ABSTRACT
In this chapter, the authors reduce all operations to so many periods, and such a rate per period, but it is usual to speak of such a rate per annum, payable so many times a year, or “convertible half yearly or quarterly.” Where the interest is payable otherwise than annually, the rate per annum is only nominally correct. The process of finding the effective rate follows naturally from the ordinary rule for compound interest. If the nominal rate is 6% per annum, and it be paid quarterly, the actual ratio is 1.015, and the fourth power of 1.015 is the amount at the end of the fourth quarter, which by multiplication or by adding logarithms is found to be 1.061364, or interest.061364. The chapter finds the ratio of increase for the lesser unit of time, which we do by dividing the logarithm of the effective rate by the number of conversions.
