.668 5.092 5.162 2.484 2.489 16 4.938 3.283 5.954 6.047 17 6.729 5.749 5.475 5.222 4.988 4.675 4.730 4.775 4.812 4.843 3.910 3.295 2.492 1.998 18 6.840 6.128 5.534 5.273 5.033 1.999 3.304 3.311 19 6.198 5.818 5.877 5.929 5.316 6.938 7.025 5.070 6.467 6.550 6.623 6.873 7.003 1.999 1.999 20 4.870 3.316 25 6.259 6.464 6.566 6.642 3.928 3.942 3.954 3.985 3.995 3.999 5.584 5.628 5.766 5.829 5.871 2.494 2.496 2.497 2.499 2.500 2.500 5.353 5.467 5.517 7.330 7.496 7.634 5.101 5.195 5.235 4.948 6.097 6.177 6.233 3.329 3.332 30 2.000 2.000 4.979 4.997 40 7.105 5.548 5.258 3.333 2.857 2.000 50 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999 4.000 3.333 2.857 2.500 2.000