Amortization dismantling to remove any doubt of anatocism

Abstract

We propose in this paper a method for verifying the non-existence of anatocism in a periodic amortization with n periodic installments, by the replication of its cash flows. The cash flows are obtained by recursively constructing an appropriate sequence of n consecutive single period loans, at the periodic interest rate i, each one with repayment of principal and interest at the end of the single period. Since each elementary transaction is concluded within one time unit, there is no possibility of interest accruing on interest and hence anatocism is ruled out. Therefore, this characteristic must be acknowledged to be valid also for the loan amortization schedule with n periodic installments whose cash flows are perfectly replicated by the unique loan sequence obtained.