# Effective interest rate calculator

Effective annual interest rate or annual equivalent rate calculator.

 Nominal annual interest rate: % per year Compounding period: Days Weeks Months Quarters Other Compounding periods per year: Effective period interest rate: % per month Effective annual interest rate: % per year

## Effective interest rate calculation

### Effective period interest rate calculation

So The effective period interest rate is equal to the  nominal annual interest rate divided by the number of periods per year  n:

Effective Period Rate = Nominal Annual Rate / n

#### Example 1

What is the effective period interest rate for nominal annual interest rate of 3% compounded monthly?

Solution:

Effective Period Rate = 3% / 12months = 0.03 / 12 = 0.250%

#### Example 2

What is the effective period interest rate for nominal annual interest rate of 7% compounded monthly?

Solution:

Effective Period Rate = 7% / 12months = 0.07 / 12 = 0.583%

#### Example 3

What is the effective period interest rate for nominal annual interest rate of 9% compounded monthly?

Solution:

Effective Period Rate = 9% / 12months = 0.9 / 12 = 0.750%

### Effective annual interest rate calculation

So The effective annual interest rate is equal to 1 plus the nominal interest rate in percent divided by the number of compounding persiods per year n, to the power of n, minus 1.

Effective Rate = (1 +  Nominal Rate /  n)n - 1

#### Example 1

What is the effective annual interest rate for nominal annual interest rate of 3% compounded monthly?

Solution:

Effective Rate = (1 + 3% / 12)12 - 1

= (1 + 0.03 / 12)12 - 1

= 0.03042 = 3.042%

#### Example 2

What is the effective annual interest rate for nominal annual interest rate of 7% compounded monthly?

Solution:

Effective Rate = (1 + 7% / 12)12 - 1

= (1 + 0.07 / 12)12 - 1

= 0.07229 = 7.229%

#### Example 3

What is the effective annual interest rate for nominal annual interest rate of 9% compounded monthly?

Solution:

Effective Rate = (1 + 9% / 12)12 - 1

= (1 + 0.9 / 12)12 - 1

= 0.09381 = 9.381%

Effective interest rate calculation ►

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