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 $17,000 per year for four years (cost assumed to come at the end of each year). Anticipating Linda's ambitions, your parents started investing $2,000 per year five years ago and will continue to do so for five more years. Use 10 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 $2,000 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? 2 A? A? A? ? A? A? 1 2 2 2 2 2 2 2 2 2 2 -17 -17 -17 -17 -N -5 -4 -3 -2 -1 0 1 2 3 4 5 07 6 7 8 9 Additional annual savings required Appendix C Future value of an annuity of $1, FIFA (1+i)" FVA= A =a[19-1 ] Percent 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% Period 1 2. 1.000 1.000 1.000 1.000 1.000 2.020 1.000 2.110 2.010 2.050 2.060 2.090 1.000 2.030 3.091 4.184 1.000 2.040 3.122 4.246 1.000 2.080 3.246 4.506 1.000 2.100 3.310 3 3.030 3.060 3.184 3.342 3.153 4.310 3.278 4.573 4 4.641 4.710 4.060 5.101 4.122 5.204 4.375 5.637 5 5.416 5.526 5.867 6.105 6.228 6 5.309 6.468 7.662 6.633 6.802 6.152 7.214 7.336 6.975 8.394 7.913 9.783 7 7.898 6.308 7.434 8.583 9.755 8 1.000 2.070 3.215 4.440 5.751 7.153 8.654 10.260 11.978 13.816 15.784 17.888 20.141 22.550 8.286 9.369 8.142 9.549 11.027 8.892 10.159 11.464 9.214 10.583 8.923 10.637 12.488 7.716 9.487 11.436 13.579 15.937 18.531 11.859 14.164 9 10 10.462 12.006 14.487 16.722 12.578 14.207 11 10.950 12.169 13.412 11.567 12.808 9.897 11.491 13.181 14.972 16.870 18.882 21.015 16.645 19.561 22.713 12 13.486 15.026 16.627 12.683 14.192 15.917 18.977 21.384 13 15.618 17.713 21.495 24.523 13.809 14.947 14.680 15.974 5.985 7.523 9.200 11.028 13.021 15.193 17.560 20.141 22.953 26.019 29.361 33.003 36.974 41.301 46.018 51.160 84.701 136.31 14 17.086 18.292 19.599 27.975 31.772 15 21.579 23.276 25.129 16.097 17.258 17.293 18.639 24.215 27.152 30.324 18.599 20.157 21.762 20.024 21.825 16 25.673 35.950 23.657 25.840 17 18.430 20.012 23.698 28.213 33.750 40.545 18 21.412 23.414 25.645 19.615 20.811 19 22.841 28.132 30.539 33.066 27.671 26.212 30.095 34.405 39.190 44.501 50.396 56.939 64.203 114.41 199.02 581.83 1,668.8 27.888 30.840 33.999 37.379 40.995 63.249 94.461 20 45.599 51.159 57.275 98.347 22.019 24.297 37.450 41.446 45.762 73.106 113.28 25.117 26.870 36.459 47.575 75.401 29.778 41.646 25 30.906 33.760 36.786 54.865 79.058 154.76 290.34 32.030 28.243 34.785 47.727 66.439 30 40.588 56.085 164.49 40 95.026 120.80 199.64 48.886 64.463 60.402 84.579 259.06 573.77 337.89 815.08 442.59 1,163.9 50 112.80 152.67 209.35 406.53 Appendix C (concluded) Future value of an annuity of $1 Percent 17% Period 12% 13% 14% 15% 16% 18% 19% 20% 25% 30% 1.000 1.000 1.000 1.000 1.000 1. 2 3 2 1.000 2.160 3.506 3.640 2.300 3.990 6.187 2.140 3.440 4.921 6.610 4 1.000 2.120 3.374 4.779 6.353 8.115 10.089 12.300 5.066 2.130 3.407 4.850 6.480 8.323 10.405 5 6.877 9.043 2.250 3.813 5.766 8.207 11.259 15.073 19.842 25.802 6 8.536 8.977 2.150 3.473 4.993 6.742 8.754 11.067 13.727 16.786 20.304 24.349 12.756 7 10.730 11.414 17.583 23.858 8 12.757 13.233 14.240 9 14.776 15.416 16.085 17.519 32.015 10 18.420 19.337 42.619 21.321 25.733 11 21.814 23.045 56.405 12 17.549 20.655 24.133 28.029 32.393 25.650 29.985 34.883 27.271 32.089 29.002 34.352 1.000 1.000 1.000 1.000 2.170 2.180 2.190 2.200 3.539 3.572 3.606 5.141 5.215 5.291 5.368 7.014 7.154 7.297 7.442 9.207 9.442 9.683 9.930 11.772 12.142 12.523 12.916 14.773 15.327 15.902 16.499 18.285 19.086 19.923 20.799 22.393 23.521 24.701 25.959 27.200 28.755 30.404 32.150 32.824 34.931 37.180 39.581 39.404 42.219 45.244 48.497 47.103 50.818 54.841 59.196 56.110 60.965 66.261 72.035 66.649 72.939 79.850 87.442 78.979 87.068 96.022 105.93 93.406 103.74 115.27 128.12 110.29 123.41 138.17 154.74 130.03 146.63 165.42 186.69 292.11 342.60 402.04 471.98 647.44 790.95 966.7 1,181.9 3,134.5 4,163.21 5,529.8 7,343.9 15,090.0 21,813.0 31,515.0 45,497.0 33.253 42.566 54.208 68.760 86.949 13 74.327 97.625 127.91 14 15 37.280 40.417 37.581 43.842 50.980 40.505 47.580 55.717 167.29 109.69 138.11 16 42.753 46.672 218.47 17 18 48.884 55.750 65.075 75.836 30.850 36.786 43.672 51.660 60.925 71.673 84.141 98.603 115.38 249.21 530.31 2,360.8 10,436.0 173.64 218.05 285.01 371.52 19 63.440 483.97 20 53.739 61.725 70.749 80.947 155.62 293.20 1,013.7 3,459.5 72.052 59.118 68.394 78.969 91.025 181.87 356.79 1,342.0 4,994.5 88.212 102.44 212.79 25 133.33 273.56 342.95 1,054.8 3,227.2 30,089.0 280,256.0 30 241.33 630.17 2,348.80 8,730.0 120,393.0 1,659,76.0 40 434.75 1,779.1 7,217.7 767.09 50 2,400.0 Appendix D Present value of an annuity of $1, PVIFA , PVA=A 1 1 - (1 + i)" 1% 2% 3% 4% 5% 8% 9% 12% 10% 0.909 11% 0.901 0.990 0.980 0.971 0.952 0.926 0.893 Period 1 1 2 3 1.970 1.942 1.736 1.913 2.829 1.690 0.917 1.759 2.531 1.859 2.723 0.962 1.886 2.775 3.630 4.452 1.783 2.577 1.713 2.444 2.941 2.884 2.487 4 3.312 3.240 3.170 3.902 4.853 3.808 4.713 3.717 4.580 3.546 4.329 3.102 3.696 2.402 3.037 3.605 5 3.993 3.791 3.890 4.486 6 5.601 5.417 5.242 5.076 4.623 4.355 4.231 4.111 7 5.795 6.728 7.652 4.712 6.472 7.325 6.230 7.020 6.002 6.733 5.786 6.463 5.206 5.747 4.564 4.968 8 8 5.146 9 8.566 7.786 8.530 7.435 8.111 6.247 6.710 5.537 5.889 5.033 5.535 5.995 6.418 6.805 7.161 5.328 5.650 10 8.162 8.983 9.787 10.575 9.471 7.108 7.722 8.306 8.863 4.868 5.335 5.759 6.145 6.495 6.814 7.103 11 12 9.253 9.954 Percent 6% 7% 0.943 0.935 1.833 1.808 2.673 2.624 3.465 3.387 4.212 4.100 4.917 4.767 5.582 5.389 6.210 5.971 6.802 6.515 7.360 7.024 7.887 7.499 8.384 7.943 8.853 8.358 9.295 8.745 9.712 9.108 10.106 9.447 10.477 9.763 10.828 10.059 11.158 10.336 11.470 10.594 12.783 11.654 13.765 12.409 15.046 13.332 15.762 13.801 8.760 9.385 7.139 7.536 6.207 6.492 5.938 6.194 6.424 13 11.348 9.986 9.394 7.904 10.368 11.255 12.134 13.004 13.865 14.718 7.487 14 12.106 10.563 9.899 8.244 7.786 7.367 10.635 11.296 11.938 12.561 6.750 6.982 7.191 7.379 15 12.849 13.578 8.061 8.313 10.380 10.838 11.274 7.606 7.824 6.628 6.811 6.974 16 11.118 11.652 12.166 12.659 8.559 8.851 9.122 9.372 17 14.292 13.166 7.549 15.562 16.398 8.544 8.756 8.022 8.201 7.120 7.250 18 14.992 13.754 11.690 7.702 19 13.134 12.085 9.604 7.839 7.366 20 15.678 16.351 19.523 14.324 14.877 17.413 12.462 9.818 8.365 8.514 9.077 7.963 7.469 25 14.094 10.675 17.226 18.046 22.023 25.808 32.835 39.196 8.950 9.129 9.823 10.274 10.757 7.843 30 40 22.396 27.355 31.424 13.590 15.622 17.292 19.793 21.482 19.600 23.115 15.372 17.159 11.258 11.925 9.427 9.779 8.422 8.694 8.951 8.055 8.244 8.304 50 25.730 18.256 12.233 10.962 9.915 9.042 Appendix D (concluded) Present value of an annuity of $1 Percent 19% Period 13% 14% 15% 16% 17% 18% 20% 25% 30% 40% 50% 35% 0.741 0.870 0.714 1 2 0.862 1.605 0.855 1.585 0.800 1.440 0.847 1.566 2.174 0.769 1.361 0.667 1.111 1.626 1.289 0.885 1.668 2.361 2.974 1.224 0.840 1.547 2.140 2.639 3 1.952 0.877 1.647 2.322 2.914 3.433 3.889 1.696 2.283 2.855 2.246 2.798 0.833 1.528 2.106 2.589 2.991 3.326 1.589 1.849 1.407 1.605 4 2.690 1.8 16 2.166 2.436 2.362 2.210 2.743 3.199 3.589 1.997 5 3.058 2.220 1.737 3.517 3.998 3.352 3.784 3.274 3.685 3.127 3.498 2.689 2.951 2.035 2.168 6 3.410 2.643 2.385 1.824 7 4.423 4.288 4.160 4.039 3.922 3.812 3.161 2.802 2.508 2.263 1.883 8 4.639 3.329 2.331 1.922 4.207 4.451 2.598 2.665 3.463 2.379 1.948 9 10 4.799 5.132 5.426 5.687 5.918 4.487 4.772 5.019 5.234 5.421 4.659 3.706 3.954 4.163 4.339 4.486 4.611 4.078 4.303 4.494 4.656 4.793 4.946 5.216 5.453 5.660 3.605 3.837 4.031 4.192 4.327 4.439 3.571 4.344 4.607 4.833 5.029 5.197 5.342 2.414 2.925 3.019 3.092 3.147 3.190 1.965 11 3.656 3.725 2.715 2.752 2.779 2.438 2.456 1.977 1.985 12 13 6.122 4.910 4.533 3.780 3.223 2.799 2.469 5.583 5.724 4.715 4.802 1.990 1.993 14 6.302 5.468 5.008 3.824 3.249 2.814 2.478 4.611 4.675 15 4.876 3.268 4.836 4.988 5.118 5.229 5.324 5.405 5.475 5.534 5.584 2.825 2.484 6.462 6.604 1.995 5.842 6.002 6.142 6.265 6.373 6.467 6.550 5.847 5.954 5.575 5.668 16 5.092 5.162 5.222 3.859 3.887 4.938 4.730 3.283 2.834 2.489 1.997 1.998 17 4.775 2.492 6.729 6.840 6.938 6.047 6.128 18 5.749 5.818 5.877 2.840 2.844 3.910 3.928 3.942 5.273 5.316 2.494 2.496 19 6.198 2.848 20 7.025 3.954 2.497 5.929 6.097 4.988 5.033 5.070 5.101 5.195 5.235 5.258 5.262 5.628 5.766 5.829 2.850 2.856 25 4.812 4.843 4.870 4.948 4.979 4.997 3.295 3.304 3.311 3.316 3.329 3.332 3.333 3.333 6.623 6.873 7.003 7.105 7.133 6.259 6.464 6.566 6.642 3.985 7.330 7.496 2.499 5.353 5.467 5.517 5.548 5.554 1.999 1.999 1.999 2.000 2.000 2.000 2.000 30 40 50 2.857 2.500 6.177 6.233 3.995 3.999 2.857 2.500 7.634 7.675 5.871 5.880 6.661 6.246 4.999 4.000 2.857 2.500 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 $17,000 per year for four years (cost assumed to come at the end of each year). Anticipating Linda's ambitions, your parents started investing $2,000 per year five years ago and will continue to do so for five more years. Use 10 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 $2,000 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? 2 A? A? A? ? A? A? 1 2 2 2 2 2 2 2 2 2 2 -17 -17 -17 -17 -N -5 -4 -3 -2 -1 0 1 2 3 4 5 07 6 7 8 9 Additional annual savings required Appendix C Future value of an annuity of $1, FIFA (1+i)" FVA= A =a[19-1 ] Percent 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% Period 1 2. 1.000 1.000 1.000 1.000 1.000 2.020 1.000 2.110 2.010 2.050 2.060 2.090 1.000 2.030 3.091 4.184 1.000 2.040 3.122 4.246 1.000 2.080 3.246 4.506 1.000 2.100 3.310 3 3.030 3.060 3.184 3.342 3.153 4.310 3.278 4.573 4 4.641 4.710 4.060 5.101 4.122 5.204 4.375 5.637 5 5.416 5.526 5.867 6.105 6.228 6 5.309 6.468 7.662 6.633 6.802 6.152 7.214 7.336 6.975 8.394 7.913 9.783 7 7.898 6.308 7.434 8.583 9.755 8 1.000 2.070 3.215 4.440 5.751 7.153 8.654 10.260 11.978 13.816 15.784 17.888 20.141 22.550 8.286 9.369 8.142 9.549 11.027 8.892 10.159 11.464 9.214 10.583 8.923 10.637 12.488 7.716 9.487 11.436 13.579 15.937 18.531 11.859 14.164 9 10 10.462 12.006 14.487 16.722 12.578 14.207 11 10.950 12.169 13.412 11.567 12.808 9.897 11.491 13.181 14.972 16.870 18.882 21.015 16.645 19.561 22.713 12 13.486 15.026 16.627 12.683 14.192 15.917 18.977 21.384 13 15.618 17.713 21.495 24.523 13.809 14.947 14.680 15.974 5.985 7.523 9.200 11.028 13.021 15.193 17.560 20.141 22.953 26.019 29.361 33.003 36.974 41.301 46.018 51.160 84.701 136.31 14 17.086 18.292 19.599 27.975 31.772 15 21.579 23.276 25.129 16.097 17.258 17.293 18.639 24.215 27.152 30.324 18.599 20.157 21.762 20.024 21.825 16 25.673 35.950 23.657 25.840 17 18.430 20.012 23.698 28.213 33.750 40.545 18 21.412 23.414 25.645 19.615 20.811 19 22.841 28.132 30.539 33.066 27.671 26.212 30.095 34.405 39.190 44.501 50.396 56.939 64.203 114.41 199.02 581.83 1,668.8 27.888 30.840 33.999 37.379 40.995 63.249 94.461 20 45.599 51.159 57.275 98.347 22.019 24.297 37.450 41.446 45.762 73.106 113.28 25.117 26.870 36.459 47.575 75.401 29.778 41.646 25 30.906 33.760 36.786 54.865 79.058 154.76 290.34 32.030 28.243 34.785 47.727 66.439 30 40.588 56.085 164.49 40 95.026 120.80 199.64 48.886 64.463 60.402 84.579 259.06 573.77 337.89 815.08 442.59 1,163.9 50 112.80 152.67 209.35 406.53 Appendix C (concluded) Future value of an annuity of $1 Percent 17% Period 12% 13% 14% 15% 16% 18% 19% 20% 25% 30% 1.000 1.000 1.000 1.000 1.000 1. 2 3 2 1.000 2.160 3.506 3.640 2.300 3.990 6.187 2.140 3.440 4.921 6.610 4 1.000 2.120 3.374 4.779 6.353 8.115 10.089 12.300 5.066 2.130 3.407 4.850 6.480 8.323 10.405 5 6.877 9.043 2.250 3.813 5.766 8.207 11.259 15.073 19.842 25.802 6 8.536 8.977 2.150 3.473 4.993 6.742 8.754 11.067 13.727 16.786 20.304 24.349 12.756 7 10.730 11.414 17.583 23.858 8 12.757 13.233 14.240 9 14.776 15.416 16.085 17.519 32.015 10 18.420 19.337 42.619 21.321 25.733 11 21.814 23.045 56.405 12 17.549 20.655 24.133 28.029 32.393 25.650 29.985 34.883 27.271 32.089 29.002 34.352 1.000 1.000 1.000 1.000 2.170 2.180 2.190 2.200 3.539 3.572 3.606 5.141 5.215 5.291 5.368 7.014 7.154 7.297 7.442 9.207 9.442 9.683 9.930 11.772 12.142 12.523 12.916 14.773 15.327 15.902 16.499 18.285 19.086 19.923 20.799 22.393 23.521 24.701 25.959 27.200 28.755 30.404 32.150 32.824 34.931 37.180 39.581 39.404 42.219 45.244 48.497 47.103 50.818 54.841 59.196 56.110 60.965 66.261 72.035 66.649 72.939 79.850 87.442 78.979 87.068 96.022 105.93 93.406 103.74 115.27 128.12 110.29 123.41 138.17 154.74 130.03 146.63 165.42 186.69 292.11 342.60 402.04 471.98 647.44 790.95 966.7 1,181.9 3,134.5 4,163.21 5,529.8 7,343.9 15,090.0 21,813.0 31,515.0 45,497.0 33.253 42.566 54.208 68.760 86.949 13 74.327 97.625 127.91 14 15 37.280 40.417 37.581 43.842 50.980 40.505 47.580 55.717 167.29 109.69 138.11 16 42.753 46.672 218.47 17 18 48.884 55.750 65.075 75.836 30.850 36.786 43.672 51.660 60.925 71.673 84.141 98.603 115.38 249.21 530.31 2,360.8 10,436.0 173.64 218.05 285.01 371.52 19 63.440 483.97 20 53.739 61.725 70.749 80.947 155.62 293.20 1,013.7 3,459.5 72.052 59.118 68.394 78.969 91.025 181.87 356.79 1,342.0 4,994.5 88.212 102.44 212.79 25 133.33 273.56 342.95 1,054.8 3,227.2 30,089.0 280,256.0 30 241.33 630.17 2,348.80 8,730.0 120,393.0 1,659,76.0 40 434.75 1,779.1 7,217.7 767.09 50 2,400.0 Appendix D Present value of an annuity of $1, PVIFA , PVA=A 1 1 - (1 + i)" 1% 2% 3% 4% 5% 8% 9% 12% 10% 0.909 11% 0.901 0.990 0.980 0.971 0.952 0.926 0.893 Period 1 1 2 3 1.970 1.942 1.736 1.913 2.829 1.690 0.917 1.759 2.531 1.859 2.723 0.962 1.886 2.775 3.630 4.452 1.783 2.577 1.713 2.444 2.941 2.884 2.487 4 3.312 3.240 3.170 3.902 4.853 3.808 4.713 3.717 4.580 3.546 4.329 3.102 3.696 2.402 3.037 3.605 5 3.993 3.791 3.890 4.486 6 5.601 5.417 5.242 5.076 4.623 4.355 4.231 4.111 7 5.795 6.728 7.652 4.712 6.472 7.325 6.230 7.020 6.002 6.733 5.786 6.463 5.206 5.747 4.564 4.968 8 8 5.146 9 8.566 7.786 8.530 7.435 8.111 6.247 6.710 5.537 5.889 5.033 5.535 5.995 6.418 6.805 7.161 5.328 5.650 10 8.162 8.983 9.787 10.575 9.471 7.108 7.722 8.306 8.863 4.868 5.335 5.759 6.145 6.495 6.814 7.103 11 12 9.253 9.954 Percent 6% 7% 0.943 0.935 1.833 1.808 2.673 2.624 3.465 3.387 4.212 4.100 4.917 4.767 5.582 5.389 6.210 5.971 6.802 6.515 7.360 7.024 7.887 7.499 8.384 7.943 8.853 8.358 9.295 8.745 9.712 9.108 10.106 9.447 10.477 9.763 10.828 10.059 11.158 10.336 11.470 10.594 12.783 11.654 13.765 12.409 15.046 13.332 15.762 13.801 8.760 9.385 7.139 7.536 6.207 6.492 5.938 6.194 6.424 13 11.348 9.986 9.394 7.904 10.368 11.255 12.134 13.004 13.865 14.718 7.487 14 12.106 10.563 9.899 8.244 7.786 7.367 10.635 11.296 11.938 12.561 6.750 6.982 7.191 7.379 15 12.849 13.578 8.061 8.313 10.380 10.838 11.274 7.606 7.824 6.628 6.811 6.974 16 11.118 11.652 12.166 12.659 8.559 8.851 9.122 9.372 17 14.292 13.166 7.549 15.562 16.398 8.544 8.756 8.022 8.201 7.120 7.250 18 14.992 13.754 11.690 7.702 19 13.134 12.085 9.604 7.839 7.366 20 15.678 16.351 19.523 14.324 14.877 17.413 12.462 9.818 8.365 8.514 9.077 7.963 7.469 25 14.094 10.675 17.226 18.046 22.023 25.808 32.835 39.196 8.950 9.129 9.823 10.274 10.757 7.843 30 40 22.396 27.355 31.424 13.590 15.622 17.292 19.793 21.482 19.600 23.115 15.372 17.159 11.258 11.925 9.427 9.779 8.422 8.694 8.951 8.055 8.244 8.304 50 25.730 18.256 12.233 10.962 9.915 9.042 Appendix D (concluded) Present value of an annuity of $1 Percent 19% Period 13% 14% 15% 16% 17% 18% 20% 25% 30% 40% 50% 35% 0.741 0.870 0.714 1 2 0.862 1.605 0.855 1.585 0.800 1.440 0.847 1.566 2.174 0.769 1.361 0.667 1.111 1.626 1.289 0.885 1.668 2.361 2.974 1.224 0.840 1.547 2.140 2.639 3 1.952 0.877 1.647 2.322 2.914 3.433 3.889 1.696 2.283 2.855 2.246 2.798 0.833 1.528 2.106 2.589 2.991 3.326 1.589 1.849 1.407 1.605 4 2.690 1.8 16 2.166 2.436 2.362 2.210 2.743 3.199 3.589 1.997 5 3.058 2.220 1.737 3.517 3.998 3.352 3.784 3.274 3.685 3.127 3.498 2.689 2.951 2.035 2.168 6 3.410 2.643 2.385 1.824 7 4.423 4.288 4.160 4.039 3.922 3.812 3.161 2.802 2.508 2.263 1.883 8 4.639 3.329 2.331 1.922 4.207 4.451 2.598 2.665 3.463 2.379 1.948 9 10 4.799 5.132 5.426 5.687 5.918 4.487 4.772 5.019 5.234 5.421 4.659 3.706 3.954 4.163 4.339 4.486 4.611 4.078 4.303 4.494 4.656 4.793 4.946 5.216 5.453 5.660 3.605 3.837 4.031 4.192 4.327 4.439 3.571 4.344 4.607 4.833 5.029 5.197 5.342 2.414 2.925 3.019 3.092 3.147 3.190 1.965 11 3.656 3.725 2.715 2.752 2.779 2.438 2.456 1.977 1.985 12 13 6.122 4.910 4.533 3.780 3.223 2.799 2.469 5.583 5.724 4.715 4.802 1.990 1.993 14 6.302 5.468 5.008 3.824 3.249 2.814 2.478 4.611 4.675 15 4.876 3.268 4.836 4.988 5.118 5.229 5.324 5.405 5.475 5.534 5.584 2.825 2.484 6.462 6.604 1.995 5.842 6.002 6.142 6.265 6.373 6.467 6.550 5.847 5.954 5.575 5.668 16 5.092 5.162 5.222 3.859 3.887 4.938 4.730 3.283 2.834 2.489 1.997 1.998 17 4.775 2.492 6.729 6.840 6.938 6.047 6.128 18 5.749 5.818 5.877 2.840 2.844 3.910 3.928 3.942 5.273 5.316 2.494 2.496 19 6.198 2.848 20 7.025 3.954 2.497 5.929 6.097 4.988 5.033 5.070 5.101 5.195 5.235 5.258 5.262 5.628 5.766 5.829 2.850 2.856 25 4.812 4.843 4.870 4.948 4.979 4.997 3.295 3.304 3.311 3.316 3.329 3.332 3.333 3.333 6.623 6.873 7.003 7.105 7.133 6.259 6.464 6.566 6.642 3.985 7.330 7.496 2.499 5.353 5.467 5.517 5.548 5.554 1.999 1.999 1.999 2.000 2.000 2.000 2.000 30 40 50 2.857 2.500 6.177 6.233 3.995 3.999 2.857 2.500 7.634 7.675 5.871 5.880 6.661 6.246 4.999 4.000 2.857 2.500