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This paper demonstrates that both mortgage loan systems are equally advantageous for lenders, while varying outcomes for borrowers depend on their internal rate of return.
In Brazil, the financial institutions usually offer two kinds of mortgage loan to their customers: Price System and Constant Amortization System (CAS). This paper aims to check which of the two options is mathematically more advantageous for the lender and which is more advantageous for the borrower. In this sense, this paper proves that Price and CAS are equally advantageous for the lender. Related to the borrower, the paper proves that if his internal rate of return is less than the financing rate then CAS is more advantageous. Otherwise, if his internal rate of return is greater than the financing rate then Price is more 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 Price and CAS for any underlying values, both being in equal conditions.
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Tiago S. dos Reis (2025) studied this question.
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