Supplement to the Fourth, Fifth, and Sixth Editions of the Encyclopædia Britannica/Annuities/Tables
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TABLE I.
Showing the present Value of One Pound to be received at the End of any Number of Years not exceeding 50.
(See No. 9—12 of the preceding Article.)
| Years | 2 per Cent. |
2½ per Cent. |
3 per Cent. |
4 per Cent. |
5 per Cent. |
6 per Cent. |
7 per Cent. |
8 per Cent. |
9 per Cent. |
Years |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | ·980392 | ·975610 | ·970874 | ·961538 | ·952381 | ·943396 | ·934579 | ·925926 | ·917431 | 1 |
| 2 | ·961169 | ·951814 | ·942596 | ·924556 | ·907029 | ·889996 | ·873439 | ·857339 | ·841680 | 2 |
| 3 | ·942322 | ·928599 | ·915142 | ·888996 | ·863838 | ·839619 | ·816298 | ·793832 | ·772183 | 3 |
| 4 | ·923845 | ·905951 | ·888487 | ·854804 | ·822702 | ·792094 | ·762895 | ·735030 | ·708425 | 4 |
| 5 | ·905731 | ·883854 | ·862609 | ·821927 | ·783526 | ·747258 | ·712986 | ·680583 | ·649931 | 5 |
| 6 | ·887971 | ·862297 | ·837484 | ·790315 | ·746215 | ·704961 | ·666342 | ·630170 | ·596267 | 6 |
| 7 | ·870560 | ·841265 | ·813092 | ·759918 | ·710681 | ·665057 | ·622750 | ·583490 | ·547034 | 7 |
| 8 | ·853490 | ·820747 | ·789409 | ·730690 | ·676839 | ·627412 | ·582009 | ·540269 | ·501866 | 8 |
| 9 | ·836755 | ·800728 | ·766417 | ·702587 | ·644609 | ·591898 | ·543934 | ·500249 | ·460428 | 9 |
| 10 | ·820348 | ·781198 | ·744094 | ·675564 | ·613913 | ·558395 | ·508349 | ·463193 | ·422411 | 10 |
| 11 | ·804263 | ·762145 | ·722421 | ·649581 | ·584679 | ·526788 | ·475093 | ·428883 | ·387533 | 11 |
| 12 | ·788493 | ·743556 | ·701380 | ·624597 | ·556837 | ·496969 | ·444012 | ·397114 | ·355535 | 12 |
| 13 | ·773033 | ·725420 | ·680951 | ·600574 | ·530321 | ·468839 | ·414964 | ·367698 | ·326179 | 13 |
| 14 | ·757875 | ·707727 | ·661118 | ·577475 | ·505068 | ·442301 | ·387817 | ·340461 | ·299246 | 14 |
| 15 | ·743015 | ·690466 | ·641862 | ·555265 | ·481017 | ·417265 | ·362446 | ·315242 | ·274538 | 15 |
| 16 | ·728446 | ·673625 | ·623167 | ·533908 | ·458112 | ·393646 | ·338735 | ·291890 | ·251870 | 16 |
| 17 | ·714163 | ·657195 | ·605016 | ·513373 | ·436297 | ·371364 | ·316574 | ·270269 | ·231073 | 17 |
| 18 | ·700159 | ·641166 | ·587395 | ·493628 | ·415521 | ·350344 | ·295864 | ·250249 | ·211994 | 18 |
| 19 | ·686431 | ·625528 | ·570286 | ·474642 | ·395734 | ·330513 | ·276508 | ·231712 | ·194490 | 19 |
| 20 | ·672971 | ·610271 | ·553676 | ·456387 | ·376889 | ·311805 | ·258419 | ·214548 | ·178431 | 20 |
| 21 | ·659776 | ·595386 | ·537549 | ·438834 | ·358942 | ·294155 | ·241513 | ·198656 | ·163698 | 21 |
| 22 | ·646839 | ·580865 | ·521893 | ·421955 | ·341850 | ·277505 | ·225713 | ·183941 | ·150182 | 22 |
| 23 | ·634156 | ·566697 | ·506692 | ·405726 | ·325571 | ·261797 | ·210947 | ·170315 | ·137781 | 23 |
| 24 | ·621721 | ·552875 | ·491934 | ·390121 | ·310068 | ·246979 | ·197147 | ·157699 | ·126405 | 24 |
| 25 | ·609531 | ·539391 | ·477606 | ·375117 | ·295303 | ·232999 | ·184249 | ·146018 | ·115968 | 25 |
| 26 | ·597579 | ·526235 | ·463695 | ·360689 | ·281241 | ·219810 | ·172195 | ·135202 | ·106393 | 26 |
| 27 | ·585862 | ·513400 | ·450189 | ·346817 | ·267848 | ·207368 | ·160930 | ·125187 | ·097608 | 27 |
| 28 | ·574375 | ·500878 | ·437077 | ·333477 | ·255094 | ·195630 | ·150402 | ·115914 | ·089548 | 28 |
| 29 | ·563112 | ·488661 | ·424346 | ·320651 | ·242946 | ·184557 | .140563 | ·107328 | ·082155 | 29 |
| 30 | ·552071 | ·476743 | ·411987 | ·308319 | ·231377 | ·174110 | ·131367 | ·099377 | ·075371 | 30 |
| 31 | ·541246 | ·465115 | ·399987 | ·296460 | ·220359 | ·164255 | ·122773 | ·092016 | ·069148 | 31 |
| 32 | ·530633 | ·453771 | ·388337 | ·285058 | ·209866 | ·154957 | ·114741 | ·085200 | ·063438 | 32 |
| 33 | ·520229 | ·442703 | ·377026 | ·274094 | ·199873 | ·146186 | ·107235 | ·078889 | ·058200 | 33 |
| 34 | ·510028 | ·431905 | ·366045 | ·263552 | ·190355 | ·137912 | ·100219 | ·073045 | ·053395 | 34 |
| 35 | ·500028 | ·421371 | ·355383 | ·253415 | ·181290 | ·130105 | ·093663 | ·067635 | ·048986 | 35 |
| 36 | ·490223 | ·411094 | ·345032 | ·243669 | ·172657 | ·122741 | ·087535 | ·062625 | ·044941 | 36 |
| 37 | ·480611 | ·401067 | ·334983 | ·234297 | ·164436 | ·115793 | ·081809 | ·057986 | ·041231 | 37 |
| 38 | ·471187 | ·391285 | ·325226 | ·225285 | ·156605 | ·109239 | ·076457 | ·053690 | ·037826 | 38 |
| 39 | ·461948 | ·381741 | ·315754 | ·216621 | ·149148 | ·103056 | ·071455 | ·049713 | ·034703 | 39 |
| 40 | ·452890 | ·372431 | ·306557 | ·208289 | ·142046 | ·097222 | ·066780 | ·046031 | ·031838 | 40 |
| 41 | ·444010 | ·363347 | ·297628 | ·200278 | ·135282 | ·091719 | ·062412 | ·042621 | ·029209 | 41 |
| 42 | ·435304 | ·354485 | ·288959 | ·192575 | ·128840 | ·086527 | ·058329 | ·039464 | ·026797 | 42 |
| 43 | ·426769 | ·345839 | ·280543 | ·185168 | ·122704 | ·081630 | ·054513 | ·036541 | ·024584 | 43 |
| 44 | ·418401 | ·337404 | ·272372 | ·178046 | ·116861 | ·077009 | ·050946 | ·033834 | ·022555 | 44 |
| 45 | ·410197 | ·329174 | ·264439 | ·171198 | ·111297 | ·072650 | ·047613 | ·031328 | ·020692 | 45 |
| 46 | ·402154 | ·321146 | ·256737 | ·164614 | ·105997 | ·068538 | ·044499 | ·029007 | ·018984 | 46 |
| 47 | ·394268 | ·313313 | ·249259 | ·158283 | ·100949 | ·064658 | ·041587 | ·026859 | ·017416 | 47 |
| 48 | ·386538 | ·305671 | ·241999 | ·152195 | ·096142 | ·060998 | ·038867 | ·024869 | ·015978 | 48 |
| 49 | ·378958 | ·298216 | ·234950 | ·146341 | ·091564 | ·057546 | ·036324 | ·023027 | ·014659 | 49 |
| 50 | ·371528 | ·290942 | ·228107 | ·140713 | ·087204 | ·054288 | ·033948 | ·021321 | ·013449 | 50 |
TABLE II.
Showing the present Value of an Annuity of One Pound for any Number of Years not exceeding 50.
(No. 9—12.)
| Years | 2 per Cent. |
2½ per Cent. |
3 per Cent. |
4 per Cent. |
5 per Cent. |
6 per Cent. |
7 per Cent. |
8 per Cent. |
9 per Cent. |
Years |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | ·9804 | 9·756 | ·9709 | ·9615 | ·9524 | ·9434 | ·9346 | ·9259 | ·9174 | 1 |
| 2 | 1·9416 | 1·9274 | 1·9135 | 1·8861 | 1·8594 | 1·8334 | 1·8080 | 1·7833 | 1·7591 | 2 |
| 3 | 2·8839 | 2·8560 | 2·8286 | 2·7751 | 2·7232 | 2·6730 | 2·6243 | 2·5771 | 2·5313 | 3 |
| 4 | 3·8077 | 3·7620 | 3·7171 | 3·6299 | 3·5460 | 3·4651 | 3·3872 | 3·3121 | 3·2397 | 4 |
| 5 | 4·7135 | 4·6458 | 4·5797 | 4·4518 | 4·3295 | 4·2124 | 4·1002 | 3·9927 | 3·8897 | 5 |
| 6 | 5·6014 | 5·5081 | 5·4172 | 5·2421 | 5·0757 | 4·9173 | 4·7665 | 4·6229 | 4·4859 | 6 |
| 7 | 6·4720 | 6·3494 | 6·2303 | 6·0021 | 5·7864 | 5·5824 | 5·3893 | 5·2064 | 5·0330 | 7 |
| 8 | 7·3255 | 7·1701 | 7·0197 | 6·7327 | 6·4632 | 6·2098 | 5·9713 | 5·7466 | 5·5348 | 8 |
| 9 | 8·1622 | 7·9709 | 7·7861 | 7·4353 | 7·1078 | 6·8017 | 6·5152 | 6·2469 | 5·9952 | 9 |
| 10 | 8·9826 | 8·7521 | 8·5302 | 8·1109 | 7·7217 | 7·3601 | 7·0236 | 6·7101 | 6·4177 | 10 |
| 11 | 9·7868 | 9·5142 | 9·2526 | 8·7605 | 8·3064 | 7·8869 | 7·4987 | 7·1390 | 6·8052 | 11 |
| 12 | 10·5753 | 10·2578 | 9·9540 | 9·3851 | 8·8633 | 8·3838 | 7·9427 | 7·5361 | 7·1607 | 12 |
| 13 | 11·3484 | 10·9832 | 10·6350 | 9·9856 | 9·3936 | 8·8527 | 8·3577 | 7·9038 | 7·4869 | 13 |
| 14 | 12·1062 | 11·6909 | 11·2961 | 10·5631 | 9·8986 | 9·2950 | 8·7455 | 8·2442 | 7·7862 | 14 |
| 15 | 12·8493 | 12·3814 | 11·9379 | 11·1184 | 10·3797 | 9·7122 | 9·1079 | 8·5595 | 8·0607 | 15 |
| 16 | 13·5777 | 13·0550 | 12·5611 | 11·6523 | 10·8378 | 10·1059 | 9·4466 | 8·8514 | 8·3126 | 16 |
| 17 | 14·2919 | 13·7122 | 13·1661 | 12·1657 | 11·2741 | 10·4773 | 9·7632 | 9·1216 | 8·5436 | 17 |
| 18 | 14.9920 | 14·3534 | 13·7535 | 12·6593 | 11·6896 | 10·8276 | 10·0591 | 9·3719 | 8·7556 | 18 |
| 19 | 15·6785 | 14·9789 | 14·3238 | 13·1339 | 12·0853 | 11·1581 | 10·3356 | 9·6036 | 8·9501 | 19 |
| 20 | 16·3514 | 15·5892 | 14·8775 | 13·5903 | 12·4622 | 11·4699 | 10·5940 | 9·8181 | 9·1285 | 20 |
| 21 | 17·0112 | 16·1845 | 15·4150 | 14·0292 | 12·8212 | 11·7641 | 10·8355 | 10·0168 | 9·2922 | 21 |
| 22 | 17·6580 | 16·7654 | 15·9369 | 14·4511 | 13·1630 | 12·0416 | 11·0612 | 10·2007 | 9·4424 | 22 |
| 23 | 18·2922 | 17·3321 | 16·4436 | 14·8568 | 13·4886 | 12·3034 | 11·2722 | 10·3711 | 9·5802 | 23 |
| 24 | 18·9139 | 17·8850 | 16·9355 | 15·2470 | 13·7986 | 12·5504 | 11·4693 | 10·5288 | 9·7066 | 24 |
| 25 | 19·5235 | 18·4244 | 17·4131 | 15·6221 | 14·0939 | 12·7834 | 11·6536 | 10·6748 | 9·8226 | 25 |
| 26 | 20·1210 | 18·9506 | 17·8768 | 15·9828 | 14·3752 | 13·0032 | 11·8258 | 10·8100 | 9·9290 | 26 |
| 27 | 20·7069 | 19·4640 | 18·3270 | 16·3296 | 14·6430 | 13·2105 | 11·9867 | 10·9352 | 10·0266 | 27 |
| 28 | 21·2813 | 19·9649 | 18·7641 | 16·6631 | 14·8981 | 13·4062 | 12·1371 | 11·0511 | 10·1161 | 28 |
| 29 | 21·8444 | 20·4535 | 19·1885 | 16·9837 | 15·1411 | 13·5907 | 12·2777 | 11·1584 | 10·1983 | 29 |
| 30 | 22·3965 | 20·9303 | 19·6004 | 17·2920 | 15·3725 | 13·7648 | 12·4090 | 11·2578 | 10·2737 | 30 |
| 31 | 22·9377 | 21·3954 | 20·0004 | 17·5885 | 15·5928 | 13·9291 | 12·5318 | 11·3498 | 10·3428 | 31 |
| 32 | 23·4683 | 21·8492 | 20·3888 | 17·8736 | 15·8027 | 14·0840 | 12·6466 | 11·4350 | 10·4062 | 32 |
| 33 | 23·9886 | 22·2919 | 20·7658 | 18·1476 | 16·0025 | 14·2302 | 12·7538 | 11·5139 | 10·4644 | 33 |
| 34 | 24·4986 | 22·7238 | 21·1318 | 18·4112 | 16·1929 | 14·3681 | 12·8540 | 11·5869 | 10·5178 | 34 |
| 35 | 24·9986 | 23·1452 | 21·4872 | 18·6646 | 16·3742 | 14·4982 | 12·9477 | 11·6546 | 10·5668 | 35 |
| 36 | 25·4888 | 23·5563 | 21·8323 | 18·9083 | 16·5469 | 14·6210 | 13·0352 | 11·7172 | 10·6118 | 36 |
| 37 | 25·9695 | 23·9573 | 22·1672 | 19·1426 | 16·7113 | 14·7368 | 13·1170 | 11·7752 | 10·6530 | 37 |
| 38 | 26·4406 | 24·3486 | 22·4925 | 19·3679 | 16·8679 | 14·8460 | 13·1935 | 11·8289 | 10·6908 | 38 |
| 39 | 26·9026 | 24·7303 | 22·8082 | 19·5845 | 17·0170 | 14·9491 | 13·2649 | 11·8786 | 10·7255 | 39 |
| 40 | 27·3555 | 25·1028 | 23·1148 | 19·7928 | 17·1591 | 15·0463 | 13·3317 | 11·9246 | 10·7574 | 40 |
| 41 | 27·7995 | 25·4661 | 23·4124 | 19·9931 | 17·2944 | 15·1380 | 13·3941 | 11·9672 | 10·7866 | 41 |
| 42 | 28·2348 | 25·8206 | 23·7014 | 20·1856 | 17·4232 | 15·2245 | 13·4524 | 12·0067 | 10·8134 | 42 |
| 43 | 28·6616 | 26·1664 | 23·9819 | 20·3708 | 17·5459 | 15·3062 | 13·5070 | 12·0432 | 10·8380 | 43 |
| 44 | 29·0800 | 26·5038 | 24·2543 | 20·5488 | 17·6628 | 15·3832 | 13·5579 | 12·0771 | 10·8605 | 44 |
| 45 | 29·4902 | 26·8330 | 24·5187 | 20·7200 | 17·7741 | 15·4558 | 13·6055 | 12·1084 | 10·8812 | 45 |
| 46 | 29·8923 | 27·1542 | 24·7754 | 20·8847 | 17·8801 | 15·5244 | 13·6500 | 12·1374 | 10·9002 | 46 |
| 47 | 30·2866 | 27·4675 | 25·0247 | 21·0429 | 17·9810 | 15·5890 | 13·6916 | 12·1643 | 10·9176 | 47 |
| 48 | 30·6731 | 27·7732 | 25·2667 | 21·1951 | 18·0772 | 15·6500 | 13·7305 | 12·1891 | 10·9336 | 48 |
| 49 | 31·0521 | 28·0714 | 25·5017 | 21·3415 | 18·1687 | 15·7076 | 13·7668 | 12·2122 | 10·9482 | 49 |
| 50 | 31·4236 | 28·3623 | 25·7298 | 21·4822 | 18·2559 | 15·7619 | 13·8007 | 12·2335 | 10·9617 | 50 |
| Perp | 50·0000 | 40·0000 | 33.3333 | 25·0000 | 20·0000 | 16·6667 | 14·2857 | 12·5000 | 11·1111 | Perp. |
TABLE III.
Showing the Sum to which One Pound will increase when improved at Compound Interest during any Number of Years not exceeding 50.
(No. 9—12.)
| Years | 2 per Cent. |
2½ per Cent. |
3 per Cent. |
4 per Cent. |
5 per Cent. |
6 per Cent. |
7 per Cent. |
8 per Cent. |
Years |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1·02000 | 1·02500 | 1·030000 | 1·040000 | 1·050000 | 1·060000 | 1·070000 | 1·080000 | 1 |
| 2 | 1·04040 | 1·05063 | 1·060900 | 1·081600 | 1·102500 | 1·123600 | 1·144900 | 1·166400 | 2 |
| 3 | 1·06121 | 1·07689 | 1·092727 | 1·124864 | 1·157625 | 1·191016 | 1·225043 | 1·259712 | 3 |
| 4 | 1·08243 | 1·10381 | 1·125509 | 1·169859 | 1·215506 | 1·262477 | 1·310796 | 1·360489 | 4 |
| 5 | 1·10408 | 1·13141 | 1·159274 | 1·216653 | 1·276282 | 1·338226 | 1·402552 | 1·469328 | 5 |
| 6 | 1·12616 | 1·15969 | 1·194052 | 1·265319 | 1·340096 | 1·418519 | 1·500730 | 1·586874 | 6 |
| 7 | 1·14869 | 1·18869 | 1·229874 | 1·315932 | 1·407100 | 1·503630 | 1·605781 | 1·713824 | 7 |
| 8 | 1·17166 | 1·21840 | 1·266770 | 1·368569 | 1·477455 | 1·593848 | 1·718186 | 1·850930 | 8 |
| 9 | 1·19509 | 1·24886 | 1·304773 | 1·423312 | 1·551328 | 1·689479 | 1·838459 | 1·999005 | 9 |
| 10 | 1·21899 | 1·28008 | 1·343916 | 1·480244 | 1·628895 | 1·790848 | 1·967151 | 2·158925 | 10 |
| 11 | 1·24337 | 1·31209 | 1·384234 | 1·539454 | 1·710339 | 1·898299 | 2·104852 | 2·331639 | 11 |
| 12 | 1·26824 | 1·34489 | 1·425761 | 1·601032 | 1·795856 | 2·012196 | 2·252192 | 2·518170 | 12 |
| 13 | 1·29361 | 1·37851 | 1·468534 | 1·665074 | 1·885649 | 2·132928 | 2·409845 | 2·719624 | 13 |
| 14 | 1·31948 | 1·41297 | 1·512590 | 1·731676 | 1·979932 | 2·260904 | 2·578534 | 2·937194 | 14 |
| 15 | 1·34587 | 1·44830 | 1·557967 | 1·800944 | 2·078928 | 2·396558 | 2·759032 | 3·172169 | 15 |
| 16 | 1·37279 | 1·48451 | 1·604706 | 1·872981 | 2·182875 | 2·540352 | 2·952164 | 3·425943 | 16 |
| 17 | 1·40024 | 1·52162 | 1·652848 | 1·947901 | 2·292018 | 2·692773 | 3·158815 | 3·700018 | 17 |
| 18 | 1·42825 | 1·55966 | 1·702433 | 2·025817 | 2·406619 | 2·854339 | 3·379932 | 3·996020 | 18 |
| 19 | 1·45681 | 1·59865 | 1·753506 | 2·106849 | 2·526950 | 3·025600 | 3·616528 | 4·315701 | 19 |
| 20 | 1·48595 | 1·63862 | 1·806111 | 2·191123 | 2·653298 | 3·207135 | 3·869684 | 4·660957 | 20 |
| 21 | 1·51567 | 1·67958 | 1·860295 | 2·278768 | 2·785963 | 3·399564 | 4·140562 | 5·033834 | 21 |
| 22 | 1·54598 | 1·72157 | 1·916103 | 2·369919 | 2·925261 | 3·603537 | 4·430402 | 5·436540 | 22 |
| 23 | 1·57690 | 1·76461 | 1·973587 | 2·464716 | 3·071524 | 3·819750 | 4·740530 | 5·871464 | 23 |
| 24 | 1·60844 | 1·80873 | 2·032794 | 2·563304 | 3·225100 | 4·048935 | 5·072367 | 6·341181 | 24 |
| 25 | 1·64061 | 1·85394 | 2·093778 | 2·665836 | 3·386355 | 4·291871 | 5·427433 | 6·848475 | 25 |
| 26 | 1·67342 | 1·90029 | 2·156591 | 2·772470 | 3·555673 | 4·549383 | 5·807353 | 7·396353 | 26 |
| 27 | 1·70689 | 1·94780 | 2·221289 | 2·883369 | 3·733456 | 4·822346 | 6·213868 | 7·988061 | 27 |
| 28 | 1·74102 | 1·99650 | 2·287928 | 2·998703 | 3·920129 | 5·111687 | 6·648838 | 8·627106 | 28 |
| 29 | 1·77584 | 2·04641 | 2·356566 | 3·118651 | 4·116136 | 5·418388 | 7·114257 | 9·317275 | 29 |
| 30 | 1·81136 | 2·09757 | 2·427262 | 3·243398 | 4·321942 | 5·743491 | 7·612255 | 10·062657 | 30 |
| 31 | 1·84759 | 2·15001 | 2·500080 | 3·373133 | 4·538039 | 6·088101 | 8·145113 | 10·867669 | 31 |
| 32 | 1·88454 | 2·20376 | 2·575083 | 3·508059 | 4·764941 | 6·453387 | 8·715271 | 11·737083 | 32 |
| 33 | 1·92223 | 2·25885 | 2·652335 | 3·648381 | 5·003189 | 6·840590 | 9·325340 | 12·676050 | 33 |
| 34 | 1·96068 | 2·31532 | 2·731905 | 3·794316 | 5·253348 | 7·251025 | 9·978114 | 13·690134 | 34 |
| 35 | 1·99989 | 2·37321 | 2·813862 | 3·946089 | 5·516015 | 7·686087 | 10·676581 | 14·785344 | 35 |
| 36 | 2·03989 | 2·43254 | 2·898278 | 4·103933 | 5·791816 | 8·147252 | 11·423942 | 15·968172 | 36 |
| 37 | 2·08069 | 2·49335 | 2·985227 | 4·268090 | 6·081407 | 8·636087 | 12·223618 | 17·245626 | 37 |
| 38 | 2·12230 | 2·55568 | 3·074783 | 4·438813 | 6·385477 | 9·154252 | 13·079271 | 18·625276 | 38 |
| 39 | 2·16474 | 2·61957 | 3·167027 | 4·616366 | 6·704751 | 9·703507 | 13·994820 | 20·115298 | 39 |
| 40 | 2·20804 | 2·68506 | 3·262038 | 4·801021 | 7·039989 | 10·285718 | 14·974458 | 21·724522 | 40 |
| 41 | 2·25220 | 2·75219 | 3·359899 | 4·993061 | 7·391988 | 10·902861 | 16·022670 | 23·462483 | 41 |
| 42 | 2·29724 | 2·82100 | 3·460696 | 5·192784 | 7·761588 | 11·557033 | 17·144257 | 25·339482 | 42 |
| 43 | 2·34319 | 2·89152 | 3·564517 | 5·400495 | 8·149667 | 12·250455 | 18·344355 | 27·366640 | 43 |
| 44 | 2·39005 | 2·96381 | 3·671452 | 5·616515 | 8·557150 | 12·985482 | 19·628460 | 29·555972 | 44 |
| 45 | 2·43785 | 3·03790 | 3·781596 | 5·841176 | 8·985008 | 13·764611 | 21·002452 | 31·920449 | 45 |
| 46 | 2·48661 | 3·11385 | 3·895044 | 6·074823 | 9·434258 | 14·590487 | 22·472623 | 34·474085 | 46 |
| 47 | 2·53634 | 3·19170 | 4·011895 | 6·317816 | 9·905971 | 15·465917 | 24·045707 | 37·232012 | 47 |
| 48 | 2·58707 | 3·27149 | 4·132252 | 6·570528 | 10·401270 | 16·393872 | 25·728907 | 40·210573 | 48 |
| 49 | 2·63881 | 3·35328 | 4·256219 | 6·833349 | 10·921333 | 17·377504 | 27·529930 | 43·427419 | 49 |
| 50 | 2·69159 | 3·43711 | 4·383906 | 7·106683 | 11·467400 | 18·420154 | 29·457025 | 46·901613 | 50 |
TABLE IV.
Showing the Amount to which One Pound per Annum will increase at Compound Interest in any Number of Years not exceeding 50.
(No. 9—12.)
| Years | 2 per Cent. |
2½ per Cent. |
3 per Cent. |
4 per Cent. |
5 per Cent. |
6 per Cent. |
7 per Cent. |
Years |
|---|---|---|---|---|---|---|---|---|
| 1 | 1·0000 | 1·0000 | 1·000000 | 1·000000 | 1·000000 | 1·000000 | 1·000000 | 1 |
| 2 | 2·0200 | 2·0250 | 2·030000 | 2·040000 | 2·050000 | 2·060000 | 2·070000 | 2 |
| 3 | 3·0604 | 3·0756 | 3·090900 | 3·121600 | 3·152500 | 3·183600 | 3·214900 | 3 |
| 4 | 4·1216 | 4·1525 | 4·183627 | 4·246464 | 4·310125 | 4·374616 | 4·439943 | 4 |
| 5 | 5·2040 | 5·2563 | 5·309136 | 5·416323 | 5·525631 | 5·637093 | 5·750739 | 5 |
| 6 | 6·3081 | 6·3877 | 6·468410 | 6·632975 | 6·801913 | 6·975319 | 7·153291 | 6 |
| 7 | 7·4343 | 7·5474 | 7·662462 | 7·898294 | 8·142008 | 8·393838 | 8·654021 | 7 |
| 8 | 8·5830 | 8·7361 | 8·892336 | 9·214226 | 9·549109 | 9·897468 | 10·259803 | 8 |
| 9 | 9·7546 | 9·9545 | 10·159106 | 10·582795 | 11·026564 | 11·491316 | 11·977989 | 9 |
| 10 | 10·9497 | 11·2034 | 11·463879 | 12·006107 | 12·577893 | 13·180795 | 13·816448 | 10 |
| 11 | 12·1687 | 12·4835 | 12·807796 | 13·486351 | 14·206787 | 14·971643 | 15·783599 | 11 |
| 12 | 13·4121 | 13·7956 | 14·192030 | 15·025805 | 15·917127 | 16·869941 | 17·888451 | 12 |
| 13 | 14·6803 | 15·1404 | 15·617790 | 16·626838 | 17·712983 | 18·882138 | 20·140643 | 13 |
| 14 | 15·9739 | 16·5190 | 17·086324 | 18·291911 | 19·598632 | 21·015066 | 22·550488 | 14 |
| 15 | 17·2934 | 17·9319 | 18·598914 | 20·023588 | 21·578564 | 23·275970 | 25·129022 | 15 |
| 16 | 18·6393 | 19·3802 | 20·156881 | 21·824531 | 23·657492 | 25·672528 | 27·888054 | 16 |
| 17 | 20·0121 | 20·8647 | 21·761588 | 23·697512 | 25·840366 | 28·212880 | 30·840217 | 17 |
| 18 | 21·4123 | 22·3863 | 23·414435 | 25·645413 | 28·132385 | 30·905653 | 33·999033 | 18 |
| 19 | 22·8406 | 23·9460 | 25·116868 | 27·671229 | 30·539004 | 33·759992 | 37·378965 | 19 |
| 20 | 24·2974 | 25·5447 | 26·870374 | 29·778079 | 33·065954 | 36·785591 | 40·995492 | 20 |
| 21 | 25·7833 | 27·1833 | 28·676486 | 31·969202 | 35·719252 | 39·992727 | 44·865177 | 21 |
| 22 | 27·2990 | 28·8629 | 30·536780 | 34·247970 | 38·505214 | 43·392290 | 49·005739 | 22 |
| 23 | 28·8450 | 30·5844 | 32·452884 | 36·617889 | 41·430475 | 46·995828 | 53·436141 | 23 |
| 24 | 30·4219 | 32·3490 | 34·426470 | 39·082604 | 44·501999 | 50·815577 | 58·176671 | 24 |
| 25 | 32·0303 | 34·1578 | 36·459264 | 41·645908 | 47·727099 | 54·864512 | 63·249038 | 25 |
| 26 | 33·6709 | 36·0117 | 38·553042 | 44·311745 | 51·113454 | 59·156383 | 68·676470 | 26 |
| 27 | 35·3443 | 37·9120 | 40·709634 | 47·084214 | 54·669126 | 63·705766 | 74·483823 | 27 |
| 28 | 37·0512 | 39·8598 | 42·930923 | 49·967583 | 58·402583 | 68·528112 | 80·697691 | 28 |
| 29 | 38·7922 | 41·8563 | 45·218850 | 52·966286 | 62·322712 | 73·639798 | 87·346529 | 29 |
| 30 | 40·5681 | 43·9027 | 47·575416 | 56·084938 | 66·438848 | 79·058186 | 94·460786 | 30 |
| 31 | 42·3794 | 46·0003 | 50·002678 | 59·328335 | 70·760790 | 84·801677 | 102·073041 | 31 |
| 32 | 44·2270 | 48·1503 | 52·502759 | 62·701469 | 75·298829 | 90·889778 | 110·218154 | 32 |
| 33 | 46·1116 | 50·3540 | 55·077841 | 66·209527 | 80·063771 | 97·343165 | 118·933425 | 33 |
| 34 | 48·0338 | 52·6129 | 57·730177 | 69·857909 | 85·066959 | 104·183755 | 128·258765 | 34 |
| 35 | 49·9945 | 54·9282 | 60·462082 | 73·652225 | 90·320307 | 111·434780 | 138·236878 | 35 |
| 36 | 51·9944 | 57·3014 | 63·275944 | 77·598314 | 95·836323 | 119·120867 | 148·913460 | 36 |
| 37 | 54·0343 | 59·7339 | 66·174223 | 81·702246 | 101·628139 | 127·268119 | 160·337402 | 37 |
| 38 | 56·1149 | 62·2273 | 69·159449 | 85·970336 | 107·709546 | 135·904206 | 172·561020 | 38 |
| 39 | 58·2372 | 64·7830 | 72·234233 | 90·409150 | 114·095023 | 145·058458 | 185·640292 | 39 |
| 40 | 60·4020 | 67·4026 | 75·401260 | 95·025516 | 120·799774 | 154·761966 | 199·635112 | 40 |
| 41 | 62·6100 | 70·0876 | 78·663298 | 99·826536 | 127·839763 | 165·047684 | 214·609570 | 41 |
| 42 | 64·8622 | 72·8398 | 82·023196 | 104·819598 | 135·231751 | 175·950545 | 230·632240 | 42 |
| 43 | 67·1595 | 75·6608 | 85·483892 | 110·012382 | 142·993339 | 187·507577 | 247·776496 | 43 |
| 44 | 69·5027 | 78·5523 | 89·048409 | 115·412877 | 151·143006 | 199·758032 | 266·120851 | 44 |
| 45 | 71·8927 | 81·5161 | 92·719861 | 121·029392 | 159·700156 | 212·743514 | 285·749311 | 45 |
| 46 | 74·3306 | 84·5540 | 96·501457 | 126·870568 | 168·685164 | 226·508125 | 306·751763 | 46 |
| 47 | 76·8172 | 87·6679 | 100·396501 | 132·945390 | 178·119422 | 241·098612 | 329·224386 | 47 |
| 48 | 79·3535 | 90·8596 | 104·408396 | 139·263206 | 188·025393 | 256·564529 | 353·270093 | 48 |
| 49 | 81·9406 | 94·1311 | 108·540648 | 145·833734 | 198·426663 | 272·958401 | 378·999000 | 49 |
| 50 | 84·5794 | 97·4843 | 112·796867 | 152·667084 | 209·347996 | 290·335905 | 406·528929 | 50 |
TABLE V.
Exhibiting the Law of Mortality at Carlisle. (No. 32.)
| Age. | Number who | Age. | Number who | Age. | Number who | |||
|---|---|---|---|---|---|---|---|---|
| complete that Age. | die in the next interval. | complete that | die in their next | complete that | die in their next | |||
| Year. | Year. | |||||||
| 0 | 10,000 | 533 | 32 | 5528 | 56 | 69 | 2525 | 124 |
| 1 Month | 9467 | 154 | 33 | 5472 | 55 | 70 | 2401 | 124 |
| 2 Months | 9313 | 87 | 34 | 5417 | 55 | 71 | 2277 | 134 |
| 3 | 9226 | 256 | 35 | 5362 | 55 | 72 | 2143 | 146 |
| 6 | 8970 | 255 | 36 | 5307 | 56 | 73 | 1997 | 156 |
| 9 | 8715 | 254 | 37 | 5251 | 57 | 74 | 1841 | 166 |
| 1 Year | 8461 | 682 | 38 | 5194 | 58 | 75 | 1675 | 160 |
| 2 Years | 7779 | 505 | 39 | 5136 | 61 | 76 | 1515 | 156 |
| 3 | 7274 | 276 | 40 | 5075 | 66 | 77 | 1359 | 146 |
| 4 | 6998 | 201 | 41 | 5009 | 69 | 78 | 1213 | 132 |
| 5 | 6797 | 121 | 42 | 4940 | 71 | 79 | 1081 | 128 |
| 6 | 6676 | 82 | 43 | 4869 | 71 | 80 | 953 | 116 |
| 7 | 6594 | 58 | 44 | 4798 | 71 | 81 | 837 | 112 |
| 8 | 6536 | 43 | 45 | 4727 | 70 | 82 | 725 | 102 |
| 9 | 6493 | 33 | 46 | 4657 | 69 | 83 | 623 | 94 |
| 10 | 6460 | 29 | 47 | 4588 | 67 | 84 | 529 | 84 |
| 11 | 6431 | 31 | 48 | 4521 | 63 | 85 | 445 | 78 |
| 12 | 6400 | 32 | 49 | 4458 | 61 | 86 | 367 | 71 |
| 13 | 6368 | 33 | 50 | 4397 | 59 | 87 | 296 | 64 |
| 14 | 6335 | 35 | 51 | 4338 | 62 | 88 | 232 | 51 |
| 15 | 6300 | 39 | 52 | 4276 | 65 | 89 | 181 | 39 |
| 16 | 6261 | 42 | 53 | 4211 | 68 | 90 | 142 | 37 |
| 17 | 6219 | 43 | 54 | 4143 | 70 | 91 | 105 | 30 |
| 18 | 6176 | 43 | 55 | 4073 | 73 | 92 | 75 | 21 |
| 19 | 6133 | 43 | 56 | 4000 | 76 | 93 | 54 | 14 |
| 20 | 6090 | 43 | 57 | 3924 | 82 | 94 | 40 | 10 |
| 21 | 6047 | 42 | 58 | 3842 | 93 | 95 | 30 | 7 |
| 22 | 6005 | 42 | 59 | 3749 | 106 | 96 | 23 | 5 |
| 23 | 5963 | 42 | 60 | 3643 | 122 | 97 | 18 | 4 |
| 24 | 5921 | 42 | 61 | 3521 | 126 | 98 | 14 | 3 |
| 25 | 5879 | 43 | 62 | 3395 | 127 | 99 | 11 | 2 |
| 26 | 5836 | 43 | 63 | 3268 | 125 | 100 | 9 | 2 |
| 27 | 5793 | 45 | 64 | 3143 | 125 | 101 | 7 | 2 |
| 28 | 5748 | 50 | 65 | 3018 | 124 | 102 | 5 | 2 |
| 29 | 5698 | 56 | 66 | 2894 | 123 | 103 | 3 | 2 |
| 30 | 5642 | 57 | 67 | 2771 | 123 | 104 | 1 | 1 |
| 31 | 5585 | 57 | 68 | 2648 | 123 | |||
TABLE VI.
Showing the Value of an Annuity on a Single Life at every Age, according to the Carlisle Table of Mortality, when the rate of Interest is Five per Cent. (No. 65.)
| Age. | Value. | Age. | Value. | Age. | Value. | Age. | Value. | Age. | Value. | Age. | Value. |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 12·083 | 18 | 15·987 | 35 | 14·127 | 52 | 11·154 | 69 | 6·643 | 86 | 2·830 |
| 1 | 13·995 | 19 | 15·904 | 36 | 13·987 | 53 | 10·892 | 70 | 6·336 | 87 | 2·685 |
| 2 | 14·983 | 20 | 15·817 | 37 | 13·843 | 54 | 10·624 | 71 | 6·015 | 88 | 2·597 |
| 3 | 15·824 | 21 | 15·726 | 38 | 13·695 | 55 | 10·347 | 72 | 5·711 | 89 | 2·495 |
| 4 | 16·271 | 22 | 15·628 | 39 | 13·542 | 56 | 10.063 | 73 | 5·435 | 90 | 2·339 |
| 5 | 16·590 | 23 | 15·525 | 40 | 13·390 | 57 | 9·771 | 74 | 5·190 | 91 | 2·321 |
| 6 | 16·735 | 24 | 15·417 | 41 | 13·245 | 58 | 9·478 | 75 | 4·989 | 92 | 2·412 |
| 7 | 16·790 | 25 | 15·303 | 42 | 13·101 | 59 | 9·199 | 76 | 4·792 | 93 | 2·518 |
| 8 | 16·786 | 26 | 15·187 | 43 | 12·957 | 60 | 8·940 | 77 | 4·609 | 94 | 2·569 |
| 9 | 16·742 | 27 | 15·065 | 44 | 12·806 | 61 | 8·712 | 78 | 4·422 | 95 | 2·596 |
| 10 | 16·669 | 28 | 14·942 | 45 | 12·648 | 62 | 8·487 | 79 | 4·210 | 96 | 2·555 |
| 11 | 16·581 | 29 | 14·827 | 46 | 12·480 | 63 | 8·258 | 80 | 4·015 | 97 | 2·428 |
| 12 | 16·494 | 30 | 14·723 | 47 | 12·301 | 64 | 8·016 | 81 | 3·799 | 98 | 2·278 |
| 13 | 16·406 | 31 | 14·617 | 48 | 12·107 | 65 | 7·765 | 82 | 3·606 | 99 | 2·045 |
| 14 | 16·316 | 32 | 14·506 | 49 | 11·892 | 66 | 7·503 | 83 | 3·406 | 100 | 1·624 |
| 15 | 16·227 | 33 | 14·387 | 50 | 11·660 | 67 | 7·227 | 84 | 3·211 | 101 | 1·192 |
| 16 | 16·144 | 34 | 14·260 | 51 | 11·410 | 68 | 6·941 | 85 | 3·009 | 102 | 0·753 |
| 17 | 16·066 | 103 | 0·317 |
TABLE VII.
Showing the Value of an Annuity on the Joint Continuance of Two Lives, according to the Carlisle Table of Mortality, when the difference of their Ages is Five Years, and the rate of Interest Five per Cent. (No. 65.)
| Ages. | Value. | Ages. | Value. | Ages. | Value. | Ages. | Value. | Ages. | Value. |
|---|---|---|---|---|---|---|---|---|---|
| 0 & 5 | 10·551 | 20 & 25 | 13·398 | 40 & 45 | 10·598 | 59 & 64 | 6·127 | 79 & 84 | 2·045 |
| 1 & 6 | 12·331 | 21 & 26 | 13·272 | 41 & 46 | 10·444 | 60 & 65 | 5·895 | 80 & 85 | 1·895 |
| 2 & 7 | 13·258 | 22 & 27 | 13·137 | 42 & 47 | 10·287 | 61 & 66 | 5·678 | 81 & 86 | 1·747 |
| 3 & 8 | 14·019 | 23 & 28 | 13·000 | 43 & 48 | 10·121 | 62 & 67 | 5·458 | 82 & 87 | 1·626 |
| 4 & 9 | 14·402 | 24 & 29 | 12·867 | 44 & 49 | 9·937 | 63 & 68 | 5·230 | 83 & 88 | 1·535 |
| 5 & 10 | 14·649 | 25 & 30 | 12·742 | 45 & 50 | 9·737 | 64 & 69 | 4·988 | 84 & 89 | 1·433 |
| 6 & 11 | 14·731 | 26 & 31 | 12·615 | 46 & 51 | 9·519 | 65 & 70 | 4·737 | 85 & 90 | 1·279 |
| 7 & 12 | 14·736 | 27 & 32 | 12·482 | 47 & 52 | 9·292 | 66 & 71 | 4·469 | 86 & 91 | 1·203 |
| 8 & 13 | 14·689 | 28 & 33 | 12·344 | 48 & 53 | 9·054 | 67 & 72 | 4·207 | 87 & 92 | 1·192 |
| 9 & 14 | 14·606 | 29 & 34 | 12·208 | 49 & 54 | 8·799 | 68 & 73 | 3·961 | 88 & 93 | 1·219 |
| 10 & 15 | 14·500 | 30 & 35 | 12·078 | 50 & 55 | 8·528 | 69 & 74 | 3·731 | 89 & 94 | 1·214 |
| 11 & 16 | 14·389 | 31 & 36 | 11·944 | 51 & 56 | 8·242 | 70 & 75 | 3.528 | 90 & 95 | 1·167 |
| 12 & 17 | 14·284 | 32 & 37 | 11·806 | 52 & 57 | 7·950 | 71 & 76 | 3·319 | 91 & 96 | 1·161 |
| 13 & 18 | 14·178 | 33 & 38 | 11·661 | 53 & 58 | 7·657 | 72 & 77 | 3·127 | 92 & 97 | 1·181 |
| 14 & 19 | 14·069 | 34 & 39 | 11·508 | 54 & 59 | 7·375 | 73 & 78 | 2·948 | 93 & 98 | 1·215 |
| 15 & 20 | 13·959 | 35 & 40 | 11·354 | 55 & 60 | 7·106 | 74 & 79 | 2·767 | 94 & 99 | 1·191 |
| 16 & 21 | 13·853 | 36 & 41 | 11·204 | 56 & 61 | 6·860 | 75 & 80 | 2·623 | 95 & 100 | 1·038 |
| 17 & 22 | 13·746 | 37 & 42 | 11·056 | 57 & 62 | 6·615 | 76 & 81 | 2·467 | 96 & 101 | 0·828 |
| 18 & 23 | 13·636 | 38 & 43 | 10·907 | 58 & 63 | 6·370 | 77 & 82 | 2·333 | 97 & 102 | 0·555 |
| 19 & 24 | 13·520 | 39 & 44 | 10·753 | 78 & 83 | 2·194 | 98 & 103 | 0·249 |
TABLE VIII.
Showing the Value of an Annuity on the Joint Continuance of Two Lives, according to the
Carlisle Table of Mortality, when the difference of their Ages is Ten Years, and the rate of Interest Five per Cent. (No. 65.)
| Ages. | Value. | Ages. | Value. | Ages. | Value. | Ages. | Value. | Ages. | Value. |
|---|---|---|---|---|---|---|---|---|---|
| 0 & 10 | 10·649 | 19 & 29 | 13·117 | 38 & 48 | 10·396 | 56 & 66 | 6·156 | 75 & 85 | 2·100 |
| 1 & 11 | 12·275 | 20 & 30 | 13·008 | 39 & 49 | 10·195 | 57 & 67 | 5·881 | 76 & 86 | 1·956 |
| 2 & 12 | 13·087 | 21 & 31 | 12·896 | 40 & 50 | 9·984 | 58 & 68 | 5·600 | 77 & 87 | 1·838 |
| 3 & 13 | 13·769 | 22 & 32 | 12·776 | 41 & 51 | 9·766 | 59 & 69 | 5·319 | 78 & 88 | 1·759 |
| 4 & 14 | 14·106 | 23 & 33 | 12·648 | 42 & 52 | 9·548 | 60 & 70 | 5·044 | 79 & 89 | 1·657 |
| 5 & 15 | 14·334 | 24 & 34 | 12·510 | 43 & 53 | 9·329 | 61 & 71 | 4·779 | 80 & 90 | 1·515 |
| 6 & 16 | 14·419 | 25 & 35 | 12·365 | 44 & 54 | 9·104 | 62 & 72 | 4·529 | 81 & 91 | 1·450 |
| 7 & 17 | 14·432 | 26 & 36 | 12·214 | 45 & 55 | 8·870 | 63 & 73 | 4·302 | 82 & 92 | 1·460 |
| 8 & 18 | 14·395 | 27 & 37 | 12·058 | 46 & 56 | 8·626 | 64 & 74 | 4·094 | 83 & 93 | 1·479 |
| 9 & 19 | 14·321 | 28 & 38 | 11·900 | 47 & 57 | 8·372 | 65 & 75 | 3·921 | 84 & 94 | 1·468 |
| 10 & 20 | 14·221 | 29 & 39 | 11·747 | 48 & 58 | 8·111 | 66 & 76 | 3·746 | 85 & 95 | 1·443 |
| 11 & 21 | 14·106 | 30 & 40 | 11·607 | 49 & 59 | 7·851 | 67 & 77 | 3·580 | 86 & 96 | 1·397 |
| 12 & 22 | 13·987 | 31 & 41 | 11·474 | 50 & 60 | 7·601 | 68 & 78 | 3·407 | 87 & 97 | 1·324 |
| 13 & 23 | 13·864 | 32 & 42 | 11·342 | 51 & 61 | 7·370 | 69 & 79 | 3·210 | 88 & 98 | 1·280 |
| 14 & 24 | 13·737 | 33 & 43 | 11·207 | 52 & 62 | 7·142 | 70 & 80 | 3·020 | 89 & 99 | 1·192 |
| 15 & 25 | 13·608 | 34 & 44 | 11·063 | 53 & 63 | 6·911 | 71 & 81 | 2·807 | 90 & 100 | 0·950 |
| 16 & 26 | 13·483 | 35 & 45 | 10·912 | 54 & 64 | 6·669 | 72 & 82 | 2·616 | 91 & 101 | 0·733 |
| 17 & 27 | 13·359 | 36 & 46 | 10·750 | 55 & 65 | 6·418 | 73 & 83 | 2·430 | 92 & 102 | 0·508 |
| 18 & 28 | 13·235 | 37 & 47 | 10·579 | 74 & 84 | 2·260 | 93 & 103 | 0·235 |