Problem 9-2 Solving for Rates 1. Calculate the Annual rate of return. Solving for Rates -...

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Problem 9-2 Solving for Rates 1. Calculate the Annual rate of return. Solving for Rates - Excel FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Sign In Connections 24 A Clear Properties From From From From Other Access Web Text Sources Existing Connections Refresh All- Sort Reapply Filter Data Outline Edit Links Advanced Tools" Get External Data Connections Sort & Filter A1 A B fx D E F G H J 123 st 5 What annual rate of return is earned on a $5,000 investment when it grows to $10,750 in six years? (Do not round intermediate calculations and round your final answer to 2 decimal places.) 6100 7 Present value $ 5,000 8 Future value $ 10,750 9 Number of periods 6 10 11 12 13 14 15 Complete the following analysis. Do not hard code values in your calculations. Annual rate of return 16 17 18 Sheet1 READY E 100% Problem 9-25 (Algo) Quarterly compounding [LO9-5] Juan Garza invested $118,000 10 years ago at 8 percent, compounded quarterly. How much has he accumulated? Use Appendix A for an approximate answer but calculate your final answer using the formula and financial calculator methods. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Future value Problem 9-3 (Algo) Present value [LO9-3] a. What is the present value of $280,000 to be received after 40 years with a 16 percent discount rate? Use Appendix B as an approximate answer, but calculate your final answer using the formula and financial calculator methods. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Present value b. Would the present value of the funds in part a be enough to buy a $800 concert ticket? No Yes Problem 9-4 (Algo) Present value [LO9-4] You will receive $5,000 three years from now. The discount rate is 12 percent. a. What is the value of your investment two years from now? Multiply $5,000 1.12 or divide by 1.12 (one year's discount rate at 12 percent). Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Value of investment b. What is the value of your investment one year from now? Multiply your answer to part a by 1.12 Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Value of investment c. What is the value of your investment today? Multiply your answer to part b by 1.12 Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Value of investment d. Use the formula PV = FV (1+) to find the present value of $4,800 received three years from now at 12 percent interest. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Present value Problem 9-7 (Algo) Present value [LO9-3] Your uncle offers you a choice of $120,000 in 10 years or $54,000 today. Use Appendix B as an approximate answer, but calculate your final answer using the formula and financial calculator methods. a-1. If money is discounted at 9 percent, what is the present value of the $120,000? Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Present value a-2. Which offer should you choose? $54,000 today O $120,000 after 10 years Appendix A Future value of $1, FV IF FV=PV(1 + i)" Percent Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120 1.130 1.140 1.150 1.160 1.170 1.180 1.190 1.200 1.250 1.300 2 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.440 1.563 1.690 3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 1.728 1.953 2.197 4 1.041 1.082 1.126 1.170 5 1.051 1.104 1.159 1.217 6 1.062 1.126 1.194 1.265 7 1.072 1.149 1.230 1.316 8 1.083 1.172 1.267 9 1.094 1.195 1.305 1.369 1.423 10 1.105 1.219 1.344 11 1.116 1.243 1.384 12 13 14 15 16 17 1.216 1.262 1.276 1.338 1.340 1.419 1.407 1.504 1.477 1.594 1.551 1.689 1.480 1.629 1.791 1.967 1.539 1.710 1.898 2.105 1.127 1.268 1.426 1.601 1.796 2.012 2.252 1.138 1.294 1.469 1.665 1.886 2.133 2.410 1.149 1.319 1.513 1.732 1.161 1.346 1.558 1.801 1.173 1.373 1.605 1.873 1.184 1.400 1.653 1.948 1.311 1.360 1.412 1.464 1.518 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005 2.074 2.441 2.856 1.403 1.501 1.587 1.606 1.718 1.851 1.993 1.838 1.469 1.539 1.611 1.685 1.762 1.842 1.925 2.011 2.100 2.192 2.288 2.386 2.488 3.052 3.713 1.677 1.772 1.870 1.974 2.082 2.195 2.313 2.436 2.565 2.700 2.840 2.986 3.815 4.827 1.714 1.828 1.949 2.076 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379 3.583 4.768 6.276 2.144 2.305 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021 4.300 5.960 8.157 1.999 2.172 2.358 2.558 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785 5.160 7.451 10.604 2.159 2.367 2.594 2.839 3.106 3.395 3.707 4.046 4.411 4.807 5.234 5.696 6.192 9.313 13.786 2.332 2.580 2.853 3.152 3.479 3.836 4.226 4.652 5.117 5.624 6.176 6.777 7.430 11.642 17.922 2.518 2.813 3.138 3.498 3.896 4.335 4.818 5.350 5.936 6.580 7.288 8.064 8.916 14.552 23.298 2.720 3.066 3.452 3.883 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596 10.699 18.190 30.288 1.980 2.261 2.579 2.937 3.342 3.797 4.310 4.887 5.535 6.261 7.076 7.988 9.007 10.147 11.420 12.839 22.737 39.374 18 2.079 2.397 2.759 3.172 2.183 2.540 2.952 3.426 2.292 2.693 3.159 3.700 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.642 4.177 4.785 5.474 6.254 7.138 8.137 9.266 10.539 11.974 13.590 15.407 28.422 51.186 3.970 4.595 5.311 6.130 7.067 8.137 9.358 10.748 12.330 14.129 16.172 18.488 35.527 66.542 4.328 5.054 5.895 6.866 7.986 9.276 10.761 12.468 14.426 16.672 19.244 22.186 44.409 86.504 3.996 4.717 5.560 6.544 7.690 9.024 10.575 12.375 14.463 16.879 19.673 22.091 26.623 55.511 112.460 19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 20 1.220 1.486 1.806 2.191 2.653 25 1.282 1.641 2.094 2.666 3.386 30 40 50 3.870 4.661 4.292 5.427 6.848 8.623 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063 13.268 1.489 2.208 3.262 4.801 7.040 10.286 14.974 21.725 31.409 1.645 2.692 4.384 7.107 11.467 18.420 29.457 46.902 74.358 3.207 4.316 5.142 5.604 6.116 7.263 8.613 10.197 12.056 14.232 16.777 19.748 23.214 27.252 31.948 69.389 146.190 6.727 10.835 16.367 19.461 8.062 9.646 11.523 13.743 13.585 17.000 21.231 26.462 32.919 40.874 50.658 17.449 22.892 29.960 39.116 50.950 66.212 85.850 111.070 143.370 184.680 237.380 807.790 45.259 65.001 93.051 132.780 188.880 267.860 378.720 533.870 750.380 1,051.700 1,469.800 7,523.200 36,119.000 23.106 27.393 32.429 38.338 86.736 190.050 62.669 77.388 95.396 264.700 705.640 2,620.000 117.390 184.570 289.000 450.740 700.230 1,083.700 1,670.700 2,566.200 3,927.400 5,988.900 9,100.400 70,065.000 497,929.000 Appendix B Present value of $1. PV IF PV=FV[1 / (1 + i)"] Percent Period 1% 2% 1 0.990 3% 4% 0.980 0.971 0.962 2 0.980 0.961 0.943 0.925 0.907 5% 6% 0.952 0.943 0.890 8% 3 0.971 0.942 0.915 0.889 0.864 4 0.961 0.924 0.888 0.855 0.823 5 0.951 0.906 0.863 6 7 8 9 0.853 0.789 0.731 0.677 0.627 0.582 0.914 0.837 0.766 10 0.905 0.820 0.744 11 12 13 14 15 0.870 0.758 0.661 0.861 0.743 16 17 18 19 40 0.672 0.453 0.307 0.208 50 0.009 7% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 35% 40% 50% 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.800 0.769 0.741 0.714 0.667 0.873 0.857 0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.640 0.592 0.549 0.510 0.444 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0.512 0.455 0.406 0.364 0.296 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.515 0.499 0.482 0.410 0.350 0.301 0.260 0.198 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402 0.328 0.269 0.223 0.186 0.132 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 0.262 0.207 0.165 0.133 0.088 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.210 0.159 0.122 0.095 0.059 0.923 0.540 0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 0.168 0.123 0.091 0.068 0.039 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 0.134 0.094 0.067 0.048 0.026 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 0.107 0.073 0.050 0.035 0.017 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.086 0.056 0.037 0.025 0.012 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 0.069 0.043 0.027 0.018 0.008 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 0.055 0.033 0.020 0.013 0.005 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 0.044 0.025 0.015 0.009 0.003 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 0.035 0.020 0.011 0.006 0.002 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.163 0.141 0.123 0.107 0.093 0.081 0.071 0.062 0.054 0.028 0.015 0.008 0.005 0.002 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.023 0.012 0.006 0.003 0.001 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038 0.018 0.009 0.005 0.002 0.001 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.014 0.007 0.003 0.002 20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 0.012 0.005 0.002 0.001 25 0.780 0.610 0.478 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.004 0.001 0.001 30 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 0.001 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001 0.608 0.372 0.228 0.141 0.087 0.054 0.034 0.021 0.013 0 0 0 0 0 0 0 0 0.001 0.001 0 0 0 0 0 0.005 0.003 0.002 0.001 0.001 0.001 0 0 0 0 0 0 0 0 0 Problem 9-2 Solving for Rates 1. Calculate the Annual rate of return. Solving for Rates - Excel FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Sign In Connections 24 A Clear Properties From From From From Other Access Web Text Sources Existing Connections Refresh All- Sort Reapply Filter Data Outline Edit Links Advanced Tools" Get External Data Connections Sort & Filter A1 A B fx D E F G H J 123 st 5 What annual rate of return is earned on a $5,000 investment when it grows to $10,750 in six years? (Do not round intermediate calculations and round your final answer to 2 decimal places.) 6100 7 Present value $ 5,000 8 Future value $ 10,750 9 Number of periods 6 10 11 12 13 14 15 Complete the following analysis. Do not hard code values in your calculations. Annual rate of return 16 17 18 Sheet1 READY E 100% Problem 9-25 (Algo) Quarterly compounding [LO9-5] Juan Garza invested $118,000 10 years ago at 8 percent, compounded quarterly. How much has he accumulated? Use Appendix A for an approximate answer but calculate your final answer using the formula and financial calculator methods. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Future value Problem 9-3 (Algo) Present value [LO9-3] a. What is the present value of $280,000 to be received after 40 years with a 16 percent discount rate? Use Appendix B as an approximate answer, but calculate your final answer using the formula and financial calculator methods. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Present value b. Would the present value of the funds in part a be enough to buy a $800 concert ticket? No Yes Problem 9-4 (Algo) Present value [LO9-4] You will receive $5,000 three years from now. The discount rate is 12 percent. a. What is the value of your investment two years from now? Multiply $5,000 1.12 or divide by 1.12 (one year's discount rate at 12 percent). Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Value of investment b. What is the value of your investment one year from now? Multiply your answer to part a by 1.12 Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Value of investment c. What is the value of your investment today? Multiply your answer to part b by 1.12 Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Value of investment d. Use the formula PV = FV (1+) to find the present value of $4,800 received three years from now at 12 percent interest. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Present value Problem 9-7 (Algo) Present value [LO9-3] Your uncle offers you a choice of $120,000 in 10 years or $54,000 today. Use Appendix B as an approximate answer, but calculate your final answer using the formula and financial calculator methods. a-1. If money is discounted at 9 percent, what is the present value of the $120,000? Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Present value a-2. Which offer should you choose? $54,000 today O $120,000 after 10 years Appendix A Future value of $1, FV IF FV=PV(1 + i)" Percent Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120 1.130 1.140 1.150 1.160 1.170 1.180 1.190 1.200 1.250 1.300 2 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.440 1.563 1.690 3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 1.728 1.953 2.197 4 1.041 1.082 1.126 1.170 5 1.051 1.104 1.159 1.217 6 1.062 1.126 1.194 1.265 7 1.072 1.149 1.230 1.316 8 1.083 1.172 1.267 9 1.094 1.195 1.305 1.369 1.423 10 1.105 1.219 1.344 11 1.116 1.243 1.384 12 13 14 15 16 17 1.216 1.262 1.276 1.338 1.340 1.419 1.407 1.504 1.477 1.594 1.551 1.689 1.480 1.629 1.791 1.967 1.539 1.710 1.898 2.105 1.127 1.268 1.426 1.601 1.796 2.012 2.252 1.138 1.294 1.469 1.665 1.886 2.133 2.410 1.149 1.319 1.513 1.732 1.161 1.346 1.558 1.801 1.173 1.373 1.605 1.873 1.184 1.400 1.653 1.948 1.311 1.360 1.412 1.464 1.518 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005 2.074 2.441 2.856 1.403 1.501 1.587 1.606 1.718 1.851 1.993 1.838 1.469 1.539 1.611 1.685 1.762 1.842 1.925 2.011 2.100 2.192 2.288 2.386 2.488 3.052 3.713 1.677 1.772 1.870 1.974 2.082 2.195 2.313 2.436 2.565 2.700 2.840 2.986 3.815 4.827 1.714 1.828 1.949 2.076 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379 3.583 4.768 6.276 2.144 2.305 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021 4.300 5.960 8.157 1.999 2.172 2.358 2.558 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785 5.160 7.451 10.604 2.159 2.367 2.594 2.839 3.106 3.395 3.707 4.046 4.411 4.807 5.234 5.696 6.192 9.313 13.786 2.332 2.580 2.853 3.152 3.479 3.836 4.226 4.652 5.117 5.624 6.176 6.777 7.430 11.642 17.922 2.518 2.813 3.138 3.498 3.896 4.335 4.818 5.350 5.936 6.580 7.288 8.064 8.916 14.552 23.298 2.720 3.066 3.452 3.883 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596 10.699 18.190 30.288 1.980 2.261 2.579 2.937 3.342 3.797 4.310 4.887 5.535 6.261 7.076 7.988 9.007 10.147 11.420 12.839 22.737 39.374 18 2.079 2.397 2.759 3.172 2.183 2.540 2.952 3.426 2.292 2.693 3.159 3.700 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.642 4.177 4.785 5.474 6.254 7.138 8.137 9.266 10.539 11.974 13.590 15.407 28.422 51.186 3.970 4.595 5.311 6.130 7.067 8.137 9.358 10.748 12.330 14.129 16.172 18.488 35.527 66.542 4.328 5.054 5.895 6.866 7.986 9.276 10.761 12.468 14.426 16.672 19.244 22.186 44.409 86.504 3.996 4.717 5.560 6.544 7.690 9.024 10.575 12.375 14.463 16.879 19.673 22.091 26.623 55.511 112.460 19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 20 1.220 1.486 1.806 2.191 2.653 25 1.282 1.641 2.094 2.666 3.386 30 40 50 3.870 4.661 4.292 5.427 6.848 8.623 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063 13.268 1.489 2.208 3.262 4.801 7.040 10.286 14.974 21.725 31.409 1.645 2.692 4.384 7.107 11.467 18.420 29.457 46.902 74.358 3.207 4.316 5.142 5.604 6.116 7.263 8.613 10.197 12.056 14.232 16.777 19.748 23.214 27.252 31.948 69.389 146.190 6.727 10.835 16.367 19.461 8.062 9.646 11.523 13.743 13.585 17.000 21.231 26.462 32.919 40.874 50.658 17.449 22.892 29.960 39.116 50.950 66.212 85.850 111.070 143.370 184.680 237.380 807.790 45.259 65.001 93.051 132.780 188.880 267.860 378.720 533.870 750.380 1,051.700 1,469.800 7,523.200 36,119.000 23.106 27.393 32.429 38.338 86.736 190.050 62.669 77.388 95.396 264.700 705.640 2,620.000 117.390 184.570 289.000 450.740 700.230 1,083.700 1,670.700 2,566.200 3,927.400 5,988.900 9,100.400 70,065.000 497,929.000 Appendix B Present value of $1. PV IF PV=FV[1 / (1 + i)"] Percent Period 1% 2% 1 0.990 3% 4% 0.980 0.971 0.962 2 0.980 0.961 0.943 0.925 0.907 5% 6% 0.952 0.943 0.890 8% 3 0.971 0.942 0.915 0.889 0.864 4 0.961 0.924 0.888 0.855 0.823 5 0.951 0.906 0.863 6 7 8 9 0.853 0.789 0.731 0.677 0.627 0.582 0.914 0.837 0.766 10 0.905 0.820 0.744 11 12 13 14 15 0.870 0.758 0.661 0.861 0.743 16 17 18 19 40 0.672 0.453 0.307 0.208 50 0.009 7% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 35% 40% 50% 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.800 0.769 0.741 0.714 0.667 0.873 0.857 0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.640 0.592 0.549 0.510 0.444 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0.512 0.455 0.406 0.364 0.296 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.515 0.499 0.482 0.410 0.350 0.301 0.260 0.198 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402 0.328 0.269 0.223 0.186 0.132 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 0.262 0.207 0.165 0.133 0.088 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.210 0.159 0.122 0.095 0.059 0.923 0.540 0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 0.168 0.123 0.091 0.068 0.039 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 0.134 0.094 0.067 0.048 0.026 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 0.107 0.073 0.050 0.035 0.017 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.086 0.056 0.037 0.025 0.012 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 0.069 0.043 0.027 0.018 0.008 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 0.055 0.033 0.020 0.013 0.005 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 0.044 0.025 0.015 0.009 0.003 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 0.035 0.020 0.011 0.006 0.002 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.163 0.141 0.123 0.107 0.093 0.081 0.071 0.062 0.054 0.028 0.015 0.008 0.005 0.002 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.023 0.012 0.006 0.003 0.001 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038 0.018 0.009 0.005 0.002 0.001 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.014 0.007 0.003 0.002 20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 0.012 0.005 0.002 0.001 25 0.780 0.610 0.478 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.004 0.001 0.001 30 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 0.001 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001 0.608 0.372 0.228 0.141 0.087 0.054 0.034 0.021 0.013 0 0 0 0 0 0 0 0 0.001 0.001 0 0 0 0 0 0.005 0.003 0.002 0.001 0.001 0.001 0 0 0 0 0 0 0 0 0