ANNUITIES, in the strict meaning of the term, signifies a stated sum of money payable at regular periods, and derived from a fund, or source, in which the annuitant has no further property than the claim for the payment of his annuity. By this definition, annuities arc distin guished from the interest of money, rents of land, pro fits of trade, &c. where the same person who receives the income also holds in property the capital which pro duces it. Yet the doctrines of annuities may, in many cases, be advantageously applied to questions relating to the latter kinds of income. Annuities are generally divided into ANNUITIES CERTAIN and ANNUITIES CON TINGENT: the former meaning such as commence at a fixed time, and continue for a determinate number of years; the latter, those whose commencement, or con tinuance, depend on some contingency, such as the life or death of some particular person or persons.
The theory of Annuities Certain flows directly from the doctrines of compound interest ; that of Annuities Contingent, requires an application of the laws of chance to the particular contingencies on which they depend. Annuities are further divided into Annuities in Posses sion, or such as commence at the end of the first period ; and Annuities in Reversion, which do not commence till a greater period of time has elapsed, or till some particular event has taken place.
The present value of an annuity is that sum which, being immediately laid out at compound interest, will be just sufficient to pay the annuity as it becomes due.
The present article is divided into two distinct Chap ters, addressed to two distinct classes of readers, viz.
such as are desirous to understand the principles on which the theory of annuities is founded, and others who merely wish for a set of easy rules, applicable tc, the affairs of common life.
The First Chapter unfolds the theory of annuities, and gives the algebraic formula, by which any annuity may be calculated, independent of Tables, and by which the several tables, useful in practice, may be formed with most facility. The second contains these tables and rules for their use.
There are few subjects capable of being submitted to calculation, in which so many errors have been com mitted, or errors in theory led to so much individual distress, as in the subject of annuities. Even the justly celebrated Dr Price has, we conceive, fallen into two such mistakes, in which he has been followed by all subsequent writers, and which completely vitiate all his peculiar rules for comparing the values of annuities, according as they are payable, yearly, half yearly, quar terly, &c. In the theory of annuities, we enter into an ample discussion of these, and present to the render both Dr Price's formula, and those different ones which flow from what we consider as just principles. In a similar manner, in the second chapter, his practical rules are also given, leaving the reader to adopt those which his judgment may decide to be most correct. Such a procedure is due both to the reader, and to the great authority which this excellent writer has acquired in whatever relates to annuities.