Annual percentage rate (APR) is the simplified counterpart to the effective interest rate that the borrower will pay on a loan. In many countries and jurisdictions, lenders (such as banks) are required to disclose the "cost" of borrowing in some standardized way as a form of consumer protection. APR is intended to make it easier to compare lenders and loan options. The APR is likely to differ from the "note rate" or "headline rate" advertised by the lender, due to the addition of other fees that may need to be included in the APR. APRs can be found by asking the lender or by reading the appropriate section in the contract.

In the U.S. and the UK, lenders are required to disclose the APR before the loan (or credit application) is finalized (although the definition of "APR" is not the same in these two countries – see below]]). Credit card companies can advertise monthly interest rates, but they are required to clearly state the annual percentage rate before an agreement is signed. APR is a term used with regard to deposit accounts as well. However, when dealing with deposit accounts, the annual percentage yield (APY) or annual equivalent rate (AER) is quoted to consumers for comparison purposes.

Rate format

An effective annual interest rate of 10% can also be expressed in several ways:

• 0.7974% effective monthly interest rate, because 1.007974^12=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=1-0.091

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 a loan at "9.1% annually in advance".

The APR does not necessarily convey the total amount of interest paid over the course of a year: if one pays part of the interest prior to the end of the year, the total amount of interest paid is less.

In the case of a loan with no fees, the amortization schedule would be worked out by taking the principal left at the end of each month, multiplying by the monthly rate and then subtracting the monthly payment. This can be expressed mathematically by

$p\; =\; \backslash frac\{P\_0*r^\{(n+1)\}\}\{\backslash sum\_\{l=1\}^n\; r^l\}$

where:

$P\_0$ is the initial principal

$r$ is the percentage rate used each payment

$n$ is the number of payments

This also explains why a 15 year mortgage and a 30 year mortgage with the same APR would have different monthly payments and a different total amount of interest paid. There are many more periods over which to spread the principal, which makes the payment smaller, but there are just as many periods over which to charge interest at the same rate, which makes the total amount of interest paid much greater. For example, $100,000 mortgaged (without fees, since they add into the calculation in a different way) over 15 years costs a total of $193,429.80 (interest is 93.430% of principal), but over 30 years, costs a total of $315,925.20 (interest is 215.925% of principal).