Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.
It is used to compare the yearly interest between loans with different compounding periods like week, month, year, etc. The effective interest rate differs in two important respects from the annual percentage rate (APR):
By contrast, the effective APR is used as a legal term, where front-fees and other costs can be included, as defined by local law.
Annual percentage yield or effective annual yield is the analogous concept used for savings or investment products, such as a certificate of deposit. Since any loan is an investment product for the lender, the terms may be used to apply to the same transaction, depending on the point of view.
Effective annual interest or yield may be calculated or applied differently depending on the circumstances, and the definition should be studied carefully. For example, a bank may refer to the yield on a loan portfolio after expected losses as its effective yield and include income from other fees, meaning that the interest paid by each borrower may differ substantially from the bank's effective yield.
The effective interest rate is calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective annual rate, i the nominal rate, and n the number of compounding periods per year (for example, 12 for monthly compounding):
For example, a nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. 6% compounded monthly is credited as 6%/12 = 0.005 every month. After one year, the initial capital is increased by the factor (1 + 0.005)12 ≈ 1.0617.
When the frequency of compounding is increased up to infinity the calculation will be:
The yield depends on the frequency of compounding:
The effective interest rate is a special case of the internal rate of return.
...
Wikipedia