Interest rates calculation in certain ordinary annuities

Abstract

Certain annuities are annuities whose payments occur on fixed dates; while a certain ordinary annuity is one in which payments are made at the end of each established period. The calculation of the interest rate, which governs the certain ordinary annuity, involves the use of a non-analytical equation that requires the application of numerical techniques to obtain the value of the aforementioned rate. The literature indicates that any of these techniques requires one or several numerical values for initialization, which generally are estimated using trial techniques, graphical methods or values present in pre-established tables. Through this article, a new robust methodology is proposed that calculates the useful numerical values to initialize the linear interpolation technique, which is used to calculate the interest rate linked to the certain ordinary annuity. The proposed methodology generates initialization values, one by default and the other by excess, which allow us to limit the value of the certain ordinary annuity interest rate considered. Finally, we generated a new strategy that constitutes a novel mathematical model for interest rates calculation in the context of certain ordinary annuity. The percentage relative error obtained indicates the excellent performance of the aforementioned mathematical model.