TABLE IV.

SHEWING THE PRESENT WORTH OF £1 OR $1 ANNUITY, FOR ANY NUMBER OF YEARS FROM 1 TO 40.

ys.14 per cent. 4 per ct. 15 per cent.| 54 per ct. 16 per cent.17 per ct.

1 0,96154 0,95694| 0,95238 0,94786

1,88609 1,87267] 1,85941 1 8463
2,77509 2,74896 2,72325 2,6979

0,94339| 0,9345) 1,83339 1,8080 2,67301 2,6243]

4 3,62989 3,53752 3,54595 3,49862 3,4651 3,3872 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| 5,58233| 5,3892|| 86,73274 6,59589 6,46321 6,30522 6,20979) 5,9712| 97,43533 7,26379 7,10782 6,91786 6,80169 6,5152 10 8,11089 7,91272 7,72173 7.49856| 7,36008| 7,0235 11 8,76048 8,52892| 8,30641 8,04893 7,88687 7,4986| 12 9,38507 9,11858 8,86325 8,5707 8,38384 7,9426 13 9,98565 9,68285 9,39557 9,06522 8,85268 8,3576 14 10,56312 10,22282 9,89864 9,53395 9,29498 8,7454 1511,11839 10,73954 10,37966 9,97824 9,71225 9,1079 1611,65229 11,23401|10,33777 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 1913,13394 12,59329|12,08532 11,53549 11,15811|10,335 |20|13,59032|13,00793|12,46221 11,87541 11,46992|10,594 2114,0291613,4047212,8211512,1976 11,7640710,835 |22|14,45111|13,79442|13,163 12,50299 12,04158 11,061

|23|14,95684|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|14,0939413,3688 12,7833511,653 2615,98277 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|16,9837116,02189|15,14107|14,23838|13,59072|12,277 30 17,20202 16,28889 15.37245 14,43733 13,7648312,409 31 17,58849 16,54439|15,59281 14,6259 13,92908|12,531 3217,87355 16,78889|15,80268 14,80463 14,08398 12,646 [3318,14764 17,02286|16,00255|14,97404|14,22917|12,753 34 18,4112 17,24676 16,1929 15,13461 14,3661312,854 [35 18,6646117,46101 16,37419 15,2868 14,49533 12,947 36 18,9082817,6660416,54685 15,4310514,6172213,035 3719,14258 17.86224 16,71129 15.56779 14,73211 13,117 3819,36787 18,04999 16,86789 15,6974 14,84048 13,193 3919,58448 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. [41 per ct. 5 per ct. 154 per ct. 6 per ct. 7 per ct,

1,045 1,05

11,04
2,5302 ,534

,5378 ,54162,54544,55309 3,36035,36377,36721,37065,37411,38105]

4,27549,27874,28201 ,28582,28859,29523

5,22463,22779,23097,23487,23739,24389)

6,19076,19388,19702| ,20092,20336,20977
7,16661,1697 ,17282,17671,17913,18556

8,14853,15161,15473,15859,16103|,16747

9,13449,13757,14069 14455,14702,15349 10,12329,12638,1295 ,13334,13587,14238 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

15,08994,09311,09624 ,10022,10296,10979

16,08582,08901,09227 ,0962

,09895,10586)

171,0822 ,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

22,0692

,09230

,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

,08457

26,06257,06602,06956,07367,0769
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

31,05685,06044,06413,06837,07179,07980)

32,05595,05956,06328,06754,071 ,07908

133,0551 ,05874,06249,06678,07027,07841

34,05431,05798,06175,06607,06959,07779
35,05358,05727,06107,06541,06899,077241

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.

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 133 per 4 per 14 per[5 per 16 per
Age. cent. cent. cent. cent. cent. cent.

10 19,87 18,27 16,88 15,67 14,60|12,80|
1219,60 18,05 16,69 15,51 14,47|12,70|
1519,19 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 15,2114,27 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 11,14 10,10
48 13,01 12,36 11,74 11,19 10,68| 9,75|
50 12,5111,92 11,34 10,82 10,35| 9,45|
5311,73 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
9,69 8,39 7,30

60 9,73 9,36 9,01
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 4,29 4,22 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.

TABLE VIII.

EXPECTATION OF LIFE AT SEVERAL AGES.

Age. Expec. Age. Expec. | Age. Expec. | Age. Expec. | Age. Expec.

129,80 20 33,62|| 4221,65| 6211,68 82 3,31
237,92 22 32,46 45 20,10 65 10,20

85 2,64

87 2,40

7,80 90 2,12
7,00|92| 1,50

75 5,84 93 1,14 57|14,12| 77 5,15| 94 0,90 59 13,15 79 4,40 95 0,66 60 12,66 80 4,00 96 0,50

CIRCULATING DECIMALS

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 writtea

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 47-31578, 9-73528 and 05163, &c.