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TABLES, shewing the Sums payable at Removals, to Contributors who have begun their Contributions in the several Years of their Age, after the 21st, without Fines.

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NOTE.

In the original Tables the sums to be paid at removal have been computed for all the Eleven Classes at every age from 22 to 50; but I have only inserted the First Class for each age in these Tables, because the insertion of the other Ten Classes would have swelled the work without answering any essential purpose. If the sums payable at removal be known when the weekly contributions are 21d. in the 1st Column, 24d. in the 2d. Column, and so on: the sums to be paid in those respective cases when the weekly contributions are 3 d., 31d, &c. are easily obtained by the common rule of proportion. Thus, if instead of 21d. in the 1st Column, the weekly contribution had been 33d. the sum to be paid on removal would have been a fourth proportional to 24d. 9s. and 3 d.; that is, expressing these numbers in decimals, it would have been = .67497 = 13s. 6d. or more simply = .45 X If the weekly contributions had been 7d. the sum to be paid on re.45 x .032812 moval would have been .009375

=

.45 x .014062

2

.009375

3

= 1.575 = 11. 11s. 6d. or

.45. But if the contributions had been 61d. 114d. or any other multiple of 24d. the sum to be paid would have been the same multiple of 9s. and therefore immediately ascertained.

M.

FINIS.

INDEX

INDEX

TO THE

TWO VOLUMES.

ACCOUNT of a method of deducing from the correct values
of any single or joint lives at one rate of interest, the same
values at other rates of interest, i, 221.

Ackworth in Yorkshire, expectations of life in that parish, ii.
35. Annual proportion of deaths there, ii. 41. note. State
of population there, ii. 220.

Aggregate fund, account of, i. 298. The surpluses of, how
applied, i, 299.

Aikin, Dr. Observations on the tables formed from his register
of mortality at Warrington in Lancashire, ii. 249.

Air, how its purity is restored by natural causes when it be
comes noxious, ii. 130.

All Saints parish in Northampton, estimation of the duration
of life there, ii. 45. Proportion of births and burials in
ii. 95.
America, North, rapid progress of population there, ii. 50.
Remarks on the state of population in the colonies there,
ii. 145. The inland, and maritime parts of, distinguished,

ii. 146.

Amicable Society of Annuitants for the Benefit of Age, their
terms of admission, i. 141. The plan of, reformed, i. 154.
Amicable Society for perpetual Assurance in Serjeants Inn,
terms of, i. 158. Remarks on the plan of, i. 160. Increase of
shares and dividends, i. 166. Cautions offered to them, ibid.
Remarks on the state of their affairs in 1802, i. 173, note.
Amsterdam, the institution for the sale of annuities on sur-
vivorship there, dropped, i. 131.

Amsterdam, number of inhabitants, and annual medium of
births and burials in, ii. 23, note.

Annuitants, a body of, generally a selection of the best lives
from the common mass, ii. 454. See Amicable, Equitable,
Laudable, London, &c.

Annuities,

Annuities, payable yearly, and half-yearly, their different values
stated, i. 263. The amounts of, for any number of years, at
compound interest payable half-yearly, i. 265. Application
to the national debt, i. 266. Application to life-annuities,
i. 267. Theorems for finding the differences in their values,
according to the frequency of their payments, i. 238.
Annuities for limited terms, the raising money for public ser-
vice by the grant of, a sure mode of prescribing bounds to
the national debt, i. 274. Short annuities and life-annuities,
always undervalued, i. 287. A fund raised for paying life
annuities, capable of paying the sum borrowed in a shorter
time, i. 288.

Annuities, reversionary, questions adapted to various schemes,
for granting, i. 1. The value of the expectation of an an-
nuity for a widow, in one present payment, idem, ibid.
The value of a like expectation in annual payments, i. 18.
Premium to be paid, where the annual payments are limited,
i. 16. The value in a single payment, and also in annual
payments, of an annuity to a person of thirty-five, to com-
mence fifteen years hence, i. 18. The value in annual pay-
ments, of an annuity increasing according the number of
years before a woman becomes a widow, i. 26. The value
of an annuity to commence at the death of another person,
provided that person lives a given time, i. 30, 32, note.
What present money and annual payments ought to be paid
by a person of a given age, for an assurance of a given sum
on his life, i. 82. The value, where the payment of a sum
is contingent, depending on the survivorship of one life be-
yond another, i. 36, 40. note. The value of the expectation
of a certain sum to children, where no widow is left, i. 42,
43, note. The annual payments proper to secure annuities
to widows under a local or professional establishment, i. 46.
Remarks on Mr. De Moivre's rules for calculating the values
of joint lives, i. 204. Easy and expeditious method of cal-
culating the values of two joint lives, i. 211. Method of
calculating the values of reversions, depending on survivor-
ships, i. 192. Tables of the probabilities of life for males
and females, wanted to calculate them to exactness, ii. 111.
Annuities for old age, a table of the value of, i. 138. General
rule for finding the value of, in admission money and annual
payments, i. 139. General character of the schemes of the
societies established for granting such annuities, i. 140, 145.
Their fallacy demonstrated, i. 143. Plan of an institution
to provide for old age, recommended, i. 148. Plan of a
benefit club for the labouring poor, i. 149, note. Scheme
for establishing parochial life annuities for the poor, i. 151:
note. Hints for growing annuities, to commence at a cer-
tain age, i. 187.

Annuity

Annuity for 100 years, nearly equal in value to one for ever,
i. 274.

Annuity for ever, the present value of, i. 49, note.

Assurance, the more correct method of computing the annual
payments, i. 20, note. The value of a given sum on a given
life; in present money and annual payments, i. 32. The
value, where the payment of the sum assured is contingent,
depending on the survivorship of the receiver, i. 36. 40, note.
Where an estate is liable to fail by death within a given
term, the value of the assurance for that term; i. 51. 53,
note. Rule for calculating the price of assurances on two
joint lives, or the longest of two lives, for given terms, i. 54.
The value of a given sum to be received at the death of an-
other within a given time, i. 60, 61, note. The value of a
given sum payable at the death of B, provided he survives.
A, and dies within a given time, i. 65, 66, note. 70, note.
The doctrine of assurances applied to schemes for raising
annuities for widows, i. 85, note.

Assurances, equitable, on lives and survivorships, remarks on
the plan of the society for, i. 174. The society ought to be
furnished with necessary tables, i. 180. Its rapid increase,
i. 182. Ratio of the decrements of life in this society, ibid.
note, and ii. 443. Account of the tables ordered for the use
of the society, i. 184. Advantages possessed by this society
enumerated, i. 186. Tables still requisite for the society to
procure, i. 187. Hints for growing annuities to be offered
to the public by, i. 188. Table of the probabilities of life,
accepted by this society, ii. 305. Remarks on their terms,
and management, ii. 372. Have extended their plan to
making a provision for widows, ii. 434. Observations on
their plan for widows, ii. 439. Comparison of the premiums
required for assurances on single lives, with their values
deduced from the Sweden tables, ii. 441. State of their
affairs in 1800, i. 191, note. Number of assurances and
ratio of the decrements of life at different ages for the last
33 years, ii. 443, note.

Aynhoe in Northamptonshire, proportion of births and deathe
to marriages there, for 118 years, ii. 34, note.

B.

Bacon, lord, his remarks on inclosures, ii. 156.

Belfast, comparative surveys of the state of population there,
ii. 204, note.

Bergen in Norway, expectations of life there, i. 45, note.
Berlin, state of population in that city, i. 67. 107. Its disad
vantages, ii. 121. Tables of the probabilities of life there,
ii. 126.
VOL. II.

KK

Biddulph

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