Questions 1, 2 and 3... tables are required if needed

1. What is the duration of a bond? Explain how the bond characteristics influence the size of a bond's duration? 2. What is the convexity of a bond? Explain how the bond characteristics influence the size of a bond's convexity? 3. With the aid of a diagram show why: (i) for a small change in interest rates using the modified duration (MD) approximation produces a reasonable approximation of the percentage change in a bond's price, (ii) for a large change in interest rates the MD approximation is relatively poor.\fTable 4b Present Value Annuity Factors (at R percent period) for $1 received per period for each of N periods N 14% 15% 16% 18% 35% 45% 50% 0.877 0.870 0.862 0.847 0.820 0.806 0.800 0.769 0.741 0.714 0.690 0.667 2 1.647 1.626 1.528 1.492 1.457 1.440 1.361 1.289 1.224 1.165 1.111 2.322 2.283 2.246 2.106 2.042 1.981 1.696 1.589 1.493 1.407 2.914 2.855 2.798 2.494 2.404 2.362 2.166 1.997 1.849 1.720 1.605 5 3.433 3.352 2.991 2.864 2.745 2.689 2.436 2.220 2.035 1.876 1.737 6 3.889 3.685 3.498 3.326 3.167 3.020 2.951 2.643 2.385 2.168 1.983 1.824 4.288 3.812 3.605 3.416 3.242 3.161 2.802 2.508 2.263 2.057 1.883 8 4.639 4.487 4.344 4.078 3.837 3.619 3.421 3.329 2.925 2.598 2.331 2.109 1.922 9 4.031 3.786 3.566 3.463 3.019 2.665 2.379 2.144 1.948 10 5.216 5.019 4.833 4.494 3.923 3.682 3.571 2.715 2.414 2.168 1.965 5.234 5.029 4.656 4.327 4.035 3.776 3.656 3.147 2.752 2.438 2.185 12 5.660 5.421 5.197 4.439 4.127 3.851 2.456 2.196 1.985 5.583 5.342 4.910 4.533 4.203 3.912 3.780 3.223 2.799 2.469 2.204 1.990 14 6.002 5.008 4.611 4.265 3.962 3.824 3.249 2.814 2.478 2.210 1.993 15 6.142 5.092 4.675 4.315 3.859 3.268 2.825 2.484 2.214 1.995 16 6.265 5.668 5.162 4.730 4.357 3.887 3.283 2.834 2.489 2.216 1.997 17 6.373 4.775 4.391 3.910 3.295 2.840 2.492 2.218 1.998 18 6.467 6.128 5.818 4.812 4.419 4.080 3.304 2.844 2.494 2.219 1.999 19 6.550 6.198 5.877 5.316 4.843 4.442 4.097 3.311 2.848 2.496 2.220 1.999 20 6.623 6.259 5.929 5.353 4.870 4.460 4.1 10 3.954 3.316 2.850 2:497 2.221 1.999 21 6.687 6.312 5.973 4.891 4.476 4.121 3.963 2.852 2.498 2.221 2.000 22 6.743 6.359 6.011 5.410 4.909 4.130 3.970 3.323 2.853 2.498 2.222 2.000 23 6.792 6.044 5.432 4.499 4.137 3.976 2.854 24 6.835 6.073 5.451 4.937 4.507 4.143 3.981 3.327 2.855 2.499 2.222 2.000 25 6.097 5.467 4.948 4.514 4.147 3.985 2.856 2.222 2.000 30 7.003 6.566 6.177 5.517 4.979 4.534 4.160 3.995 3.332 2.857 2.500 2.222 2.00 35 7.070 6.617 6.215 5.539 4.992 4.541 4.164 3.998 3.333 2.857 2.500 2.000. 40 7.105 6.642 6.233 5.548 4.997 4.544 4.166 3.999 3.333 2.857 2.500 2.222 2.000 45 7.123 6.242 5.552 4.999 4.545 4.166 4.000 3.333 2.857 2.500 50 7.133 6.661 4.999 4.545 4.167 4.000 3.333 2.857 2.500 2.2.22 2.000Table 1b Compound (Future) Value Factors for 1 Compounded at R Percent for N periods N 44% 45% 46% 40% 20% 22% 24% 25% 30% 35% 40% 45% 50% -.._._.._____________ | 4.44 4.45 4.46 4.40 4.2 4.22 4.25 4.25 4.3 4.35 4.4 4.45 4.5 4.3 4.323 4.346 4.392 4.44 4.400 4.530 L563 4.69 4.023 4.96 2403 2.25 4.402 4.524 4.564 4.643 4.720 4.046 4.907 4.953 2497 2.46 2.744 3.049 3.375 4.609 4.749 4.04 4 4.939 2.074 2245 2364 2444 2.056 3.322 3.042 4.424 5.063 4.925 204 4 2.4 2.200 2.400 2703 2.932 3.052 3.743 4.404 5.370 6.44 7.594 2495 2343 2.436 2.7 2906 3.297 3.635 30 45 4.027 6053 7.53 9294 I 4.394 2.502 266 2.026 3.405 3.503 4.023 4.500 4.760 6275 0.472 40.544 43.476 47.006 2.053 3.059 3.270 3.759 4.3 4.900 5.59 5.96 0457 | 4.032 44.750 49.544 25.629 3.252 3.540 3023 4.435 5.46 5.907 6.934 7.454 40.604 44.094 20.664 20.334 30.443 40 3.707 4.046 4.444 5.234 6492 7.305 0594 9.343 43.706 20.407 20.925 44.005 57.665 44 4226 4.652 5.447 6.476 7.43 0.942 40.657 44.642 47.922 27.444 40.496 59.573 06.490 42 4040 5.35 5.936 7.200 0.946 40.072 43.245 44.552 23.290 36.644 56.694 06.304 429.746 43 5.492 6.453 6.006 0.599 40.699 43.264 46.306 40.49 30.200 49.47 79.374 425.25 494.62 44 6.264 7.076 7.900 40.447 42.039 46.402 20.349 22.737 39.374 66.704 444.42 404.64 294.929 45 7.430 0.437 9.266 44.974 45.407 49.742 25.496 20.422 54.406 90.450 455.56 263.34 437094 46 0437 9.350 40.740 44.429 40.400 24.006 34.243 35.527 66.542 424.74 247.79 304.04 656.044 47 9.276 40.764 42.460 46672 22406 29.304 30.744 44.409 06504 464.34 304.94 553.67 905.264 40 40575 42.375 44.463 49.673 26.623 35.049 40039 55.544 442.45 224.02 426.07 002.03 4477.092 49 42.056 44.232 46.777 23.244 34.940 43.736 59.560 69.309 446.49 299.46 597.63 4464.4 2246.030 40 43.743 46.367 49.464 27.393 30.330 53.350 73.064 06.736 490.05 404.27 036.60 4607.9 3325.257 44 45.660 40022 22574 32.324 46.005 65.096 94.592 40042 247.06 545.76 4474.3 2447.5 4907.005 42 47.064 24.645 26.406 30442 55.206 79.440 443.57 43552 324.40 746.70 4639.0 35409 7404.020 43 20.362 24.094 30.376 45.000 66.247 96.009 44003 469.40 447.53 994.66 2297.0 54459 4422274 4423.242 20.626 35.236 53.409 79.497 440.20 474.63 244.75 54200 4342.7 3244.2 7464.6 46034.44 45 26.462 32.949 40.074 62669 95.396 444.24 24654 264.69 705.64 40427 4499.0 40049. 25254.47 40 50.95 66.242 05.05 443.37 237.37 309.75 63402 007.79 2649.9 0420.5 24204. 69340. 4947544 45 90.4 433.47 400.34 327.99 590.66 4053.4 4064.0 2465.4 9727.0 36440. 430464. 444500. 40400.00 267.06 370.72 750.37 4469.7 2047.0 5455.9 7523.4 36440. 463437. 700037. 45363.67 530.76 795.44 4746.6 3657.2 7694.7 45994. 22950 434406. 732057. 40700.23 4003.6 4670.7 3927.3 9400.4 20796. 46090. 70064. 497929. Table 1a Compound (Future) Value Factors for $1 Compounded at R Percent for N periods R = N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 1% 12% 13% 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 2 1.02 1.04 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.21 1.232 1.254 1.277 3 1.03 1.061 1.093 1.125 1.158 1.191 1.225 1.26 1.295 1.331 1.368 1.405 1.443 4 1.041 1.082 1.126 1.17 1.216 1.262 1.311 1.36 1.412 1.464 1.518 1.574 1.53 un 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 1.685 1.762 1.842 1.062 1.126 1.194 1.265 1.34 1.419 1.501 1.587 1.677 1.772 1.87 1.974 2.082 1.072 1.149 1.23 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.076 2.211 2.353 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.305 2.476 2.658 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 2.558 2.773 3.004 10 1.105 1.219 1.344 1.48 1.629 1.791 1.967 2.159 2.367 2.594 2.839 3.106 3.395 1.116 1.243 1.384 1.539 1.71 1.898 2.105 2.332 2.58 2.853 3.152 3.479 3.836 12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 3.498 3.896 4.335 13 1.138 1.294 1.469 1.665 1.886 2.133 2.41 2.72 3.066 3.452 3.883 4.363 4.898 14 1.149 1.319 1.513 1.732 1.98 2.261 2.579 2.937 3.342 3.797 4.31 4.887 5.535 15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 4.785 5.474 6.254 16 1.173 1.373 1.605 1.873 2.183 2.54 2.952 3.426 3.97 4.595 5.311 6.13 7.067 17 1.184 1.4 1.653 2.292 2.693 3.159 3.7 4.328 5.054 5.895 6.866 7.986 18 1.196 1.428 1.702 2.026 2.407 2.854 3.38 3.96 4.717 5.56 6.544 7.69 9.024 19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 7.263 8.613 10.197 20 1.22 1.806 2.191 2.653 3.207 3.87 4.661 5.604 6.727 8.062 9.646 11.523 21 1.232 1.516 1.86 2.279 2.786 3.4 4.141 5.034 6.109 7.4 8.949 10.804 13.021 22 1.245 1.546 1.916 2.37 2.925 3.604 4.43 5.437 6.659 8,14 9.934 . 12.1 14.714 23 1.257 1.577 1.974 2.465 3.072 3.82 4.741 5.871 7.258 8.954 10.026 13.552 16.627 24 1.27 1.608 2.033 2.563 3.225 4.049 5.072 6.341 7.911 9.85 12.239 15.179 18.788 25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.835 13.585 17 21.231 30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063 13.268 17.449 22.892 29.96 39.1 16 5 1.417 2 2.814 3.946 5.516 7.686 10.677 14.785 20.414 28.102 38.575 52.8 72.069 40 1.489 2.208 3.262 4.801 7.04 10.286 14.974 21.725 31.409 45.259 65.001 93.051 132.782 45 1.565 2.438 3.782 5.841 8.985 13.765 21.002 31.92 48.327 72.89 109.53 163.98 244.641 50 1.645 2.692 4.384 7.107 11.467 18.42 29.457 46.902 74.358 17.39 184.56 289.00 450.735Table 2b Present Value Factors (at R per cent) for 1 received at end of N periods N 74% 75% 76% 70% 20% 22% 24% 25% 30% 35% 40% 45% 50% .077 | .070 .062 .047 .033 .020 .006 .000 .769 .747 .774 .690 .667 2 .769 .756 .743 .770 .694 .672 .650 .640 .592 .449 .570 .476 .444 3 .675 .650 .647 .609 .579 557 .524 .572 .455 .406 .364 .320 .296 4 .592 .572 .552 .576 .402 .457 .423 .470 .350 .307 .260 .226 .790 5 .579 .497 .476 .437 .402 .370 .347 .320 .269 .223 .706 .756 .732 6 .456 .432 .470 .370 .335 .303 .275 .262 207 .765 .733 .700 .000 7 .400 .376 .354 .374 279 .249 .222 .270 .759 .722 .095 .074 .059 0 .357 .327 .305 .266 .233 .204 .779 .760 .723 .097 .060 .057 .039 9 .300 .204 .263 .225 .794 .767 .744 .734 .094 .067 .040 .035 .026 70 .270 .247 .227 .797 .762 .737 .I I6 .707 .073 .050 .035 .024 .077 || .237 .275 .795 .762 .735 .772 .094 .006 .056 .037 _ .025 .077 .072 72 .200 .707 .760 .737 .7 72 .092 .076 .069 .043 .027 .070 .072 .000 73 .702 .763 .745 .I I6 .093 .075 .067 .055 .033 .020 .073 .000 .005 I4 .760 .747 .725 .099 .070 .062 .049 .044 .025 .075 .009 .006 .003 75 .740 . I23 . 700 .004 .065 .057 .040 .035 .020 .07 7 .006 .004 .002 76 .723 .707 .093 .077 .054 .042 .032 .020 .075 .000 .005 .003 .002 77 .700 .093 .000 .060 .045 .034 .026 .023 .072 .006 .003 .002 .007 70 .095 .007 .069 .057 .030 .020 .027 .070 .009 .005 .002 .007 .007 I9 .003 .070 .060 .043 .037 .023 .077 .074 .007 .003 .002 .007 20 .073 .067 .057 .037 .026 .079 .074 .072 .005 .002 ...007 .007 2| .064 .053 .044 .037 .022 .075 .07 l .009 .004 .002 .007 22 .056 .046 .030 .026 .070 .073 .009 .007 .003 .007 .007 23 .049 .040 .033 .022 .075 .070 .007 .006 .002 .007 24 .043 .035 .020 .079 .073 .000 .006 .005 .002 .007 25 .030 .030 .024 .076 .070 .007 .005 .004 .007 .007 30 .020 .075 .072 .007 .004 .003 .002 .007 35 .070 .000 .006 .003 .002 .007 .007 40 .005 .004 .003 .007 .007 45 .003 .002 .07 | .007 50 .007 .007 .007 Table 4a Present Value Annuity Factors (at R percent period) for $1 received per period for each of N periods V 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 0.990 0.980 0.971 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 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 2.941 2.884 2.829 2.723 2.673 2.624 2.531 2.487 2.444 2.402 2.361 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.974 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.517 5.795 5.601 5.417 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 3.998 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 4.423 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 4.968 4.799 8.566 8.162 7.786 7.435 7.108 5.802 6.515 6.247 5.995 5.759 5.537 5.328 5.132 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.426 11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 5.918 3 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 6.122 14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.367 6.982 6.628 6.302 15 13.865 12.849 11.938 11.1 18 10.380 8.061 7.606 7.191 6.811 6.462 16 14.718 13.578 8 12.561 11.652 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 6.604 17 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120 6.729 18 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250 6.840 19 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366 6.938 20 18.046 14.877 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.469 7.025 21 18.857 17.011 15.415 1 14.029 12.821 11.764 10.836 1 10.017 9.292 8.075 7.562 7.102 22 17.658 15.937 14.451 13.163 12.042 11.061 10.201 9.442 8.772 8.176 7.654 7.170 23 20.456 18.292 16.444 14.857 1 13.489 12.303 11.272 10.371 9.580 8.883 8.266 7.718 7.230 24 21.243 18.914 16.936 15.247 13.799 12.550 11.469 10.529 9.707 8.985 8.348 7.784 7.283 25 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.843 7.330 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 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 40 32.835 27.355 23.1 15 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.951 8.244 7.634 45 36.095 29.490 24.519 20.720 17.774 15.456 13.606 12.108 10.881 9.008 8.283 7.661 50 39.196 31.424 25.730 21.482 18.256 6 15.762 13.801 12.233 10.962 9 9.915 9.042 8.304 7.675\fTable 2a Present Value Factors (at R per cent) for &1 received at end of N periods 2% 5% 6% 7% 8% 9% 11% 12% 13% .917 .893 .962 .943 .935 .926 .909 .901 .885 .826 .812 797 .783 961 .873 .857 .842 .840 .816 .772 .751 .731 .712 942 .961 924 .855 .823 .763 .735 .708 .683 .659 .636 .613 .543 .822 .784 .747 .713 .681 .650 .621 .593 .567 .480 .790 .746 .705 . 666 . 630 .596 .564 535 507 760 .711 .665 .623 .513 482 .452 425 731 .677 .627 .582 .540 .502 467 .434 .404 376 703 .645 592 .544 .500 424 .391 .361 .333 .914 .676 .614 .558 .508 .463 422 386 .352 322 650 475 429 388 350 317 261 .887 701 .625 .557 .444 397 356 .319 .286 .257 231 681 .601 530 415 368 326 290 .258 .229 .870 . 661 .577 .505 388 .340 299 263 .232 .205 .642 .555 362 315 275 239 209 .623 .534 458 394 .339 .292 252 .218 .188 .163 . 141 436 371 317 270 . 198 .170 .146 . 125 .513 494 416 350 .296 .250 .212 . 180 .153 .130 570 .475 396 331 277 .232 194 . 164 . 138 . 116 .098 .554 .456 377 .312 .258 .215 . 178 . 149 .124 .104 .087 .538 439 .359 .294 242 .199 .164 .135 . 112 .093 522 .422 .342 .278 .226 .184 . 150 .123 . 101 .068 507 406 .326 262 211 . 170 .133 091 .060 492 .390 .310 .247 .197 .158 .126 .102 059 478 .375 .295 233 . 184 .146 .116 .092 308 231 . 174 .131 .099 .075 .057 .044 .706 500 355 253 .181 . 130 .094 .068 .049 .036 .672 307 .208 .067 .046 .032 .022 .015 410 264 171 .073 .048 .031 .021 . 014 .009 .006 .004 .639 608 372 228 141 .087 .054 . 034 .021 .013 .009 .005 .003