Appendix III Present value of an annuity of £1 at compound interest
| Interest rate (J) | |||||||||||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |||
| Periods (r?) | 1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9346 | 0.9259 | 0.9174 | 0.9091 | 0.9009 | 0.8929 | 0.8850 | 0.8772 | 0.8696 | 1 |
| 2 | 1.9704 | 1.9416 | 1.9135 | 1.8861 | 1.8594 | 1.8334 | 1.8080 | 1.7833 | 1.7591 | 1.7355 | 1.7125 | 1.6901 | 1.6681 | 1.6467 | 1.6257 | 2 | |
| 3 | 2.9410 | 2.8839 | 2.8286 | 2.7751 | 2.7232 | 2.6730 | 2.6243 | 2.5771 | 2.5313 | 2.4869 | 2.4437 | 2.4018 | 2.3612 | 2.3216 | 2.2832 | 3 | |
| 4 | 3.9020 | 3.8077 | 3.7171 | 3.6299 | 3.5460 | 3.4651 | 3.3872 | 3.3121 | 3.2397 | 3.1699 | 3.1024 | 3.0373 | 2.9745 | 2.9137 | 2.8550 | bgcolor=white>4||
| 5 | 4.8534 | 4.7135 | 4.5797 | 4.4518 | 4.3295 | 4.2124 | 4.1002 | 3.9927 | 3.8897 | 3.7908 | 3.6959 | 3.6048 | 3.5172 | 3.4331 | 3.3522 | 5 | |
| 6 | 5.7955 | 5.6014 | 5.4172 | 5.2421 | 5.0757 | 4.9173 | 4.7665 | 4.6229 | 4.4859 | 4.3553 | 4.2305 | 4.1114 | 3.9975 | 3.8887 | 3.7845 | 6 | |
| 7 | 6.7282 | 6.4720 | 6.2303 | 6.0021 | 5.7864 | 5.5824 | 5.3893 | 5.2064 | 5.0330 | 4.8684 | 4.7122 | 4.5638 | 4.4226 | 4.2883 | 4.1604 | 7 | |
| 8 | 7.6517 | 7.3255 | 7.0197 | 6.7327 | 6.4632 | 6.2098 | 5.9713 | 5.7466 | 5.5348 | 5.3349 | 5.1461 | 4.9676 | 4.7988 | 4.6389 | 4.4873 | 8 | |
| 9 | 8.5660 | 8.1622 | 7.7861 | 7.4353 | 7.1078 | 6.8017 | 6.5152 | 6.2469 | 5.9952 | 5.7590 | 5.5370 | 5.3282 | 5.1317 | 4.9464 | 4.7716 | 9 | |
| 10 | 9.4713 | 8.9826 | 8.5302 | 8.1109 | 7.7217 | 7.3601 | 7.0236 | 6.7101 | 6.4177 | 6.1446 | 5.8892 | 5.6502 | 5.4262 | 5.2161 | 5.0188 | 10 | |
| 11 | 10.3676 | 9.7868 | 9.2526 | 8.7605 | 8.3064 | 7.8869 | 7.4987 | 7.1390 | 6.8052 | 6.4951 | 6.2065 | 5.9377 | 5.6869 | 5.4527 | 5.2337 | 11 | |
| 12 | 11.2551 | 10.5753 | 9.9540 | 9.3851 | 8.8633 | 8.3838 | 7.9427 | 7.5361 | 7.1607 | 6.8137 | 6.4924 | 6.1944 | 5.9176 | 5.6603 | 5.4206 | 12 | |
| 13 | 12.1337 | 11.3484 | 10.6350 | 9.9856 | 9.3936 | 8.8527 | 8.3577 | 7.9038 | 7.4869 | 7.1034 | 6.7499 | 6.4235 | 6.1218 | 5.8424 | 5.5831 | 13 | |
| 14 | 13.0037 | 12.1062 | 11.2961 | 10.5631 | 9.8986 | 9.2950 | 8.7455 | 8.2442 | 7.7862 | 7.3667 | 6.9819 | 6.6282 | 6.3025 | 6.0021 | 5.7245 | 14 | |
| 15 | 13.8651 | 12.8493 | 11.9379 | 11.1184 | 10.3797 | 9.7122 | 9.1079 | 8.5595 | 8.0607 | 7.6061 | 7.1909 | 6.8109 | 6.4624 | 6.1422 | 5.8474 | 15 | |
| 16 | 14.7179 | 13.5777 | 12.5611 | 11.6523 | 10.8378 | 10.1059 | 9.4466 | 8.8514 | 8.3126 | 7.8237 | 7.3792 | 6.9740 | 6.6039 | 6.2651 | 5.9542 | 16 | |
| 17 | 15.5623 | 14.2919 | 13.1661 | 12.1657 | 11.2741 | 10.4773 | 9.7632 | 9.1216 | 8.5436 | 8.0216 | 7.5488 | 7.1196 | 6.7291 | 6.3729 | 6.0472 | 17 | |
| 18 | 16.3983 | 14.9920 | 13.7535 | 12.6593 | 11.6896 | 10.8276 | 10.0591 | 9.3719 | 8.7556 | 8.2014 | 7.7016 | 7.2497 | 6.8399 | 6.4674 | 6.1280 | 18 | |
| 19 | 17.2260 | 15.6785 | 14.3238 | 13.1339 | 12.0853 | 11.1581 | 10.3356 | 9.6036 | 8.9501 | 8.3649 | 7.8393 | 7.3658 | 6.9380 | 6.5504 | 6.1982 | 19 | |
| 20 | 18.0456 | bgcolor=white>16.351414.8775 | 13.5903 | 12.4622 | 11.4699 | 10.5940 | 9.8181 | 9.1285 | 8.5136 | 7.9633 | 7.4694 | 7.0248 | 6.6231 | 6.2593 | 20 | ||
| 25 | 22.0232 | 19.5235 | 17.4131 | 15.6221 | 14.0939 | 12.7834 | 11.6536 | 10.6748 | 9.8226 | 9.0770 | 8.4217 | 7.8431 | 7.3300 | 6.8729 | 6.4641 | 25 | |
| 30 | 25.8077 | 22.3965 | 19.6004 | 17.2920 | 15.3725 | 13.7648 | 12.4090 | 11.2578 | 10.2737 | 9.4269 | 8.6938 | 8.0552 | 7.4957 | 7.0027 | 6.5660 | 30 | |
| 35 | 29.4086 | 24.9986 | 21.4872 | 18.6646 | 16.3742 | 14.4982 | 12.9477 | 11.6546 | 10.5668 | 9.6442 | 8.8552 | 8.1755 | 7.5856 | 7.0700 | 6.6166 | 35 | |
| 40 | 32.8347 | 27.3555 | 23.1148 | 19.7928 | 17.1591 | 15.0463 | 13.3317 | 11.9246 | 10.7574 | 9.7791 | 8.9511 | 8.2438 | 7.6344 | 7.1050 | 6.6418 | 40 | |
| 45 | 36.0945 | 29.4902 | 24.5187 | 20.7200 | 17.7741 | 15.4558 | 13.6055 | 12.1084 | 10.8812 | 9.8628 | 9.0079 | 8.2825 | 7.6609 | 7.1232 | 6.6543 | 45 | |
| 50 | 39.1961 | 31.4236 | 25.7298 | 21.4822 | 18.2559 | 15.7619 | 13.8007 | 12.2335 | 10.9617 | 9.9148 | 9.0417 | 8.3045 | 7.6752 | 7.1327 | 6.6605 | 50 | |
12 Financialconceptsandmathematics 329
| 16 | 17 | 18 | 19 | 20 | 21 | 22 | ||
| Periods (ã?) | 1 | 0.8621 | 0.8547 | 0.8475 | 0.8403 | 0.8333 | 0.8264 | 0.8197 |
| 2 | 1.6052 | 1.5852 | 1.5656 | 1.5465 | 1.5278 | 1.5095 | 1.4915 | |
| 3 | 2.2459 | 2.2096 | 2.1743 | 2.1399 | 2.1065 | 2.0739 | 2.0422 | |
| 4 | 2.7982 | 2.7432 | 2.6901 | 2.6386 | 2.5887 | 2.5404 | 2.4936 | |
| 5 | 3.2743 | 3.1993 | 3.1272 | 3.0576 | 2.9906 | 2.9260 | 2.8636 | |
| 6 | 3.6847 | 3.5892 | 3.4976 | 3.4098 | 3.3255 | 3.2446 | 3.1669 | |
| 7 | 4.0386 | 3.9224 | 3.8115 | 3.7057 | 3.6046 | 3.5079 | 3.4155 | |
| 8 | 4.3436 | 4.2072 | 4.0776 | 3.9544 | 3.8372 | 3.7256 | 3.6193 | |
| 9 | 4.6065 | 4.4506 | 4.3030 | 4.1633 | 4.0310 | 3.9054 | 3.7863 | |
| 10 | 4.8332 | 4.6586 | 4.4941 | 4.3389 | 4.1925 | 4.0541 | 3.9232 | |
| 11 | 5.0286 | 4.8364 | 4.6560 | 4.4865 | 4.3271 | 4.1769 | 4.0354 | |
| 12 | 5.1971 | 4.9884 | 4.7932 | 4.6105 | 4.4392 | 4.2784 | 4.1274 | |
| 13 | 5.3423 | 5.1183 | 4.9095 | 4.7147 | 4.5327 | 4.3624 | 4.2028 | |
| 14 | 5.4675 | 5.2293 | 5.0081 | 4.8023 | 4.6106 | 4.4317 | 4.2646 | |
| 15 | 5.5755 | 5.3242 | 5.0916 | 4.8759 | 4.6755 | 4.4890 | 4.3152 | |
| bgcolor=white>16 | 5.6685 | 5.4053 | 5.1624 | 4.9377 | 4.7296 | 4.5364 | 4.3567 | |
| 17 | 5.7487 | 5.4746 | 5.2223 | 4.9897 | 4.7746 | 4.5755 | 4.3908 | |
| 18 | 5.8178 | 5.5339 | 5.2732 | 5.0333 | 4.8122 | 4.6079 | 4.4187 | |
| 19 | 5.8775 | 5.5845 | 5.3162 | 5.0700 | 4.8435 | 4.6346 | 4.4415 | |
| 20 | 5.9288 | 5.6278 | 5.3527 | 5.1009 | 4.8696 | 4.6567 | 4.4603 | |
| 25 | 6.0971 | 5.7662 | 5.4669 | 5.1951 | 4.9476 | 4.7213 | 4.5139 | |
| ÇÎ | 6.1772 | 5.8294 | 5.5168 | 5.2347 | 4.9789 | 4.7463 | 4.5338 | |
| 35 | 6.2153 | 5.8582 | 5.5386 | 5.2512 | 4.9915 | 4.7559 | 4.5411 | |
| 40 | 6.2335 | 5.8713 | 5.5482 | 5.2582 | 4.9966 | 4.7596 | 4.5439 | |
| 45 | 6.2421 | 5.8773 | 5.5523 | 5.2611 | 4.9986 | 4.7610 | 4.5449 | |
| 50 | 6.2463 | 5.8801 | 5.5541 | 5.2623 | 4.9995 | 4.7616 | 4.5452 |
| 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| 0.8130 1.4740 2.0114 2.4483 2.8035 3.0923 3.3270 3.5179 3.6731 3.7993 3.9018 3.9852 4.0530 4.1082 4.1530 4.1894 4.2190 4.2431 4.2627 4.2786 4.3232 4.3391 4.3447 4.3467 4.3474 4.3477 | 0.8065 1.4568 1.9813 2.4043 2.7454 3.0205 3.2423 3.4212 3.5655 3.6819 3.7757 3.8514 3.9124 3.9616 4.0013 4.0333 4.0591 4.0799 4.0967 4.1103 4.1474 4.1601 4.1644 4.1659 4.1664 4.1666 | 0.8000 1.4400 1.9520 2.3616 2.6893 2.9514 3.1611 3.3289 3.4631 3.5705 3.6564 3.7251 3.7801 3.8241 3.8593 3.8874 3.9099 3.9279 3.9424 3.9539 3.9849 3.9950 3.9984 3.9995 3.9998 3.9999 | 0.7937 1.4235 1.9234 2.3202 2.6351 2.8850 3.0833 3.2407 3.3657 3.4648 3.5435 3.6059 3.6555 3.6949 3.7261 3.7509 3.7705 3.7861 3.7985 3.8083 3.8342 3.8424 3.8450 3.8458 3.8460 3.8461 | 0.7874 1.4074 1.8956 2.2800 2.5827 2.8210 3.0087 3.1564 3.2728 3.3644 3.4365 3.4933 3.5381 3.5733 3.6010 3.6228 3.6400 3.6536 3.6642 3.6726 3.6943 3.7009 3.7028 3.7034 3.7036 3.7037 | 0.7812 1.3916 1.8684 2.2410 2.5320 2.7594 2.9370 3.0758 3.1842 3.2689 3.3351 3.3868 3.4272 3.4587 3.4834 3.5026 3.5177 3.5294 3.5386 3.5458 3.5640 3.5693 3.5708 3.5712 3.5714 3.5714 | 0.7752 1.3761 1.8420 2.2031 2.4830 2.7000 2.8682 2.9986 3.0997 3.1781 3.2388 3.2859 3.3224 3.3507 3.3726 3.3896 3.4028 3.4130 3.4210 3.4271 3.4423 3.4466 3.4478 3.4481 3.4482 3.4483 | 0.7692 1.3609 1.8161 2.1662 2.4356 2.6427 2.8021 2.9247 3.0190 3.0915 3.1473 3.1903 3.2233 3.2487 3.2682 3.2832 3.2948 3.3037 3.3105 3.3158 3.3286 3.3321 3.3330 3.3332 3.3333 3.3333 |
330 PART 4 VALUING BONDS AND MONEY MARKET INSTRUMENTS