Multiple Contracts with Simple Interest: The Case of the German System of Amortization

Abstract

The classical systems of amortization, used in house financing all over the world, is based on the compound interest regime, which is characterized by the payment of interest on interest, called anatocism. There have been several questions about its use in Brazil, cf. Jusbrasil (2023) , and Italy cf. Annibali et al. (2020) . In what appears to be a pioneering contribution De-Losso et al. (2013), it is shown that if a single contract written in terms of the classical system of amortization with constant payments is substituted by multiple contracts, one for each payment of the single contract, the financial institution providing the loan may experience substantial gains in terms of the present value of tax deductions, considering compound capitalization. Other studies using Constant Amortization method, German amortization method have reached the same results. The multiple contracts scheme has been implemented in several amortization methods, such as constant installments, constant amortization and American in simple interest capitalization using simple capitalization, given the problem of anatocism, and has given the same gain in tax reduction, considering simple capitalization. This paper will address the multiple contracts schema to the German amortization method, in simple capitalization, to observe if the same results are obtained. Since this method involves payments of interest at the beginning of each period, some adaptations were required in the proposition of De-Losso (2013). Additionally, a comparison with the French system is also presented.