Compound interest is those in which, at the end of each period, the interest earned is added to the capital, constituting a new capital to be applied, this occurs successive times until reaching the maximum investment time of the money. Compound interest is the foundation of the current financial system, governing all types of financial transactions. Financial investments, mainly savings due to their practicality, are widely used by the general population, who seek to keep their savings safe and take the opportunity to earn some Yield.
The formula used in compound interest is as follows: M = C * (1 + i)t, Where:
M: amount
C: capital
t: application time
i: rate (:100)
Follow some examples involving the application of compound interest:
Example 1
What is the amount generated by the capital of R$ 1,500.00 applied during 6 months, at a rate of 2% per month?
We have:
C: 1500
i: 2% = 2/100 = 0.02
t: 6
M = 1500 * (1 + 0.02)6
M = 1500 * (1.02)6
M = 1500 * 1.126162
M = 1,689.24
Example 2
Determine the amount generated by investing a capital of R$6,000 for one year at a rate of 3% per month.
C: 6,000
t: 1 year = 12 months
i: 3% = 3/100 = 0.03
M = 6,000 * (1 + 0.03)12
M = 6000 * (1.03)12
M = 6000 * 1.425761
M = 8,554.57
Example 3
What capital, applied for 8 months, generated an amount of R$9,575.19 at a rate of 1.5% per month?
M: 9,575.19
i: 1.5% = 1.5/100 = 0.015
t: 8 months
9,575.19 = C * (1 + 0.015)8
9,575.19 = C * (1.015)8
9,575.19 = C * 1.126493
C = 9,575.19/1.126493
C = 8,500.00
by Mark Noah
Graduated in Mathematics
Brazil School Team
Financial math - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/aplicacoes-dos-juros-compostos.htm