Elements of Algebra

CHAP. XIII. OF ALGEBRA. 177 CHAP. XIII. *Of the Calculation of Interest* *. 540. We are accustomed to express the interest of any principal by *per cents*, signifying how much interest is annually paid for the sum of 100 pounds. And it is very usual to put out the principal sum at 5 *per cent*; that is, on such terms, that we receive 5 pounds interest for every 100 pounds principal. Nothing therefore is more easy than to calculate the interest for any sum; for we have only to say, according to the Rule of Three: As 100 is to the principal proposed, so is the rate *per cent* to the interest required. Let the principal, for example, be $860$l., its annual interest is found by this proportion: As $100 : 5 :: 860 : 43$. Therefore $43$l. is the annual interest. 541. We shall not dwell any longer on examples of *Simple Interest*, but pass on immediately to the calculation of *Compound Interest*; in which the chief subject of inquiry is, to what sum does a given principal amount, after a certain number of years, the interest being annually added to the principal. In order to resolve this question, we begin with the consideration, that $100$l. placed out at 5 *per cent*, becomes, at the end of a year, a principal of $105$l.: therefore let the principal be $a$; its amount, at the end of the year, will be found, by saying; As 100 is to $a$, so is 105 to the answer; which gives * The theory of the calculation of interest owes its first improvements to Leibneitz, who delivered the principal elements of it in the *Acta Eruditorum* of Leipsic for $1683$. It was afterwards the subject of several detached dissertations written in a very interesting manner. It has been most indebted to those mathematicians who have cultivated political arithmetic; in which are combined, in a manner truly useful, the calculation of interest, and the calculation of probabilities, founded on the data furnished by the bills of mortality. We are still in want of a good elementary treatise of political arithmetic, though this extensive branch of science has been much attended to in England, France, and Holland. F. T. N