Nominal rate and real interest rate

THE interest rate is a percentage value that indicates the income earned by borrowing or investing an amount of money over a period of time.

This rate may or may not be calculated considering the inflation situation in the period of application of the money. In this sense there is the nominal interest rate and the real interest rate. Understand better about these two types of fees!

nominal fee

THE nominal interest rate corresponds to the rate of return on a loan/investment without taking into account the rate of inflation in the period.

Example: João lent the amount of R$5,000.00 at an annual interest rate of 11%. At the end of the year, the debtor paid off his debt by paying a total of R$5,550.00. What is the nominal fee?

The nominal interest rate or nominal income rate of João corresponds to 11%, it is the rate without considering the inflation in the period.

This rate is also called apparent rate, in the sense that income does not match reality.

You see, the value of money is associated with the rate of inflation, as the purchasing power is lower when the inflation increases, that is, the real income of those who lend or invest money, depends on the rate of inflation.

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real interest rate

Unlike the nominal interest rate, the rate of interest real is the rate of income calculated based on the rate of inflation. Thus, we have:

High inflation rate ⇒ lower income rate;
Low inflation rate ⇒ higher income rate.

To calculate the real interest rate, use the following formula:

$\dpi{120} \mathrm{Rate \, real = \left ( \frac{1 + Rate \, nominal}{1 + rate\, inflation \tilde{a}o} \right ) -1}$

Example: João lent the amount of R$5,000.00 at an annual interest rate of 11%. At the end of the year, the debtor paid off his debt by paying a total of R$5,550.00. Determine the real interest rate, considering that during this period the inflation rate was:

a) 4.5%

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