US APR vs EU APR, and the Substitute Tax on Loan Effects on These Formulas

Abstract

In Italy, especially these days, we have been dealing with the common “mortgage constant”, technically built under the principles of the compounded interest methods. This worldwide well-known financial technique clearly shows that every single rate is constant and composed by the sum of the principal part + the accrued interest. The rates of this kind of amortization plan result in an inversely proportional scheme: higher interest reimbursed at the beginning of the amortization plan, increasing rate by rate.

If this is unquestionable everywhere, the Italian Courts and many Italian banks officially deny that this amortization plan technique incorporates compound interest and anatocism, although the mortgage constant is on the compounded interest structure, as per the anatocism effect in it.

In order to defend this thesis about the absence of anatocism in compounded interest on constant rate, basically, all the other Senior Expert Witnesses of the Italian Courts recall EU APR formula, constantly declaring that it is equal to IRR formula, without any differences, without any exceptions.

Their statement, confirmed by many Italian Courts, is that EU APR formula is exactly corresponding to the IRR formula, determined using the IRR Excel function (XIRR). My study states that this is very incorrect, that the IRR formula (and function) is equal to the US APR, which assume as an APY, and different from EU APR, better to define as EAR.