Problem 4 (25 pts). For a nominal interest of 6% per year. What is the effective...

  

 

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Problem 4 (25 pts). For a nominal interest of 6% per year. What is the effective annual interest rate if interest is: a. (5 pts) Compounded quarterly? b. (5 pts) Compounded Monthly? c. (5 pts) Compounded yearly? d. (10 pts) Compounded continuously? APPENDIX C: COMPOUND INTEREST TABLES 609 6% Compound Interest Factors 6% Single Payment Uniform Payment Series Arithmetic Gradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund Recovery Amount Worth Uniform Present Factor Factor Factor Factor Factor Factor Series Worth Find F Find P Find A Find A Find F Find P Find A Find P Given P Given F Given F Given P Given A Given A 0 F/P P/F A/F A/P F/A PIA Given G A/G Given G P/G 1 1.060 9434 1.0000 1.0600 1.000 0.943 0 0 2 1.124 .8900 .4854 5454 2.060 1.833 0.485 0.890 2 3 1.191 .8396 .3141 3741 3.184 2.673 0.961 2.569 3 4 1.262 .7921 2286 2886 4.375 3.465 1.427 4.945 4 5 1.338 7473 .1774 2374 5.637 4.212 1.884 7.934 5 6 1.419 7050 1434 2034 6.975 4.917 2.330 11.459 6 7 1.504 .6651 1191 .1791 8.394 5.582 2.768 15.450 7 8 1.594 .6274 1010 1610 9.897 6.210 3.195 19.841 8 9 1.689 .5919 .0870 1470 11.491 6.802 3.613 24.577 " 10 1.791 5584 0759 1359 13.181 7.360 4.022 29.602 10 11 1.898 .5268 0668 1268 14.972 7.887 4421 34.8701 11 12 2.012 .4970 .0593 .1193 16.870 8.384 4.811 40.337 12 13 2.133 .4688 .0530 1130 18.882 8.853 5.192 45.963 13 14 2.261 .4423 0476 .1076 21.015 9.295 5.564 51.713 14 15 2.397 4173 .0430 .1030 23.276 9.712 5.926 57.554 15 16 2.5401 .3936 0390 1990 25.672 10.106 6.279 63.459 16 17 2.693 .3714 0354 0954 28.213 10.477 6.624 69.401 17 18 2.854 3503 0324 0924 30.906 10.828 6.960 75.357 18 19 3.026 3305 .0296 .0896 33.760 11.158 7.287 81.306 19 20 3.207 3118 0272 .0872 36.786 11.470 7.605 87.230 20 21 3.400 .2942 0250 0850 39.993 11.764 7.915 93.113 21 22 3.604 .2775 0230 .0830 43.392 12.042 8.217 98.941 22 23 3.8201 .2618 0213 0813 46.996 12.303 8.510 104.700 23 24 4.049 2470 0197 .0797 50.815 12.550 8.795 110.381 24 25 4.2921 2330 0182 0782 54.864 12.783 9.072 115.973 25 26 4.549 2198 0169 0769 59.156 13.003 9.341 121.468 26 27 4.8221 .2074 .0157 0757 63.706 13.211 9.603 126.860 27 28 5.112. .1956 .0146 0746 68.528 13.406 9.857 132.142 28 29 5.418 .1846 .0136 .0736 73.640 13.591 10.103 137.309 29 30 5.743 .1741 .0126 0726 79.058 13.765 10.342 142.359 30 31 6.088 .1643 .0118 0718 84.801 13.929 10.574 147.286 31 32 6.453 .1550 .0110 .0710 90.8901 14.084 10.799 152.090 32 33 6.841 .1462 .0103 0703 97.3431 14.230 11.017 156.768 33 34 7.251 1379 00960 0696 104.184 14.368 11.228 161.319 34 35 7.686 1301 00897 0690 111.435 14.498 11.432 165.743 35 40 10.286 .0972 .00646 0665 154.762 15.046 12.359 185.957 40 45 13.765 .0727 .00470 0647 212.743 15.456 13.141 203.109 45 50 18420 ,0543 ,00344 0634 290.335 15.762 13,796 217.457 50 55 24.650 .0406 .00254 0625 394,171 15.991 14.341 229.322 55 60 32.988 .0303 00188 0619 533.126 16.161 14.791 239.043 60 65 44.145 .0227 .00139 0614 719.080 16.289 15.160 246.945 65 70 59.076 0169 .00103 0610 967.928 16.385 15.461 253.327 70 75 79.057 .0126 .00077 0608 1300.9 16.456 15.706 258.453 75 80 105.796 .00945 .00057 0606 1746.6 16.509 15.903 262.549 80 85 141.578 .00706 .00043 0604 2343.0 16.549 16.062 265.810 85 90 189.464 .00528 .00032 0603 3141.1 16.579 16.189 268.395 90 95 253.545 00394 00024 .0602 4209.1 16.601 16.290 100 339.300 00295 00018 0602 5638.3 16.618 16.371 270.437 272.047 95 100 612 APPENDIX C: COMPOUND INTEREST TABLES 9% Compound Interest Factors 9% Single Payment Uniform Payment Series Arithmetic Gradient Compound Amount Present Worth Sinking Capital Compound Present Gradient Gradient Fund Recovery Amount Worth Uniform Present Factor Factor Factor Factor Factor Factor Series Worth Find F Find P Find A Find A Find F Find P Find A Find P Given P Given F Given F Given P Given A Given A Given G Given G F/P P/F A/F A/P F/A P/A A/G P/G n 1 1.090 .9174 1.0000 1.0900 1.000 0.917 0 0 2 1.188 .8417 4785 .5685 2.090 1.759 0.478 0.842 2 1.295 .7722 3051 .3951 3.278 2.531 0.943 2.386 3 1.412 .7084 2187 .3087 4.573 3.240 1.393 4.511 4 5 1.539 6499 .1671 .2571 5.985 3.890 1.828 7.111 5 6 1.677 .5963 .1329 .2229 7.523 4.486 2.250 10.092 6 1.828 5470 .1087 .1987 9.200 5.033 2657 13.375 7 8 1.993 5019 .0907 .1807 11.028 5.535 3.051 16.888 8 9 2.172 4604 .0768 1668 13.021 5.995 3.431 20.571 9 10 2.367 4224 .0658 .1558 15.193 6.418 3.798 24.373 10 11 2.580 3875 .0569 .1469 17.560 6.805. 4.151 28.248 11 12 2.813 3555 .0497 .1397 20.141 7.161 4.491 32.159 12 13 3.066 .3262 .0436 .1336 22.953 7.487 4.818 36.073 13 14 3.342 .2992 .0384 .1284 26.019 7.786 5.133 39.963 14 15 3.642 .2745 .0341 .1241 29.361 8.061 5.435 43,807 15 16 3.970 .2519 .0303 .1203 33.003 8.313 5.724 47.585 16 17 4.328 .2311 .0270 .1170 36.974 8.544 6.002 51.282 17 18 4.717 2120 .0242 .1142 41.301 8.756 6.269 54.886 18 19 5.142 1945 .0217 1117 46.019 8.950 6.524 58.387 19 20 5.604 .1784 .0195 1095 51.160 9.129 6.767 61.777 20 21 6.109 .1637 .0176 .1076 56.765 9.292 7.001 65.051 21. 22 6.659 .1502 .0159 .1059 62.873 9.442 7.223 68.205 22 23 7.258 .1378 .0144 .1044 69.532 9.580 7.436 71.236 23 24 7.911 .1264 0130 .1030 76.790 9.707 7.638 74.143 24 25 8.623 .1160 .0118 .1018 84.7011 9.823 7.832 76.927 25 26 9.399 .1064 .0107 .1007 93.324 9.929 8.016 79.586 26 27 10.245 .0976 .00973 0997 102.723 10.027 8.191 82.124 27 28 11.167 .0895 .00885 .0989 112.968 10.116 8.357 84.542 28 29 12.172 .0822 .00806 .0981 124.136 10.198 8.515 86.842 29 30 13.268 .0754 .00734 .0973 136.308 10.274 8.666 89.028 30 31 14.462 .0691 .00669 .0967 149.575 10.343 8.808 91.102 31 32 15.763 .0634 .00610 .0961 164.037 10.406 8.944 93.069 32 33 17.182 .0582 .00556 .0956 179.801 10.464 9.072 94.931 33 34 18.728 .0534 .00508 .0951 196.983 10.518 9.193 96.693 34 35 20.414 .0490 .00464 0946 215.711 10.567 9.308 98.359 35 40 31.409 .0318 .00296 .0930 337.883 10.757 9.796 105.376 40 45 48.327 .0207 .00190 .0919 525.860 10.881 10.160 110.556 45 50 74.358 .0134 .00123 0912 815.085 10.962 10.430 114.325 50 55 114.409 .00874 .00079 0908 1260.1 11,014 10.626 117.036 55 60 176.032 .00568 00051 0905 1944.8 11,048 10.768 118.968 60 65 270.847 .00369 .00033 .0903 2998.3 11.070 10.870 120.334 65 70 416.731 00240 .00022 .0902 4619.2 11.084 10.943 121.294 70 75 641.193 .00156 .00014 .0901 7113.3 11.094 10.994 121.965 75 80 986.555 .00101 .00009 .0901 10950.6 11.100 11.030 122.431 80 85 1517.9 .00066 .00006 .0901 16854.9 11.104 11.055 122.753 85 90 2335.5 .00043 .00004 .0900 25939.3 11.106 11.073 122.976 90 95 3593.5 .00028 .00003 .0900 39916.8 11.108 11.085 123.129 95. 100 $529.1 .00018 .00002 .0900 61 422.9 11.109 11.093 123.233 100 Problem 4 (25 pts). For a nominal interest of 6% per year. What is the effective annual interest rate if interest is: a. (5 pts) Compounded quarterly? b. (5 pts) Compounded Monthly? c. (5 pts) Compounded yearly? d. (10 pts) Compounded continuously? APPENDIX C: COMPOUND INTEREST TABLES 609 6% Compound Interest Factors 6% Single Payment Uniform Payment Series Arithmetic Gradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund Recovery Amount Worth Uniform Present Factor Factor Factor Factor Factor Factor Series Worth Find F Find P Find A Find A Find F Find P Find A Find P Given P Given F Given F Given P Given A Given A 0 F/P P/F A/F A/P F/A PIA Given G A/G Given G P/G 1 1.060 9434 1.0000 1.0600 1.000 0.943 0 0 2 1.124 .8900 .4854 5454 2.060 1.833 0.485 0.890 2 3 1.191 .8396 .3141 3741 3.184 2.673 0.961 2.569 3 4 1.262 .7921 2286 2886 4.375 3.465 1.427 4.945 4 5 1.338 7473 .1774 2374 5.637 4.212 1.884 7.934 5 6 1.419 7050 1434 2034 6.975 4.917 2.330 11.459 6 7 1.504 .6651 1191 .1791 8.394 5.582 2.768 15.450 7 8 1.594 .6274 1010 1610 9.897 6.210 3.195 19.841 8 9 1.689 .5919 .0870 1470 11.491 6.802 3.613 24.577 " 10 1.791 5584 0759 1359 13.181 7.360 4.022 29.602 10 11 1.898 .5268 0668 1268 14.972 7.887 4421 34.8701 11 12 2.012 .4970 .0593 .1193 16.870 8.384 4.811 40.337 12 13 2.133 .4688 .0530 1130 18.882 8.853 5.192 45.963 13 14 2.261 .4423 0476 .1076 21.015 9.295 5.564 51.713 14 15 2.397 4173 .0430 .1030 23.276 9.712 5.926 57.554 15 16 2.5401 .3936 0390 1990 25.672 10.106 6.279 63.459 16 17 2.693 .3714 0354 0954 28.213 10.477 6.624 69.401 17 18 2.854 3503 0324 0924 30.906 10.828 6.960 75.357 18 19 3.026 3305 .0296 .0896 33.760 11.158 7.287 81.306 19 20 3.207 3118 0272 .0872 36.786 11.470 7.605 87.230 20 21 3.400 .2942 0250 0850 39.993 11.764 7.915 93.113 21 22 3.604 .2775 0230 .0830 43.392 12.042 8.217 98.941 22 23 3.8201 .2618 0213 0813 46.996 12.303 8.510 104.700 23 24 4.049 2470 0197 .0797 50.815 12.550 8.795 110.381 24 25 4.2921 2330 0182 0782 54.864 12.783 9.072 115.973 25 26 4.549 2198 0169 0769 59.156 13.003 9.341 121.468 26 27 4.8221 .2074 .0157 0757 63.706 13.211 9.603 126.860 27 28 5.112. .1956 .0146 0746 68.528 13.406 9.857 132.142 28 29 5.418 .1846 .0136 .0736 73.640 13.591 10.103 137.309 29 30 5.743 .1741 .0126 0726 79.058 13.765 10.342 142.359 30 31 6.088 .1643 .0118 0718 84.801 13.929 10.574 147.286 31 32 6.453 .1550 .0110 .0710 90.8901 14.084 10.799 152.090 32 33 6.841 .1462 .0103 0703 97.3431 14.230 11.017 156.768 33 34 7.251 1379 00960 0696 104.184 14.368 11.228 161.319 34 35 7.686 1301 00897 0690 111.435 14.498 11.432 165.743 35 40 10.286 .0972 .00646 0665 154.762 15.046 12.359 185.957 40 45 13.765 .0727 .00470 0647 212.743 15.456 13.141 203.109 45 50 18420 ,0543 ,00344 0634 290.335 15.762 13,796 217.457 50 55 24.650 .0406 .00254 0625 394,171 15.991 14.341 229.322 55 60 32.988 .0303 00188 0619 533.126 16.161 14.791 239.043 60 65 44.145 .0227 .00139 0614 719.080 16.289 15.160 246.945 65 70 59.076 0169 .00103 0610 967.928 16.385 15.461 253.327 70 75 79.057 .0126 .00077 0608 1300.9 16.456 15.706 258.453 75 80 105.796 .00945 .00057 0606 1746.6 16.509 15.903 262.549 80 85 141.578 .00706 .00043 0604 2343.0 16.549 16.062 265.810 85 90 189.464 .00528 .00032 0603 3141.1 16.579 16.189 268.395 90 95 253.545 00394 00024 .0602 4209.1 16.601 16.290 100 339.300 00295 00018 0602 5638.3 16.618 16.371 270.437 272.047 95 100 612 APPENDIX C: COMPOUND INTEREST TABLES 9% Compound Interest Factors 9% Single Payment Uniform Payment Series Arithmetic Gradient Compound Amount Present Worth Sinking Capital Compound Present Gradient Gradient Fund Recovery Amount Worth Uniform Present Factor Factor Factor Factor Factor Factor Series Worth Find F Find P Find A Find A Find F Find P Find A Find P Given P Given F Given F Given P Given A Given A Given G Given G F/P P/F A/F A/P F/A P/A A/G P/G n 1 1.090 .9174 1.0000 1.0900 1.000 0.917 0 0 2 1.188 .8417 4785 .5685 2.090 1.759 0.478 0.842 2 1.295 .7722 3051 .3951 3.278 2.531 0.943 2.386 3 1.412 .7084 2187 .3087 4.573 3.240 1.393 4.511 4 5 1.539 6499 .1671 .2571 5.985 3.890 1.828 7.111 5 6 1.677 .5963 .1329 .2229 7.523 4.486 2.250 10.092 6 1.828 5470 .1087 .1987 9.200 5.033 2657 13.375 7 8 1.993 5019 .0907 .1807 11.028 5.535 3.051 16.888 8 9 2.172 4604 .0768 1668 13.021 5.995 3.431 20.571 9 10 2.367 4224 .0658 .1558 15.193 6.418 3.798 24.373 10 11 2.580 3875 .0569 .1469 17.560 6.805. 4.151 28.248 11 12 2.813 3555 .0497 .1397 20.141 7.161 4.491 32.159 12 13 3.066 .3262 .0436 .1336 22.953 7.487 4.818 36.073 13 14 3.342 .2992 .0384 .1284 26.019 7.786 5.133 39.963 14 15 3.642 .2745 .0341 .1241 29.361 8.061 5.435 43,807 15 16 3.970 .2519 .0303 .1203 33.003 8.313 5.724 47.585 16 17 4.328 .2311 .0270 .1170 36.974 8.544 6.002 51.282 17 18 4.717 2120 .0242 .1142 41.301 8.756 6.269 54.886 18 19 5.142 1945 .0217 1117 46.019 8.950 6.524 58.387 19 20 5.604 .1784 .0195 1095 51.160 9.129 6.767 61.777 20 21 6.109 .1637 .0176 .1076 56.765 9.292 7.001 65.051 21. 22 6.659 .1502 .0159 .1059 62.873 9.442 7.223 68.205 22 23 7.258 .1378 .0144 .1044 69.532 9.580 7.436 71.236 23 24 7.911 .1264 0130 .1030 76.790 9.707 7.638 74.143 24 25 8.623 .1160 .0118 .1018 84.7011 9.823 7.832 76.927 25 26 9.399 .1064 .0107 .1007 93.324 9.929 8.016 79.586 26 27 10.245 .0976 .00973 0997 102.723 10.027 8.191 82.124 27 28 11.167 .0895 .00885 .0989 112.968 10.116 8.357 84.542 28 29 12.172 .0822 .00806 .0981 124.136 10.198 8.515 86.842 29 30 13.268 .0754 .00734 .0973 136.308 10.274 8.666 89.028 30 31 14.462 .0691 .00669 .0967 149.575 10.343 8.808 91.102 31 32 15.763 .0634 .00610 .0961 164.037 10.406 8.944 93.069 32 33 17.182 .0582 .00556 .0956 179.801 10.464 9.072 94.931 33 34 18.728 .0534 .00508 .0951 196.983 10.518 9.193 96.693 34 35 20.414 .0490 .00464 0946 215.711 10.567 9.308 98.359 35 40 31.409 .0318 .00296 .0930 337.883 10.757 9.796 105.376 40 45 48.327 .0207 .00190 .0919 525.860 10.881 10.160 110.556 45 50 74.358 .0134 .00123 0912 815.085 10.962 10.430 114.325 50 55 114.409 .00874 .00079 0908 1260.1 11,014 10.626 117.036 55 60 176.032 .00568 00051 0905 1944.8 11,048 10.768 118.968 60 65 270.847 .00369 .00033 .0903 2998.3 11.070 10.870 120.334 65 70 416.731 00240 .00022 .0902 4619.2 11.084 10.943 121.294 70 75 641.193 .00156 .00014 .0901 7113.3 11.094 10.994 121.965 75 80 986.555 .00101 .00009 .0901 10950.6 11.100 11.030 122.431 80 85 1517.9 .00066 .00006 .0901 16854.9 11.104 11.055 122.753 85 90 2335.5 .00043 .00004 .0900 25939.3 11.106 11.073 122.976 90 95 3593.5 .00028 .00003 .0900 39916.8 11.108 11.085 123.129 95. 100 $529.1 .00018 .00002 .0900 61 422.9 11.109 11.093 123.233 100