The relationships involving quantities are analyzed from the point of view of mathematical functions. The functions have numerous features and range from everyday calculations to more complex situations. In the case of Financial Mathematics, the functions are related to capital investments in the systems of simple and compound interest, which we use the 1st degree and exponential functions respectively. The graphs representing the aforementioned functions are used to analyze the progress of the amount formed month by month, observing which application is more advantageous within a given period. Observe the graphs of the situations below, they will represent the progress of the application according to the type of capitalization chosen.
Suppose that the capital of R$500 was applied at a rate of 2% per month in the simple and compound interest regimes. Let's represent the function of each application and the graphs corresponding to the first months.
simple interest
M = C + j
J = C * i * t
Amount at the end of the fourth month will be equal to R$540.00.
Compound interest
M = C * (1 + i) t 
Amount at the end of the fourth month will be equal to R$ 541.22
Graphics
simple interest
compound interest 
When comparing the data and graphs, we notice that in simple capitalization, interest grows linearly, while in compound capitalization, interest grows exponentially. According to the graphs, we can see that the investment using compound interest is more profitable than the simple capitalization, because in the simple regime the interest is fixed, that is, calculated only on the amount initial. In the case of compounds, interest on interest is applied, thus, the value of each monthly interest is always greater than that of the previous month.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Roles - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/funcoes-matematica-financeira.htm