Annuity implies a sum of money payable yearly, half-yearly, or quarterly, to continue for a certain number of years, for life, or for ever.

An annuity is called an arrear, when it continues unpaid after it becomes due; and is said to be in reversion, when the purchaser, upon paying the price, does riot immediately enter upon possession: the annuity not commencing till some time after.

The interest upon annuities may be computed either in the simple or compound manner. But the latter, being most equitable, is ge-nerally preferred.

In the first class, viz. in those which extend for a limitted period, the principal considerations are, the annuity, rate, and time being given, to find the amount, or sum of yearly payments, and interest. These are readily ascertained, by a series of algebraical calculations.

In freehold estates, the principal circumstances to-be attended to, are,

1. The annuity, or yearly rent.

2. The price, or present value ; and,

3. The rate of interest.

The value of life-annuities is determined by comparative observations and calculations derived from, the bills of mortality. Several computations have been made for this purpose; the most esteemed of which are those by Dr. Hal-LEY, Mr. Simpson, and M. De MOIVRE.

Breslaw, the capital of Silesia, being a central place, and not much crowded, was fixed upon by Dr. Halley, who had recourse to the bills of mortality, when he composed his table. He selected l000 persons, all born in one year, and observed, how many of these remained alive every year from their birth, to the extinction of the last ; and, consequently, ascertained the; number which died in each year, as follows:

As there is allowed to be a till none be left, in order to form a greater disparity between births table particularly suited to this poand burials in the city of London, pulous city.

than in any other place. The following is Mr. Simpson' son selects 1280 persons, all born table on the bills of mortality, at in the same year, and records the London : number remaining alive each year,

But these tables, however perfect they may be in themselves, must be considered only as probable conjectures, founded on the usual period of human life, which is estimated as follows:

1. The probability that a person of a given age may live a certain number of years, is measured by the proportion which the number cf persons living at the proposed age bears to the difference between the said number, and that of persons existing at the given ages.

Thus, if it be required to know what chance a person 40 years of age may have to live seven years longer, the reader should refer to Dr. Halley's table, and from445, the number of persons living at 40 years of age, subtract the number of persons living at 47 years of age, and the remainder, being 68, will be the number of those who hi died during those seven years. The probability, that the person in ques-tion will live these seven years, is in the proportion of 377 to 68, or nearly as 51/2 to 1. By Mr. Simpson's table, the chance is somewhat less than that of 4 to 1.

If it be desirable to ascertain the year, which a person of a given age has an equal chance of attaining, the inquirer ought to find half the number of persons living at that given age, in the tables; and the year required will appear in the column of ages.

The premium of insurance upon lives may also, in some degree, be regulated by these tables, as follows :

The chance which a person of 25 years has to live another year, is, by Dr. Halt.ey's table, as 80 to 1 ; but the chance that a person of 50 years has to live a year longer, is only 30 to 1 ; and consequently the premium for insuring the former ought to be the premium for insuring the latter for one year, as 30 to 80, or as 3 to 8.

Life-annuities are commonly bought or sold at a certain number of years purchase. The value of an annuity of one pound for an age of 50 years at 3 per cent. interest, is about 12l. 10s. or twelve and a half years purchase,

Among those who have written on this subject, none is more deservedly celebrated than Dr. Price, the author of Observations on Reversionary Payments, Annuities, etc. published in 1771; and his curious remarks on this subject, inserted in the lxvth vol. of the Philos. Transactions, for 1775, p. 424, are well worthy of perusal and attention.

In our opinion, life annuities, when granted by individuals whose property is already involved, or who by such an expedient injure the just expectations of their relatives, ought not to be connived at in a well-regulated State.—Viewed in a commercial light, this species of gambling, in a certain degree resembles the furious rage for the hazard or pharo-table; to which all those adventurers and avaricious money - lenders generally resort, who are anxious to amass large sums of money, which, by moderate legal interest, could not be realized.