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

By William Morse Cole | Go to book overview

CHAPTER TWELVE
THE RELATION OF PRINCIPAL AND INTEREST IN VALUATIONS

AN element of great importance in all valuations involving time is interest or discount. Both interest and discount are payment for the use of money; the fundamental distinction between them is that interest is a payment made at the end of a term of borrowing, and discount is a deduction made from principal at the beginning of a term of borrowing.

Simple interest is determined by multiplying the rate per year by the time in years and multiplying that product by the principal sum. That is, any two sums of interest at a particular rate will vary exactly in proportion to the time and the amount of the principal. The accumulation is purely by arithmetical progression. Compound interest, on the other hand, is interest in which the interest earnings of one year are allowed to accumulate and bear interest in the second and all subsequent years. That is, though at simple interest \$1000 borrowed for five years at 5% costs just five times as much as for one year, or \$250, at compound interest \$50 is charged for the first year, \$52.50 for the second year, and \$60.77 for the fifth year,--because the \$50 interest of the first year has borne interest four years, the \$50 interest of the second year has borne interest three years, and so on until the end, and in the fifth year interest must be paid on the accumulation,--so that the total interest is \$276.28, contrasted with \$250 of simple interest.

Several methods of figuring compound interest may be used. If the principal be multiplied by the rate, and the principal be added, the sum is the amount of the debt or other claim at the end of the first period; this is the same, of course, for compound as for simple interest, for compounding has not yet begun. If, now, this amount be again multiplied by the rate and the amount at the end of the first period be added, the result is the amount of the claim

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