# How to calculate effective interest rate

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 4% compounded monthly?

Solution:

*Effective Period Rate* = 4% / 12months = 0.04 / 12 = 0.333%

#### Example 2

What is the effective period interest rate for nominal annual interest rate of 6% compounded monthly?

Solution:

*Effective Period Rate* = 6% / 12months = 0.06 / 12 = 0.500%

#### Example 3

What is the effective period interest rate for nominal annual interest rate of 10% compounded monthly?

Solution:

*Effective Period Rate* = 10% / 12months = 0.10 / 12 = 0.833%

### 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 4% compounded monthly?

Solution:

*Effective Rate* = (1 + 4% / 12)^{12} - 1

= (1 + 0.04 / 12)^{12} - 1

= 0.04074 = 4.074%

#### Example 2

What is the effective annual interest rate for nominal annual interest rate of 6% compounded monthly?

Solution:

*Effective Rate* = (1 + 6% / 12)^{12} - 1

= (1 + 0.06 / 12)^{12} - 1

= 0.06168 = 6.168%

#### Example 3

What is the effective annual interest rate for nominal annual interest rate of 10% compounded monthly?

Solution:

*Effective Rate* = (1 + 10% / 12)^{12} - 1

= (1 + 0.10 / 12)^{12} - 1

= 0.04074 = 10.471%

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## See also