# Accounts: Their Construction and Interpretation for Business Men and Students of Affairs

By William Morse Cole | Go to book overview

APPENDIX F
FORMULÆ

IN many of the following formulæ several differing expressions for the same thing have been given. When good tables of interest, discount, etc., are at hand, simplified formulæ are desirable; but when such tables are not available, only the most detailed formulæ are serviceable. The most condensed form is usually given first.1

To find the amount (principal and interest) of a sum at compound interest for a number of periods

Let P=the principal sum

r=the rate of interest per period

____________________
1
For those not familiar with algebraic expressions, it may be necessary to offer a few explanations. Two symbols written side by side on the same line without a sign between them are always to be multiplied together; thus, aP means the amount of a multiplied by the amount of P. Pa is the same thing as aP, of course. A parenthesis includes all within it as one item subject to the same treatment throughout; and hence P(a+1) means that P is to be multiplied not only by a but also by I, giving Pa+P, not Pa+I. When two symbols are written as a fraction, the upper is to be divided by the lower; thus means that U is to be multiplied by d and the product divided by r. A small figure or symbol written at the right and above another indicates that the latter is to be multiplied by itself as many times as the number indicated by the former: thus, a2=aXa; a3=aXaXa; (a+b)2=(a+b)X(a+b). or a2+2ab+b2;etc. as many times as there are units in p, so that if a=3 andp=4; . A similar small figure written in fractional form means that the corresponding root is to be taken,--that is, a number is to be taken which when multiplied by itself the required number of times will produce the required amount; thus, the cube root of a. Since in any equation the two halves are equal, as 6+4+7=9+3+5, any sum may be subtracted from either side if a corresponding sum is subtracted from the other side, or such sums may be added, or both sides may be divided by the same sum, or both sides may be multiplied by the same sum : thus, if A=I+r, A-I=r, and A+I=2+r; if , , and ; and .

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