Transitando matematicamente entre as capitalizações contínua, composta e simples

Abstract

The present study aims to present an analysis of the different types of capitalization, aiming to achieve three specific objectives: to present a more general equation for continuous capitalization with an application that can only be solved mathematically by this equation; make an empirical comparison between the values of continuous and compound capitalization according to rate and time and deduce the formulation of simple capitalization from continuous capitalization, verifying when the first can function as an approximation of the second. This research is applied as to the purpose with a quantitative approach to the data, being a case study in the procedural aspect and exploratory in relation to the objectives. The results obtained show that the most general equation for the continuous capitalization has an integral in the exponent of the neperian base, that with rates greater than or equal to 3% the difference between the continuous and compound capitalizations differ by at least 1% in the amount and that when the product between rate and time is less than 0.14, continuous and simple capitalization have a difference of less than 1%. This study shows theoretical contributions in the sense of analyzing something little discussed in mathematical studies about the three types of capitalization.