Equational Arithmetic: Applied to the Questions of Interest, Annuities, Life Assurance and General Commerce

From the PREFACE. Although many Treatises on Arithmetic are already before the public, they are, for the most part, open to this objection, that they seek rather to invent labor for the student, by multiplying rules and examples, than to economise it by the most concise methods. The present work, which is not intended exclusively for a school book, nor yet to supersede the more useful of the elementary works already published, will, it is confidently believed, afford advantages to the accountant, merchant, and private student, which are not to be found in any other. It is said, "that railways have been used in this country for more than two centuries: " the recent and rapid extension of the system is a proof that the practical application and improvement of well-known arts is often of more value than an absolutely new invention. In like manner, the simplest form of fractional arithmetic, that of decimals, though so ancient, and to the present day so universal a branch of school-boy lore, has so unaccountably fallen into disuse as to be all but forgotten in after years. Another powerful motive for increasing in the public mind an interest in this mode of calculation is, that we thereby diffuse a knowledge of the great commercial benefits to be derived from an universal decimal scale of money, weights, and measures. Thus, we may ultimately obtain some parliamentary enactment which may rescue this country from the disgrace of being behind some other nations in the practical application of general principles. By giving only one or two examples, as a formula for each kind of calculation, we are enabled so to extend the work as to include Compound Interest, Annuities, Life Assurance, and almost every computation that comes within the sphere of ordinary arithmetic; thus comprising in one small volume, of which the tables alone are worth the cost, what has hitherto been diffused through many large and elaborate works, at a proportionally large expense. Every calculation in this work is reduced or reducible to one form-that of a simple equation; it has been the aim of the writer so to elucidate this method, that the accountant shall find no difficulty in applying the principle to any question whatever, though its formula be not found in these pages. By means of the decimal tables alone, which have never before been published at a moderate price, a vast amount of labor may be saved. All fractions of English money and time are already reduced to decimals in Tables I. and II., to which is added a new table of the decimals of the hundredweight, and the usual tabular values of compound interest and annuities at various rates per cent. The facilities of the decimal system may thus, in some degree, be anticipated. These advantages, together with that of reducing the innumerable rules of common arithmetic to the simple form of an equation (without assuming the merit of a new discovery), form, at least, an unique combination, affording all the facilities that could reasonably be expected, even from a new calculus, applicable to the ordinary purposes of commercial and scientific investigation.