Newton-Raphson method initialization for non-analytical equations solution linked to anticipated annuities





Vera, M
Flórez, M
Salazar-Torres, J
Huérfano, Y
Gelvez-Almeida, E
Valbuena, O
Vera, M I
Aranguen, M

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IOP Publishing


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.


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