One of the main elements in Financial Mathematics are the interest rates that correspond to the rate of return on capital at a given time. Interest rates are classified differently according to the type of percentage valuation being made. We will emphasize our study on nominal rates and real rates.
The nominal interest rate is used to demonstrate the effects of inflation in the period analyzed, based on financial funds (loans). For example, let's assume that a loan in the amount of $5,000 is repaid at the end of six months with a monetary value of $7,000. The nominal interest rate will be calculated as follows: interest paid / loan face value.
Fees
7 000 – 5 000 = 2 000
Nominal interest rate
2 000 / 5 000 = 0,4 → 40%
Therefore, the nominal interest rate on a loan of R$5,000, which had the amount of R$7,000 as repayment, had a nominal interest rate of 40%.
In the case of the real interest rate, the inflationary effect does not exist, so it tends to be lower than the nominal rate. This is because it is formed by correcting the effective rate by the inflation rate for the period of the operation. The actual rate can be calculated by the following mathematical expression:
in = nominal interest rate
j = inflation rate for the period
r = real interest rate
We can note that if the inflation rate is zero (equal to 0) the nominal and real interest rates will coincide.
Follow the example:
When making a loan, a bank offers pre-established rates, lending R$ 10 000.00 and will receive, within a maximum period of one year, the amount of R$ 13 000.00. If the inflation for the period was 3%. Determine the real interest rate on the loan?
Calculating the nominal interest rate
13 000 – 10 000 = 3 000
3 000 / 10 000 = 0,3 → 30%
Nominal rate (in) = 30%
Determining the real interest rate using the expression (1 + in) = (1 + r) * (1 + j).
in = 30% = 0.3
j = 3% = 0.03
r =?
(1 + 0.3) = (1 + r) * (1 + 0.03)
1.3 = (1 + r) * (1.03)
1.3 = 1.03 + 1.03r
1.3 - 1.03 = 1.03r
0.27 = 1.03r
r = 0.271.03
r = 0.2621
r = 26.21%
The actual interest rate on the loan is approximately 26.21%.
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by Mark Noah
Graduated in Mathematics
Brazil School Team
Financial math - Math - Brazil School
Would you like to reference this text in a school or academic work? Look:
SILVA, Marcos Noé Pedro da. "Nominal Rate and Actual Interest Rate"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/taxa-nominal-taxa-real-juros.htm. Accessed on June 28, 2021.
