On anatocism in progressive amortization: an unconventional approach

Sull'anatocismo nell'ammortamento progressivo: un'impostazione non convenzionale

Flavio Pressacco () and Laura Ziani ()
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Flavio Pressacco: DIES - DIES - Dept. of Economics and Statistics - Università degli Studi di Udine - University of Udine [Italie], Università degli Studi di Udine - University of Udine [Italie]
Laura Ziani: DIES - DIES - Dept. of Economics and Statistics - Università degli Studi di Udine - University of Udine [Italie], Università degli Studi di Udine - University of Udine [Italie]

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Abstract: In this paper we analyze, from a logical-mathematical point of view, the problem of the existence of interests on interests (so-called anatocism) in traditional amortization plans for a debt. The elementary methods of repayment of a debt (Bullet Bond and Zero Coupon Bond) are analyzed. It is noted that in them there is respectively absence (BB) or presence (ZCB) of interest on interest. We introduce the decomposition of a debt as a sequence of debts repayable with the two elementary methods. Equivalent decompositions are defined, in one or the other modality, those that give rise to a consolidated amortization that coincides with the traditional amortization plan. An apparent paradox emerges: there would be the presence of interest on interest in the equivalent decomposition ZCB and absence in the equivalent decomposition BB. The paradox can be solved by considering the mathematical consequences of the cadence of the collectability of interest.

Date: 2019-06-18
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