Newton-Raphson method initialization for non-analytical equations solution linked to anticipated annuities
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Fecha
2019
Autores
Vera, M
Flórez, M
Salazar-Torres, J
Huérfano, Y
Gelvez-Almeida, E
Valbuena, O
Vera, M I
Aranguen, M
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Editor
IOP Publishing
Resumen
The series of payments made in equal intervals of time is known, in the world of
financial mathematics, as an annuity. An anticipated annuity is one whose periodic payment
expires at the beginning of the established payment interval. The non-analytical equation that
allows us to calculate the interest rate, linked to the anticipated annuity, can be solved using
several numerical methods, in particular, the numerical method called Newton-Rhapson. The
main problem with this method is its initialization, which requires of one starting point that,
usually, is estimated without any scientific background or using random or arbitraries
mechanisms. In order to address this problem, in this paper, we establish as main objective to
demonstrate that the Newton-Rhapson method can be initialized using only the data, of an
anticipated annuity, identified as capital, income and payment intervals without the need to use
the initialization strategies, reported in the literature. Through this article, a strategy is
presented that allow us to calculate the value of the AA interest rate using the MNR. The value
of the error generated for the problematic considered in order to assess the quality of the work
performed, is a clear indicator of the good performance of the proposed strategy. This strategy
for obtaining the starting point of the aforementioned numerical method is useful in the
financial mathematical context, for example, when is necessary the interest rate calculation.