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Archive » September 2020 » Mathematics and law in the anatocism in progressive amortization plans

Mathematics and law in the anatocism in progressive amortization plans

Flavio Pressacco, Laura Ziani
September 2020 - n. 9
Keywords: Piani di ammortamento, anatocismo, scomposizione equivalente, cadenza di esigibilità degli interessi
Jel codes: G21, E4, C02

In this paper we propose an integrated mathematical-juridical approach to analyze the problem of the presence or absence of interest on interests (illicit «anatocism») in traditional progressive amortization plans. Supporters of anatocism consider it as an algebraically necessary consequence of the compound capitalization regime that rules these plans. We believe this statement is logically unfounded. It is the algebraic consequence of the hypothesis that each mortgage installment must include the joint payment of part of the initial debt and the related interest. By breaking down the loan into sequences of elementary mortgages, this in turn reflects hypothesis (juridical and not merely algebraic) of non-collectability, until the final maturity of each single loan, of the interest accrued period by period. A rather bold hypothesis and which in any case does not have the status of an unconditionally valid proposition. In our opinion, any assumption about the frequency of interest collectability must be the result of an interdisciplinary convergence between law and mathematics. Using the integrated approach, we are able to reach the fundamental conclusion of the paper: the traditional progressive amortization plan is unequivocally free from anatocism and therefore fully legitimate if the frequency of interest collectability coincides with the timing of the mortgage installments.

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