Control in loan transactions: adjusting the payments to the real inflation rates

This paper explores the effect of inflation on general financial transactions and particularly on loans. For this purpose, inflation is specified in the mathematical expression of a capitalization or discounting function. Thus, we write these functions as the product of an inflation-free capitalization or discounting function and the law of variation of the money purchasing power. As an immediate consequence, we show that the instantaneous rate of a capitalization or discounting function is the sum of the instantaneous rates of each component. Later, this decomposition is applied to simple and compound financial transactions, leading to the equivalence among deflated amounts by means of an inflation-free capitalization or discounting function. This analysis is applied to a loan transaction where we introduce six methods to adjust the payments to the real inflation, because, in a beginning, these payments were calculated with the predicted inflation rates.