# What is the Effective Annual Rate?

The effective annual rate of a loan is an expression of simple interest that estimates the actual effect of compound interest. This concept is a bit complicated because it involves some high level math.

Compound Interest

Compound interest is charged on most credit cards and mortgage loans. This means that interest charged in one payment term that is not resolved adds to the principal of the loan. Interest is charged again the next payment term, and interest is charged on the unpaid interest.

Simple Interest

Simple interest does not compound month-to-month. A principal has interest assessed against it one time. The next payment term, interest is only assessed against any new balance. This is not common on credit cards, but it is common on installment debt. This can make deciding between two forms of loans complicated. They are being expressed in different terms, and you need a common factor in order to effectively compare them.

Effective Annual Rate

The effective annual rate is the common term you can use to compare two loans. It is calculated by using the equation:

• ieff = (1 + r/k)k - 1
• Effective annual rate = (1 + rate/number of times rate compounds in a year) ^ number of times rate compounds in a year - 1

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