Appendix B:

Appendix D:

Mark Ventura has just purchased an annuity to begin payment two years from today. The annuity is for $21,000 per year and is designed to last 9 years. If the interest rate for this problem calculation is 11 percent, what is the most he should have paid for the annuity? Use Appendix B 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.) Maximum payment Appendix B Present value of $1, PVF PV = FV 1 + Percent 1% 4% 5% Period 1 6% 0.943 9% 0.917 0.842 0.772 2 3 3% 0.971 0.943 0.915 0.888 0.863 0.837 0.990 0.980 0.971 0.961 0.951 0.942 0.933 4 2% 0.980 0.961 0.942 0.924 0.906 0.888 0.871 0.853 0.837 0.820 0.804 5 10% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 6 7 7% 0.935 0.873 0.816 0.763 0.713 0.666 0.623 0.582 0.544 0.508 0.475 0.444 0.415 8 9 10 0.952 0.907 0.864 0.823 0.784 0.746 0.711 0.677 0.645 0.614 0.585 0.557 0.530 0.505 0.481 0.458 0.436 0.416 0.396 0.377 0.923 0.914 0.905 0.896 0.887 0.879 0.870 0.861 11 12 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.534 0.513 0.494 0.475 0.456 0.375 0.308 0.208 0.141 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.813 0.789 0.766 0.744 0.722 0.701 0.681 0.661 0.642 0.623 0.605 0.587 0.570 0.554 0.890 0.840 0.792 0.747 0.705 0.665 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 0.394 0.371 0.350 0.331 0.312 0.233 0.174 8% 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.429 0.397 0.368 0.340 0.315 0.292 0.270 0.250 0.232 0.215 0.146 0.099 0.046 0.021 0.708 0.650 0.596 0.547 0.502 0.460 0.422 0.388 0.356 0.326 0.299 0.275 0.252 0.231 0.212 0.194 0.178 0.788 0.773 0.758 0.743 0.728 0.714 0.700 0.686 0.673 0.610 0.552 0.453 0.372 13 11% 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 0.352 0.317 0.286 0.258 0.232 0.209 0.188 0.170 0.153 0.138 0.124 0.074 0.044 0.015 0.005 14 15 16 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149 0.092 0.057 0.022 0.009 0.388 0.362 0.339 0.317 0.296 0.277 0.853 0.844 0.836 0.828 0.820 0.780 0.742 17 18 19 20 0.163 0.146 0.130 0.116 0.104 0.059 0.033 0.258 25 30 0.184 0.131 0.478 0.412 0.307 0.228 0.295 0.231 0.142 0.087 0.116 0.075 0.032 0.013 40 0.672 0.608 0.097 0.054 0.067 0.034 0.011 0.003 50 Appendix B (concluded) Present value of $1 Percent Period 14% 17% 20 25% 40% 50% 1 30 0.769 0.592 0.455 2 3 15 0.870 0.756 0.658 0.572 0.497 0.432 13 0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376 4 5 0.667 0.444 0.296 0.198 0.132 0.088 0.059 0.039 0.026 .017 6 7 0.855 0.731 0.624 0.534 0.456 0.390 0.333 0.285 0.243 0.208 0.178 0.152 0.130 8 9 10 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 .083 0.073 .038 0.020 0.005 0.001 0.333 0.295 0.261 0.231 0.204 16% 0.862 0.743 0.64 1 0.552 0.476 0.410 0.354 0.305 0.263 0.227 0.195 0.168 0.145 0.125 0.108 0.093 0.080 0.069 0.060 0.051 0.024 0.012 0.003 0.001 11 12 18. 0.847 0.718 0.609 0.515 0.437 0.370 0.314 0.266 0.225 0.191 0.162 0.137 0.116 0.099 0.084 0.071 0.060 0.051 0.043 0.037 0.016 0.007 0.001 198 0.840 0.706 0.593 0.499 0.419 0.352 0.296 0.249 0.209 0.176 0.148 0.124 0.104 0.088 0.074 0.062 0.052 0.044 0.037 0.031 0.013 0.005 0.001 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162 0.135 0.112 0.093 0.078 0.065 0.054 0.045 0.038 0.031 0.026 0.010 0.004 0.001 0.800 0.640 0.512 0.410 0.328 0.262 0.210 0.168 0.134 0.107 .086 0.069 0.055 0.044 .035 0.028 0.023 .018 0.014 .012 0.376 0.327 0.284 0 247 0.215 0.187 0.163 0.141 0.123 0.107 0.093 0.081 0.070 0.061 0.030 0.015 0.004 0.001 35% 0.741 0.549 0.406 0.301 0.223 0.165 0.122 0.091 0.067 0.050 0.037 0.027 0.020 0.015 0.011 0.008 0.006 0.005 0.003 0.002 0.001 0.350 0.269 0.207 0.159 0.123 0.094 0.073 0.056 0.043 0.033 0.025 0.020 0.015 0.012 0.009 0.714 0.510 0.364 0.260 0.186 0.133 0.095 0.068 0.048 0.035 0.025 0.018 0.013 0.009 0.006 0.005 0.003 0.002 0.002 0.001 13 14 15 0.181 0.160 0.141 0.125 0.111 0.098 0.012 0.008 0.005 0.003 0.002 0.002 0.001 0.001 16 17 0.111 0.095 0.081 0.069 0.059 0.051 0.043 18 19 20 25 30 40 0.087 0.047 0.026 0.008 0.002 0.020 0.009 0.004 0.001 0.007 0.005 0.001 0.002 50 0 Appendix D Present value of an annuity of $1, PVIFA PVA = A 1 (1 + Y Percent 6% Period 1% 2% 4% 5% 7% 8% 9% 10% 11% 12% 3% 0.971 1 0.935 0.909 WN 0.980 1.942 2.884 3.808 1.913 2.829 3.717 0.901 1.713 2.444 3.102 0.893 1.690 2.402 3.037 4 5 4.580 5.417 6 0.990 1.970 2.941 3.902 4.853 5.795 6.728 7.652 8.566 9.471 10.368 11.255 12.134 7 0.917 1.759 2.531 3.240 3.890 4.486 5.033 5.535 5.995 6.418 6.805 8 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9 10 4.713 5.601 6.472 7.325 8.162 8.983 9.787 10.575 11.348 12.106 12.849 13.578 14.292 14.992 0.962 1.886 2.775 3.630 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 12.659 13.134 13.590 15.622 17.292 6.230 7.020 7.786 8.530 9.253 9.954 10.635 11.296 11.938 12.561 13.166 13.754 11 1.808 2.624 3.387 4.100 4.767 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8.745 9.108 9.447 9.763 10.059 0.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9.712 10.106 10.477 10.828 11.158 11.470 12.783 13.765 0.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 8.244 8.559 8.851 9.122 9.372 9.604 9.818 10.675 11.258 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 7.367 7.606 7.824 8.022 8.201 8.365 3.696 4.231 4.712 5.146 5.537 5.889 6.207 6.492 6.750 6.982 7.191 7.379 7.549 7.702 12 3.605 4.111 4.564 4.968 5.328 5.650 5.938 6.194 6.424 6.628 6.811 6.974 7.120 7.250 7.366 13 14 15 16 13.004 13.865 14.718 15.562 16.398 9.899 10.380 10.838 11.274 11.690 7.161 7.487 7.786 8.061 8.313 8.544 8.756 8.950 9.129 9.823 10.274 17 18 19 20 17.226 7.469 18.046 22.023 25.808 32.835 39.196 15.678 16.351 19.523 22.396 27.355 31.424 14.324 14.877 17.413 19.600 23.115 25.730 12.085 12.462 14.094 15.372 25 30 40 50 10.336 10.594 11.654 12.409 13.332 13.801 7.839 7.963 8.422 8.694 8.514 9.077 9.427 9.779 9.915 7.843 8.055 19.793 21.482 17.159 18.256 15.046 15.762 11.925 12.233 10.757 10.962 8.951 9.042 8.244 8.304 Appendix D (concluded) Present value of an annuity of $1 Percent Period 13% 14% 15% 16% 17% 18% 19% 35% 40% 1 2 3 4 5 6 20% 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 7 8 0.885 1.668 2.361 2.974 3.517 3.998 4.423 4.799 5.132 5.426 5.687 5.918 6.122 6.302 6.462 6.604 6.729 6.840 6.938 7.025 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.265 6.373 6.467 0.847 1.566 2.174 2.690 3.127 3.498 3.812 4.078 4.303 4.494 4.656 0.855 1.585 2.210 2.743 3.199 3.589 3.922 4.207 4.451 4.659 4.836 4.988 5.118 9 0.870 1.626 2.283 2.855 3.352 3.784 4.160 4.487 4.772 5.019 5.234 5.421 5.583 5.724 5.847 5.954 6.047 6.128 6.198 6.259 0.840 1.547 2.140 2.639 3.058 3.410 3.706 3.954 4.163 4.339 4.486 4.611 4.715 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 5.668 5.749 5.818 5.877 5.929 6.097 6.177 6.233 6.246 10 11 12 13 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 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 3.910 3.928 3.942 3.954 3.985 3.995 3.999 4.000 30% 0.769 1.361 1.816 2.166 2.436 2.643 2.802 2.925 3.019 3.092 3.147 3.190 3.223 3.249 3.268 3.283 3.295 3.304 3.311 3.316 3.329 3.332 3.333 50% 0.667 1.111 1.407 1.605 1.737 1.824 1.883 1.922 1.948 1.965 1.977 1.985 1.990 1.993 1.995 1.997 1.998 1.999 1.999 0.714 1.224 1.589 1.849 2.035 2.168 2.263 2.331 2.379 2.414 2.438 2.456 2.469 2.478 2.484 2.489 2.492 2.494 2.496 2.497 2.499 2.500 2.500 2.500 5.229 14 15 16 4.802 4.876 4.938 4.793 4.910 5.008 5.092 5.162 5.222 5.273 5.316 5.353 5.467 5.517 5.548 5.554 17 18 4.192 4.327 4.439 4.533 4.611 4.675 4.730 4.775 4.812 4.843 4.870 4.948 4.979 4.997 4.999 4.988 5.033 5.324 5.405 5.475 5.534 5.584 5.628 5.766 5.829 5.871 5.880 19 5.070 5.101 20 25 6.550 6.623 6.873 7.003 7.105 6.464 7.330 7.496 7.634 30 2.848 2.850 2.856 2.857 2.857 5.195 5.235 5.258 6.566 1.999 2.000 2.000 2.000 2.000 40 50 6.642 6.661 7.675 7.133 5.262 3.333 2.857