Abstract The article represents a yield formula for calculating irregular installment payments. A fundamental problem in the mathematics of finance is the present valuation of future payments. When they take the form of an annuity of C every period for "n" periods, we have the concise formula P= C(1 -)/I, which may be expanded in an elementary series. If there is only one future payment, the formula is even simpler, P = Cμsupn/sup, and the series is quite as elementary. There are cases in which payments are not all for the same amount. If the variations follow some law, there is still a formula to be had but it becomes more complex. In this fall increasing, decreasing, and deferred annuities, bonds and serial bonds and "balloon note" and "drop payment" installment finance deals. The author proposes to derive an approximation formula for the rate of interest in the general case of future repayments of a present indebtedness, whether they be many or one, equal or unequal and when such a formula, has been obtained, one shall find that it includes both the annuity and single payment formulas as special cases.
Ralph W. Snyder (Thu,) studied this question.