# How to calculate effective interest rate

Effective interest rate calculation.

### Effective period interest rate calculation

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

What is the effective period interest rate for nominal annual interest rate of 5% compounded monthly?

Solution:

*Effective Period Rate* = 5% / 12months =
0.05 / 12 = 0.4167%

### Effective annual interest rate calculation

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

What is the effective annual interest rate for nominal annual interest rate of 5% compounded monthly?

Solution:

*Effective Rate* = (1 + 5% / 12)^{12}
- 1

= (1 + 0.05 / 12)^{12}
- 1

= 0.05116 = 5.116%

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