When making an investment, we expect that the money deposited will get good returns. The ways to apply money are the most varied, meeting the needs of each person. A good alternative for simple and safe application is the savings account, but the interest rates used in savings accounts are low. If you want to invest monthly amounts for a certain period of time, the best option to use is compound capitalization. In this modality, the person invests a fixed monthly amount that is applied to an interest rate specified in the act of joining. At the end of the stipulated period, the person withdraws all the money invested plus interest.
Most people do not know the types of existing investments, but the main thing is to know the process of monthly capitalization of money, institutions only provide the total amount. Let's build a table that will allow us to periodically analyze the capitalization of the invested money. The situation shown will address an immediate income capitalization, that is, the expiration of the first term is at the end of the first period from the date of signature of the contract. Look at the example:
A person deposits in a bank, at the end of each month, for 8 months the amount of R$ 100.00. Calculate the amount of income, knowing that this bank pays compound interest of 2% per month, compounded semiannually.
Data
C = 100
i = 2% = 2/100 = 0.02
n = 8 months
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Note that in the 8th month there was no capitalization, that is, there will be no income, as it was applied precisely on the day the amount was requested.
The sum of monthly capitalizations can be given as follows:
S = 100 *(1 + 1.02 + 1.0404 + 1.0612 + 1.0824 + 1.1041 + 1.1262 + 1.1487)
S = 100 * 8.583
S = 858.30
In the case of long-term investments, we use an expression capable of capitalizing periodic deposits. Watch:
Observe the expression development using the data from the example mentioned above.
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. "Immediate Income Through Compound Capitalization"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/renda-imediata-atraves-capitalizacao-composta.htm. Accessed on June 29, 2021.
