TABLE IV.

SHOWING THE PRESENT WORTH OF £1 OR $1 ANNUITY, FOR ANY NUMBER OF

3s. 4 per cent. | 4 per ct.
10,96154
2 1,88609 1,87267

0,95694

YEARS FROM 1 TO 40.

15 per cent. | 5 per ct.
0,95238 0,94786
1,85941
1,85941 1,8463
2,72325 2,6979

3,49862

6 per cent. 7 per ct. 0,94339 0,9345 1,83339 1,8080

2,67301 2,6243

3,4651

7,36008 7,0235

8,04898

7,88687 7,4986 8,38384 7,9426

3 2,77509 2,74896 4 3,62989 3,58752 3,54595 3,3872 5 4,45182 4,38997 4,32948 4,25759 4,21236 4,1001 6 5,24214 5,15787 5,07569 4,97699 4,92732 4,7665 76,00205 5,8927 5,78637 5,65888 5,58238 5,3892 8 6,73274 6,59589 6,46321 6,30522 6,20979 5,9712 9 7,43533 7,26879 7,10782 6,91786 6,80169 6,5152 10 8,11089 7,91272 7,72173 7,49856 118,76048 8,52892 8,30641 12 9,38507 9,11858 8,86325 8,5707 13 9,98565 9,68285 9,39357 9,06522 8,85268 8,3576 1410,56312 10,22282 9,89864 9,53395 9,29498 8,7454 1511,11839 10,73954 10,37966 9,97824 9,71225 9,1079 16 11,65229 11,23401 10,83777 10,39936 10,10589 9,4466 17 12,16567 11,70719 11,27407 10,79852 10,47726 9,7632 18 12,65929 12,15099 11,68958 |11,17687 |10,8276 10,059 19 13,13394 12,59329 |12,08532 11,53549 |11,15811|10,335 20 13,59032 13,00793 12,46221 11,87541 11,46992 10,594 21 14,02916 |13,40472 12,82115 12,1976 11,76407 10,835 22 14,45111 13,79442 13,163 12,50299 12,04158 11,061 23 14,85684 14,14777 13,48807 12,79245 12,30338 11,272 24 15,24696 14,49548 13,79864 13,06682 12,55035 11,469 |25|15,62208 |14,82821 |14,09394|13,3688 |12,78335|11,653 26 15,98277 15,14661 14,37518 13,57338 13,00316 11,825 27 16,32959 15,4513 14,64303 13,80702 13,21053 11,986 28 16,66306 15,74287 14,89813 14,02848 13,40616 |12,137 29 16,98371 16,02189 15,14107 14,23838 13,59072 12,277 30 17,20202 16,28889 15,37245 14,43733 13,76483 12,409 31 17,58849 16,54439 15,59281 14,6259 13,92908 12,531 32 17,87355 16,78889 15,80268 14,80463 14,08398 12,646 33 18,14764 17,02286 16,00255 14,97404 14,22917 12,753 34 18,4112 17,24676 16,1929 15,13461 14,36613 12,854 35 18,66461 17,46101 16,37419 15,2868 14,49533 12,947 36 18,90828 17,66604 16,54685 15,43105 14,61722 13,035 37 19,14258 17,86224 16,71129 15,56779 14,73211|13,117 |38|19,36787 18,04999 16,86789 15,6974 14.84048 13,193 39 19,58448 18,22965 17,01704 15,82024 14,9427 13,264 40 19,79277 18,40158 17,15909 15,93667 15,03913 13,331

TABLE V.

THE ANNUITY WHICH £1 OR $1 WILL PURCHASE FOR ANY NUMBER OF YEARS
TO COME, FROM 1 TO 40.

ys. 4 per ct. 4 per ct. 5 per ct.15 per ct.16 per ct. | 7 per ct.
11,04 1,045 1,05 1,055 1,06

2,5302,534

1,07

,5378,54162,54544,55309

3,36035,36377,36721,37065,37411,38105

11,11415,11725,12039,12424,12679,13336|
12,10655,10967,11282,11667,11927|,12592|

13,10014 10327,10645,11031,11296,11965|

14,09467,09782,10102,10489,10758,11435

15,08934 09311,09624,10022,10296,10979|

16,03582,08901,09227,0962 ,09895,10586
17,0822 ,08542,0887 |,0926 ,09544 ,10243
18,07899,08224,08555,08947,09235,09941
19,07614,07941,08274,08699,08962,09676
20,07359,07688,08024,08427,08718,09439
21,07128,0746 ,078 ,08198,085 ,09230
22,0692

,07254,07597,07998,08303,09041

23,06731,07068,07414,07825,08128,08880

24,06559,06899,07247,07653,07968,08719

25,06401,06744,07095,07503,07823,08581

26,06257,06602,06956,07367,0769 ,08457

27,06124,06472,06829,07242,0757 ,08343

28,06001,06352,06712,07128,07459 ,08239

29,05888,06241,06604,07023,07358,08145

30,05783,06139,06505,06926,07272,08058

,07908

|31|,05685,06044,06413,06837,07179,07980
32 ,05595,05956,06328,06754,071
33,0551 ,05874,06249,06678,07027,07841

34,05431,05798,06175,06607,06959,07779
35 05358,05727,06107,06541,06899,07724
36,05289,0566 ,06043,0648

,06839

,07672

37 ,05224,05598,05984,06423,06785,07624
,05928,0637,06735 07579

38,05163,0554

39,05106,05485,05876,06321,06689,07539

40,05052 05434,05828,06274,06646,07501

TABLE VI.

VALUE OF AN ANNUITY OF £1 or $1, at dIFFERENT RATES PER CENT. PAYABLE YEARLY, HALF YEARLY, QUARTERLY, DAILY OR MOMENTLY, FOR EVER.

3

3445

33,333333,6022 33,6927 33,8238|33,8308 28,5714 28,7886 28,9083 29,081429,2908 25,0000|25,2525 25,3807 25,4858|25,4992 41 22,222222,4699 22,5938 22,717522,7244 20,0000 20,2429 20,3583 20,476320,4959 18, 1818 18,4298 18,5529 18,6630 18,6812 16,6666 16,9147 17,0380 17,0554 17,1635 15,5555 15,629 15,7550 15,774,15,7902

5

6

6

7

14,2857 14,5:49 14,6575 14,7694|14,7800

Note. This Table is calculated by the Rule, Case I. of “Purchasing Annuities for ever."

TABLE VII.

THE VALUE OF AN ANNUITY OF £1 OR $1, FOR A SINGLE LIFE.

13 per 13 per 4 per 14 per 5 per 6 per Age. cent. cent. cent. cent. cent. cent. 10 19,87 18,27 16,88 15,67 14,60 12,80| 12 19,60 18,05 16,69 15,51|14,47 12,70 15 19,19 17,71 16,41 15,27 14,27 12,55 18 18,76 17,33 16,10 15,01|14,05 12,48 20 18,46 17,09 15,89 14,83 13,89 12,30| 22 18,15 16,83 15,67 14,64 13,72|12,15| 25 17,66 16,42 15,31 14,34 13,46 12,00 28 17,16 15,98 14,94 14,02 13,18 11,75 30 16,80 15,68 14,68 13,79 12,99|11,60| 33 16,25 15,21|14,27|13,43|12,67|11,35| 35 15,86 14,89 13,98 13,17 12,45 11,15 38 15,29 14,34 13,52 12,77 12,09 10,90 40 14,84 13,98 13,20 12,48 11,83 10,70 43 14,19 13,40 12,68 12,02 11,43 10,35 45 13,73 12,99 12,30 11,70 11,1410,10 48 13,01 12,36 11,74 11,19|10,68 9,75 50 12,51 11,92 11,34 10,82 10,35 9,45 53 11,73 11,20 10,70 10,24 9,82 9,00 55 11,18 10,69 10,24 9,82 9,44 8,70 58 10,32 9,91 9,52 9,16 8,83 8,20 60 9,73 9,36 9,01 9,69 8,39 7,80 63 8,79 8,49 8,20 7,94 7,68 7,20 65 8,13 7,88 7,63 7,39 7,18 6,75 68 7,10 6,91 6,75 6,54 6,36 6,00 70 6,38 6,22 6,06 5,92 5,77 5,50 73 5,25 5,14 5,02 4,92 4,82 4,60 75 4,45 4,38| 4,294,22|| 4,14| 4,00| 77 3,63 3,57 3,52 3,47 3,41 3,30 79 2,78 2,74 2,70 2,67|| 2,64 2,25 80 2,34 2,31 2,28 2,26 2,23 2,15

This Table is formed by ascertaining from Bills of mortality the mean length of the lives of persons of a certain age, and then calculating the value of the annuity for the number of years they may thus be expected to live. This mean is called the Expectation of Life, at any given age, which is exhibited in the following table.

29

ARE produced from Vulgar Fractions, whose denominators do. not measure their numerators, and are distinguished by the continual repetition of the same figures.

1. The circulating figures are called repetends; and, if one figure only repeats, it is called a single repetend: As·1111, &c. 6666, &c. 2. A compound repetend has the same figures circulating alternately: As 010101, &c. 379379379, &c.

3. If other figures arise before those which circulate, the decimal is called a mixed repetend; thus, 375555, &c. is a mixed single repetend, and 378123123, &c. a mixed compound repetend.

4. A single repetend is expressed by writing only the circulating figure with a point over it; thus, 1111, &c. is denoted by

1, and 6666, &c. by 6.

5. Compound repetends are distinguished by putting a point over the first and last repeating figures; thus, 010101, &c. is written

01, and 379379379, &c. thus, 379.

6. Similar circulating decimals are such as consist of the same number of figures, and begin at the same place, either before or

after the decimal point; thus, 3 and 5 are similar circulates; as

are also 3.54 and 7.36, &c.

7. Dissimilar repetends consist of an unequal number of figures, and begin at different places.

8. Similar and conterminous circulates are such as begin and end

at the same place; as 47-34576, 9-73528 and 05463, &c.