Amortização antecipada no SAC, qual é melhor: antecipação com redução do tempo ou antecipação com redução na prestação?

In mortgage loans, the borrower can prepay, pay in advance, part of the debt. There are two options for how to proceed with the financing after an early repayment. The first is an anticipation with reduction in term, in which the installments remain unchanged and, consequently, the number of installments is reduced. The second is an anticipation with reduction in installment, in which the number of installments remains unchanged and, consequently, the installments are reduced. This text aims to analyze which of the two options is mathematically more advantageous for the borrower and which is more advantageous for the lender, under the Constant Amortization System (CAS). In this sense, this paper proves that, in the CAS, for the borrower, if its minimum attractive rate of return is less than the financing rate then the anticipation with reduction in term is more advantageous. Otherwise, if its minimum attractive rate of return is greater than the financing rate then the anticipation with reduction in installment is more advantageous. Related to the lender, the paper proves that, in the CAS, the two conventions are equally advantageous. Although the paper also uses examples and simulations with specific values, it proves those results in a general way. That is, it proves the advantage, disadvantage or equality between the two early amortization conventions for any underlying values, both being in equal conditions.