Uniform Payment Series

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:

Do not stop now... There's more after the advertising ;)



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

Would you like to reference this text in a school or academic work? Look:

RIGONATTO, Marcelo. "Uniform Payment Series"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/series-pagamentos-uniformes.htm. Accessed on June 29, 2021.

Exercises on PA and PG

Exercises on PA and PG

Study arithmetic and geometric progression with solved and commented exercises step by step.Exerc...

read more
Addition: all about this operation

Addition: all about this operation

Addition is the act of joining elements, one of the four basic operations of arithmetic. Addition...

read more
Domain, co-domain and image

Domain, co-domain and image

The domain, range and range are numerical sets related by mathematical functions. These transform...

read more