- Your uncle is 70 years old. Over the years, he has accumulated savings of $400,000. He estimates that he will live another 10 years at the most and he wants to spend his savings by then. He places his $400,000 into an account earning 8% annually and sets it up in such a way that he will be making 10 equal annual withdrawals.
How much will he be able to withdraw each year?
- Your mother is planning to retire this year. Her firm has offered her a lump-sum retirement plan of $120,000 or a $10,000 lifetime annuity, whichever she chooses. Your mother is in reasonable good health and expects to live for at least 20 more years. Which option should she choose, assuming that a 7% interest rate is appropriate to evaluate the annuity?
- You just won $200,000 in the lottery. You have decided to invest this amount and to withdraw an equal amount each year for 5 years. How much can you withdraw each year if you invest the $200,000 at 10% compounded annually?
- You want to spend $15,000 on a vacation at the end of each of the next 5 years. What lump sum do you have to invest now to take the 5 vacations, assuming that your minimum desired rate of return is 5% compounded annually.
- If you desire to have $50,000 for a down payment for a house that you plan to buy in three years, what amount would you need to deposit today? Assume that your money will earn 8 percent.
Present value interest factor of $1 per period at i% for n periods, PVIF(i,n). (TABLE #1) Period 1% 2% 3% 4% 5% 10.990 0.990 0.980 0.971 0.962 0.952 2 0.980 0.980 0.961 0.943 0.925 0.907 3 0.971 0.942 0.915 0.889 0.864 4 0.961 0.924 0.888 0.855 0.823 wooo wo 5 0.951 0.906 0.863 0.822 0.784 we vide 6 0.942 1:24 0.888 0.837 0.790 0.746 7 0.933 0.871 V. Dom 0.813 0.01 0.760 0.711 8 0.923 0.853 viac 0.789 0.731 wo 0.677 400 wer 9 0.914 0.837 0.766 0.703 Vio SO 0.645 10 0.905 0.820 0.02 0.676 Doc 0.744 0.11+ 0.org 0.614 0.014 11 0.896 0.804 0.722 0.650 0.585 12 0.887 0.788 0.701 0.625 0.557 . re ! - 20 13 0.879 0.773 0.681 0.601 0.530 wo ! 14 0.870 0.758 0.661 0.577 0.505 we 15 0.861 0.743 0.642 0.555 vice Vart JU 0.481 Video 16 0.033 0.853 0.728 0.623 0.023 0.534 20 0.458 17 0.844 0.044 0.714 0.605 0.513 0.436 0.439 18 1o 0.836 0.030 0.00 0.700 0.587 0.494 0.484 0.416 0.419 19 0.020 0.828 0.686 0.000 0.570 0.475 0 0.413 0.396 www 20 0.820 0.673 0.554 0.012 0.456 1.430 0.377 V. 25 0.780 0.610 0.478 0.375 0.295 30 0.742 0.552 0.308 0.231 35 0.706 0.500 0.355 0.253 0.181 40 0.672 0.453 0.307 0.208 0.142 50 0.608 0.372 0.228 0.087 6% 7% 0.943 0.935 0.890 0.873 0.840 0.816 0.792 0.763 0.747 0.713 0.705 0.666 1.000 D. 0.665 0.623 0.003 0.02 0.627 0.582 De 20 0.592 0.544 0.558 0.508 0.300 0.527 0.475 0.497 0.444 11 0.469 0.415 0.442 0.388 0.417 0.362 Van 0.394 0.594 0.339 0.339 0.371 0.317 0.350 Die 0.296 0.331 0.277 Ver 0.312 0.258 V.230 0.233 0.233 0.184 0.174 0.131 0.130 0.094 0.097 0.067 0.054 0.034 8% 9% 10% 11% 0.926 0.917 0.909 0.901 0.857 0.842 0.826 0.812 0.794 0.772 0.751 0.731 0.735 0.708 0.683 0.659 0.681 0.650 0.621 0.593 e 0.630 0.000 0.596 9.00 0.564 0.535 Dado 0.583 0.547 0.513 0.347 0.313 0.482 0.540 0.002 0.502 0.467 0.434 0101 1.404 0.500 0.460 0.424 0.391 0.463 0.400 0.422 0.386 0.422 V.300 0.352 Devel 0.429 0.388 0.350 0.317 0.397 0.356 0.319 0.286 0.368 we 0.326 0.290 0.258 0.340 0.299 0.263 0.232 0.315 0.275 0.239 0.209 Der Service 0.292 0.252 0.210 0.108 0.218 0.188 0.270 0.270 0.231 0.198 0.170 0.250 0.212 0.214 0.180 0.100 0.153 0.13 V.202 0.232 0.194 0.164 0.138 D. 0.215 0.178 0.110 0.149 0.124 0.127 0.146 0.116 0.092 0.074 0.099 0.075 0.057 0.044 0.068 0.049 0.036 0.026 0.046 0.032 0.022 0.015 0.021 0.013 0.009 0.005 12% 0.893 0.797 0.712 0.636 tes 0.567 0.307 0.507 0.452 0.404 1.404 0.361 0.322 Dave 0.287 0.257 0.229 0.205 0.10 0.183 0.163 0.163 0.146 0.130 Side 0.116 0.104 0.109 0.059 0.033 0.019 0.011 0.003 13% 14% 0.885 0.877 0.783 0.769 0.693 0.675 0.613 0.592 0.543 0.519 . 0.480 0.456 0.425 0.400 0.42 0.400 0.376 0.351 0.333 0.308 Vio 0.295 0.270 0.21 V.2 0.261 0.237 0.231 0.208 0.204 0.182 w 0.181 0.160 0.160 0.140 Dance . 0.141 0.123 0.12 0.125 0.111 0.095 0.098 0.098 0.083 9.00 0.087 0.00 0.073 More 0.047 0.038 0.026 0.020 0.014 0.010 0.008 0.005 0.002 0.001 15% 0.870 0.756 0.658 0.572 4 0.497 0.432 1:22 0.376 0.327 0.284 0.247 0.24 0.215 0.187 10 0.163 0.141 0.123 . 0.107 0.093 0.093 0.081 0.070 voru 0.061 0.001 0.030 0.015 0.008 0.004 0.001 16% 17% 0.862 0.855 0.743 0.731 0.641 0.624 0.552 0.534 w 0.476 0.456 114 0.410 0.390 0.419 20 0.354 0.333 0.33 0.034 0.305 0.285 0.263 0.243 wa 4 0.227 0.208 V.22 Vicce 0.195 0.178 0.168 0.152 100 0.145 0.130 war 0.125 0.111 w 0.108 0.095 Valvo a 0.093 0.081 0.001 0.09 0.000 0.080 0.069 0.069 0.059 0.060 0.051 0.051 0.043 0.043 0.024 0.020 0.012 0.009 0.006 0.004 0.003 0.002 0.001 0.000 18% 19% 20% 0.847 0.840 0.833 0.718 0.706 0.694 0.609 0.593 0.579 0.516 0.499 0.482 w 0.437 0.419 0.402 ve! 12 vre 0.370 0.10 0.334 0.352 V.233 0.335 0.314 0.296 0.14 9.2 0.279 22 0.266 0.249 0.233 2:00 0.249 Vio 0.225 0.209 0.194 194 0.191 0.19 0.176 0.170 0.162 0.162 0.148 0.135 0.137 0.124 0.112 0.116 0.104 0.093 0.099 0.088 0.078 0.084 0.074 0.065 Vivo vor 0.071 0.064 0.062 0.054 0.060 0.052 0.045 0.051 0.03 0.044 0.038 0.043 0.037 1.04 0.031 0.0" 0.037 0.031 0.00 0.00 0.026 V.UZ 0.016 0.013 0.010 0.007 0.005 0.004 0.003 0.002 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.108 0.412 0.141 5% 6% 0.926 0.901 3.902 11. 206 10 300 050 Present value interest factor of an (ordinary) annuity of $1 per period at i% for n periods, PVIFA(i,n). (TABLE #2) Period 1% 2% 3% 4% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.917 0.909 0.893 0.885 0.877 0.870 0.862 0.855 0.855 0.847 0.840 0.833 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 4 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 5 4 853 4 743 4580 4452 4329 3 4.580 4.713 4212 4.329 4.033 4.452 4100 3890 3701 3.993 4.214 4.100 3.435 3.890 3.605 3.517 3.191 3.352 3.274 3.274 3.199 3.127 ca 700 5.147 2.991 3.058 3.696 3.605 5800 6 3.433 5.795 4047 5.601 5076 2.991 787 200 5.417 5.242 1699 200 5.076 4.917 2000 4.767 4.623 4.486 4.355 4.231 4.111 3.998 3.784 2.140 3.500 3.685 3.100 3.589 3.498 3.889 2226 3.410 5002 7 70g 3.326 EOS 6.230 5200 5.786 6.628 208 CO 6.472 5023 5.582 5.206 5.389 6.002 74 er 5.033 200 499 4.712 4.564 4.868 450 ZE 3922 4.288 4.160 4.039 2042 2208 2295 3.922 3.605 4.423 3.812 2020 3.706 8 662 7.325 6240 7.652 7.020 3.605 6733 AZAZ 6.463 6.733 5071 696 we 6235 5.535 5.971 6.210 oso 5.335 5.146 5.747 MOZ 62 4.968 4.799 OBEC 4344 4.639 4.487 A 207 4.344 4.207 4.078 3937 640 3.954 9 3.837 7135 7400 8.162 7.786 7.435 8.566 7.108 247 6545 6.802 6.515 5005 6220 5.995 6627 5.759 5.537 A 216 5.328 6.247 5.132 Soz 772 4.7724.607 4.946 4154 za 203 163 10 0001 1024 4.451 0620 10 4.303 4.163 7 722 4.031 7280 8.983 8.530 9.471 2004 7.360 7.722 740 7.024 8.111 6.418 6.710 6108 6.145 Love 5 650 5.889 1400 650 5.650 5.216 5.019 4.833 5.426 4.659 4.494 4.339 4.192 mo 11 10.368 9.787 9.253 8.760 8.306 7.499 22 7.887 1926 7.139 6.805 5.938 OEM 6.495 6.207 des 5.453 5.234 40 620 5.029 5.687 200 0202 4.836 11.255 4.656 4.486 4.327 2014 10.575 12 9.954 9.385 8.863 7.943 8.384 7.536 044 7.161 104 6103 6.814 6040 6.492 6.194 124 5 B60 end 5.421 5.918 49240 1000 5.660 13 12434 702 12 4.988 4.793 5.197 10635 12.134 4.439 11.348 4.611 0.00 0304 10.635 9.986 13 250 9.394 7004 8.853 8.358 7.904 7.487 6022 7.103 750 B12 6.750 6.424 6.122 1040 5.342 5.842 5.583 245 44 5.118 4.910 4.715 533 40 562 13.004 0 000 12.106 4.533 0205 14 O 745 10.563 9.899 9.295 8.745 8.244 7.786 6.982 7.367 6.628 202 6.620 00 5460 5220 6.302 15 6.002 5.724 5.468 1902 42010 5.229 15 5.008 4.802 4.611 13.865 14929 44.440 11.938 12.849 742 11.118 9.712 0400 9.108 550 8.559 7,404 8064 8.061 7.191 6.811 7.606 5017 6.462 6142 6.462 . 5 575 6.142 5.847 are 5002 5.575 were 5.324 1675 5.092 4.876 40020 16 14.718 40 400 an 4.675 word 13.578 02 12.561 11.652 10.838 10.106 ca ce see 8.851 2020 122 mu 7.379 6.974 6.604 9.447 12 8.313 7.824 6.265 5.668 5.954 5.162 4.938 17 5.405 w 15.562 w 14.292 13.166 4.730 703 12.166 11.274 a 10.477 9.763 9.122 8.544 20 7.549 7.120 8.022 12e 1000 6.373 6.047 6.729 5.749 5.475 re 100 We 5.222 4.990 16.398 4.775 18 14.992 13.754 12.659 4700 zara 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250 ca 40 479 6.840 6.467 6.128 5.818 5.534 19 5.273 5.033 4.812 are 17.226 12422 15.678 2008 14.324 13.134 12.085 11.158 40290 ar 7000 2288 10.336 9.604 200 020 7.839 7.366 6.938 8.365 102 40 COM 20 6.550 6.198 5.877 44 077 5.316 5.070 4.843 20 42 22 5.584 4420 18.046 16.351 40 14.877 13.590 12.462 11.470 0040 10.594 9.818 9.129 0 544 7052 8.514 7.963 7.469 7.025 6.623 6.259 6020 FC 5363 6404 5.929 070 5.628 mo 5.353 5.101 4.870 25 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.8239.077 8.422 7.843 7.330 6.873 6.464 6.097 5.766 5.467 5.195 4.948 30 25.808 22.396 19.600 17.292 15.372 13.765 12.409 11.258 10.274 9.427 8.694 8.055 7.496 7.003 6.566 6.177 5.829 5.517 5.235 4.979 35 29.409 24.999 21.487 18.665 16.374 14.498 12.948 11.655 10.567 9.644 8.855 8.176 7.586 7.070 6.617 6.215 5.858 5.539 5.251 4.992 40 32.835 27.355 23.115 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.951 8.244 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 50 39.196 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962 9.915 9.042 9.042 8.304 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999
