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

By William Morse Cole | Go to book overview

at the end of the second period. This process may be continued for the full number of periods. It is better to think of periods than of years, for interest is often to be compounded semiannually or quarterly.

By another process, the amount of claim is figured directly without figuring the interest. Of course multiplying the principal by 1 reproduces that principal. Hence multiplying it by 1.05 gives the amount of the claim for one period at five per cent. By this method, therefore, the principal is multiplied by 1 plus the rate expressed decimally, and that product again multiplied by 1 plus the rate, and the process continued as many times as the number of periods requires.

Again, the rate (expressed decimally) plus 1 may be multiplied by itself, or raised to its second power. This gives the amount of one dollar at the end of the second period. This may be again multiplied by 1 plus the rate, that product again multiplied by 1 plus the rate, and so on until the number of periods has been provided for. This multiplied by the principal will give the amount for that principal at the end of the time; for the amount for one dollar multiplied by the number of dollars in the principal will give the amount for that principal. To express the same thing in another way, the rate plus 1 may be raised to the power indicated by the number of years which the claim has to run, and this multiplied by the principal will give the amount for that principal.

The principal plus interest is always technically known as the "amount." The amount minus the principal always gives the compound interest, of course.

It is obvious that if the number of periods for the compound interest is very great, the process becomes extremely tedious. In practice, where it has to be done very often, logarithms are used to reduce the work to a very few figures. By the use of logarithms it is possible to multiply or to divide or to raise to a power or to find a root by only two or three multiplications and divisions. The use of logarithms, however, involves a knowledge of mathematical principles which cannot always be assumed; and, therefore, this method will not be described here, though it is included in the illustrations given below.

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