Definition: is the series that displays the return on capital through equal payments at constant time intervals. It is well illustrated in situations of borrowing or purchasing goods.
The cash flow that characterizes this type of series is represented in the figure below:
The mathematical model for this type of series is:
Where,
PMT → is the value of installments or installments to be paid
PV → is the financed amount
i → is the interest rate
n → is the time
Example 1: A loan in the amount of $15,000 will be repaid within 24 months. Determine the amount of installments knowing that the interest rate charged is 2% per month.
Solution: We have to
PMT = ?
PV= 15000
i = 2% a.m. = 0.02
n = 24 months
Replacing the data in the formula, we get:
Example 2. In the acquisition of a financed asset in 48 months, the installments were in the amount of R$ 680.00 each. Knowing that the interest rate charged was 1.5% p.m., determine the value of this asset.
Solution: we have to,
PMT = 680
n = 48 months
i = 1.5% a.m. = 0.015
PV = ?
Replacing the data in the formula we get:
By Marcelo Rigonatto
Specialist in Statistics and Mathematical Modeling
Brazil School Team
Financial math - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/series-pagamentos-uniformes.htm