years), 52 weeks or 12 equal months. As per the standard: "An equal month is presumed to have 30.41666 days (i.e. 365/12) regardless of whether or not it is a leap year." The result is to be expressed to at least one decimal place. This algorithm for APR is required for some but not all forms of consumer debt in the EU. For example, this EU directive is limited to agreements of €50,000 and below and excludes all mortgages. In the Netherlands the formula above is also used for mortgages. In many cases the mortgage is not always paid back completely at the end of period N, but for instance when the borrower sells his house or dies. In addition, there is usually only one payment of the lender to the borrower: in the beginning of the loan. In that case the formula becomes: where: S is the borrowed amount or principal amount. A is the prepaid onetime fee R the rest debt, the amount that remains as an interest-only loan after the last cash flow. If the length of the periods are equal (monthly payments) then the summations can be simplified using the formula for a geometric series. Either way, the APR can be solved iteratively only from the formulas above, apart from trivial cases such as N=1. Additional considerations Confusion is possible in that if the word "effective" is used separately as meaning "influential" or having a "long-range effect", then the term effective APR will vary, as it is not a strict legal definition in some countries. The APR is used to find compound and simple interest rates. APR is also an abbreviation for "Annual Principal Rate" which is sometimes used in the auto sales in some countries where the interest is calculated based on the "Original Principal" not the "Current Principal Due", so as the Current Principal Due decreases, the interest due does not. Rate format An effective annual interest rate of 10% can also be expressed in several ways: 0.7974% effective monthly interest rate, because 1.00797412=1.1 9.569% annual interest rate compounded monthly, because 12×0.7974=9.569 9.091% annual rate in advance, because (1.1-1)÷1.1=0.09091 These rates are all equivalent, but to a consumer who is not trained in the mathematics of finance, this can be confusing. APR helps to standardize how interest rates are compared, so that a 10% loan is not made to look cheaper by calling it