Autopsy of a Myth: Dissecting the Anatocism Fallacy in Amortization Systems

Compound capitalization – or anatocism – in loans is prohibited by law, although widely practiced. Court decisions often require that these products be valued in simple capitalization. This article demonstrates – in four alternative ways – that there is anatocism in a family of amortization systems, called the General Amortization System – SGA, in which interest is the product of its rate and the previous outstanding balance. This includes the Constant (or Hamburg) Amortization System – SAC, the Price (or French) and the American Systems, which imply anatocism. Furthermore, an original and economically based model is developed in order to build Simple Capitalization Amortization Systems – SACS, for infinite configurations of payments or amortizations, extendable to multiple and simultaneous focal-dates. The elegance of the model lies in the direct analogy to the case of compound capitalization, making its implementation immediate and working as its natural counterfactual.