#### Definition:

Effective Annual Rate is used to find out the actual annual rate that would be paid on a loan if the specified annual rate is affected by compounding.

#### Formula:

i = [1 + (r/n)]^{n} - 1
###### Where,

r = Nominal Annual Interest Rate
n = Number of payments per year
i = Effective Interest Rate
#### Example :

Annual interest rate of a firm is 10% compounded monthly payments, then what is the effective interest rate of the firm?

##### Given,

Nominal Annual Interest Rate (r) = 10% = 0.1
Number of payments per year (n) = 12

##### To Find,

Effective Interest Rate

##### Solution :

Effective Interest Rate (i) = [1 + (r/n)]^{n} - 1
= [1 + (0.1/12)]^{12} - 1
= [1 + 0.008333]^{12} - 1
= 1.104713063 - 1
= 0.104713063 x 100
= 10.4713 %

##### Result :

Effective Annual Interest Rate is 10.4713 %