How much would you need to invest now to be able to withdraw $8,000 at the end of every year for the next 20 years? Assume a 12% interest rate. Assume that you want to have $170,000 saved seven years from now. If you can invest your funds at an 8% interest rate, how much do you currently need to invest? Your aunt Joan plans to give you $5,000 at the end of every year for the next ten years. If you invest each of her yearly gifts at a 12% interest rate, how much will they be worth at the end of the ten-year period? Suppose you want to buy a small cabin in the mountains four years from now. You estimate that the property will cost $54,000 at that time. How much money do you need to invest each year in an interest-bearing account at the rate of 6% per year to accumulate the purchase price? Present Value of $1 Periods | 1% | 2% | 3% | 4% | 5% | 6% 8% | 10% | 12% | 14% | 16% | 18% | 20% 10.990 0.9800.9710.9620.952 0.943 0.9260.9090.8930.877 0.8620.847 0.833 2 0.9800.9610.9430.9250.907 0.890 0.857 0.826 0.7970.7690.7430.718 0.694 3 0.971 0.942 0.915 0.8890.864 0.840 0.794 0.751 0.712 0.675 0.640.6090.579 40.961 0.924 0.888 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.5520.5160.482 5 0.951 0.906 0.863 0.822 0.784 0.7470.6810.6210.5670.519 0.4760.4370.402 6 0.942 0.888 0.837 0.7900.746 0.705 0.630 0.5640.507 0.4560.410 0.370 0.335 7 0.9330.871 0.813 0.760 0.711 0.665 0.5830.513 0.452 0.400 0.3540.314 0.279 8 0.923 0.8530.789 0.731 0.677 0.627 0.540 0.467 0.404 0.3510.3050.2660.233 90.914 0.837 0.7660.703 0.645 0.592 0.500 0.4240.361 0.308 0.2630.2250.194 10 0.905 0.820 0.7440.676 0.6140.558 0.463 0.3860.3220.2700.227 0.191 0.162 110.8960.804 0.722 0.650 0.5850.527 0.429 0.350 0.287 0.2370.1950.162 0.135 12 0.887 0.788 0.701 0.625 0.557 0.4970.397 0.319 0.257 0.208 0.1680.1370.112 13 0.879 0.773 0.681 0.601 0.530 0.4690.368 0.290 0.229 0.182 0.145 0.1160.093 14 0.870 0.758 0.661 0.577 0.505 0.442 0.340 0.2630.2050.1600.125 0.0990.078 15 0.861 0.743 0.642 0.555 0.481 0.417 0.3150.2390.1830.140 0.108 0.0840.065 20 0.820 0.673 0.5540.4560.377 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 25 0.780 0.610 0.478 0.375 0.295 0.233 0.146 0.092 0.059 0.038 0.024 0.016 0.010 30 0.742 0.552 0.412 0.308 0.231 0.174 0.099 0.057 0.033 0.020 0.012 0.0070.004 40 0.672 0.453 0.307 0.208 0.142 0.097 0.046 0.022 0.0110.005 0.0030.001 0.001 997 86 930 39 .7 6 1684 333 049 11 49 11122 23456 78 025 8576 11-39 689 789 8-13692 71742 125 02398 0595 38 0853 74 39 '1 '8 47 96 19 36 8 5 6831 7 2701 1 675 488 81 48284 19892 11112 22334 55679 95 523 821 8 1: 749 827 542 416 076 717 4 6001 12457 92471 48384 793 135 81471 7 075 06009 74199 2807 01234 57891 35791 6 %-86666 81595 3123 0 1. 4 6296 69 0 6 03866 07 50517 19 06609 36 52 19887 58 4456 77890 633 7 569 4 7 01369 075 360 6938 6 2615 0 2 34455 8042 96 6118 2 00011 223 5 67891 0289 0-2346 0 12345 1 2 3 4 5 6789 Present Value of Annuity of $1 Periods 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% | 14% | 16% | 18% | 20% 10.990 0.980 0.9710.9620.9520.9430.926 0.9090.8930.877 0.862 0.847 0.833 2 1.970 1.942 1.9131.886 1.859 1.833 1.7831.7361.690 1.647 .605 1.5661.528 32.9412.884 2.829 2.7752.7232.673 2.5772.487 2.402 2.322 | 2.2462.1742.106 43.9023.8083.7173.630 3.546 3.465 3.312 3.1703.037 2.914 2.7982.690 2.589 54.8534.7134.5804.452 4.329 4.212 3.9933.7913.605 3.433 3.2743.127 2.991 65.7955.6015.4175.2425.076| 4.917 4.6234.3554.111 3.8893.685 3.498 3.326 7 6.7286.4726.230 6.002 5.7865.5825.2064.8684.5644.2884.0393.812 3.605 87.652 7.3257.020 6.7336.463 6.2105.7475.3354.9684.639 4.3444.078 3.837 9 8.5668.162 7.7867.435 7.108 6.802 6.2475.7595.328 4.946 4.6074.303 4.031 10 9.4718.9838.5308.1117.7227.3606.7106.1455.6505.2164.8334.494 4.192 11 10.3689.787 9.2538.760 8.3067.8877.139 6.4955.938 5.4535.0294.6564.327 12 11.255 10.575 9.9549.385 8.8638.3847.536 6.814 6.1945.660 5.197 4.793 4.439 13 12.134 11.348 10.635 9.9869.3948.8537.9047.103 6.4245.8425.3424.9104.533 14 13.00412.106 11.29610.563 9.8999.2958.2447.3676.628 6.0025.4685.0084.611 15 13.865 12.849 11.938 11.118 10.3809.7128.5597.6066.8116.1425.575 5.092 4.675 20 18.046 16.351 14.877 13.590 12.462 11.470 9.818 8.5147.4696.6235.9295.3534.870 2522.023 19.523 17.41315.622 14.094 12.783 10.675 9.0777.8436.873 6.0975.4674.948 30 25.808 22.396 19.600 17.292 15.372 13.765 11.2589.427 8.055 7.003 6.1775.5174.979 40 32.835 27.355 23.115 19.793 17.159 15.046 11.925 9.779 8.2447.1056.2335.5484.997 Future Value of Annuity of $1 10% 1.000 Periods 12% 1.000 2.120 3.374 4.779 6.353 14% 1.000 16% .000 18% 1.000 2.010 3.030 4.060 20% 1.000 2.200 3.640 5.368 7.442 1.000 2.020 3.060 .000 2.030 3.091 1.000 2.040 3.122 4.246 5.416 6.633 7.898 9.214 1.000 2.050 1.000 2.060 2.080 3.246 4.506 5.867 7.336 8.923 3.310 4.641 6.105 7.716 9.48710.08910.730 11.414 12.14212.916 3.440 4.921 6.610 8.536 3.506 5.066 6.877 8.977 2.180 3.572 5.215 7.154 9.442 4.310 5.526 4.375 5.637 5.204 6.308 7.434 8.583 9.7550.15910.583 11.027 1149112.488 13.579 14.77616.08517.519 9.086 20.799 5.309 6.468 7.662 8.892 6.802 8.142 9.549 6.975 8.394 9.89710.637 11.436 12.300 13.23314.240 15.327 16.499 9.930 7.214 8.286 9.369 10 10.46210.950 11.464 12.006 12.57813.181 14.487 15.93717.54919.337 21.321 23.52125.959 11.56712.169 12.808 13.486 14.20714.97216.645 18.53120.655 23.045 25.733 28.755 32.150 12.68313.412 14.192 15.026 15.91716.87018.977 21.38424.133 27.27130.850 34.931 39.581 13.80914.680 15.618 16.62717.713 18.882 21.495 24.52328.029 32.089 36.786 42.219 48.497 14.9475.974 17.086 18.29219.599 21.015 24.21527.97532.393 37.58143.672 50.818 59.196 16.09717.293 18.59920.02421.57923.276 27.152 31.77237.280 43.842 51.660 60.96572.035 22.01924.297 26.870 29.77833.066 36.786 45.762 57.275 2.052 91.025 115.380 146.628 186.688 28.24332.030 36.459 41.64647.727 54.865 73.106 98.347133.334 181.871249.214 342.603 471.981 34.78540.568 47.57556.08566.43979.058113.283 164.494241.333356.787530.312790.948 1,181.882 48.88660.402 75.401 95.026120.800154.762259.057442.593767.091 1,342.0252,360.757 4,163.213 7,343.858 13 20 25 30 40