# Calculate the Effective Annual Interest Rate

By Stock Research Pro • June 28th, 2009

The effective annual interest rate refers to the rate of interest when compounding is applied more than once per year. The effective annual interest rate is used to annualize the interest rate after taking into account the effects of compounding. The concept of an effective annual interest rate is important for anyone who carries debt that compounds more than once a year to understand.

#### Nominal Interest Rate v. Effective Annual Interest Rate

The nominal or “stated” interest rate is the periodic interest rate multiplied by the number of periods per year. You cannot compare nominal interest rates unless they have the same compounding period and a nominal rate is not fully defined without its compounding frequency. The effective annual interest rate enables borrowers and investors to effectively compare loans or investments. This calculator enables you to arrive at the effective annual interest rate either by inputting the periodic or the nominal interest rate. The calculator assumes monthly compounding.

#### Calculating the Effective Annual Interest Rate

The formula for the effective annual interest rate can be written as:

##### Effective Annual Interest Rate = (1+i/n)^n -1

Where:

i = nominal annual rate of interest
n= number of compounding periods in one year

Because the effective annual interest rate accounts for compounding, it is usually higher than the stated or nominal annual interest rate. The effective annual interest rate calculation is useful to evaluate the real return on an investment or the real interest rate to be paid on a loan.

#### A Monthly Compounding Example

A nominal interest rate of 5% with monthly compounding is equal to an effective annual interest rate of 5.12%. 5% is credited annually as 5%/12 = 0.5% each month. After a year, the initial capital increases by the factor (1+0.005)12.

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The above information is educational and should not be interpreted as financial advice. For advice that is specific to your circumstances, you should consult a financial or tax advisor.

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