Question

You are paying an effective annual rate of 18.75 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account? APR=

Answer 1

Solution:

The formula for calculating the Effective annual Interest rate is

EAR = [ [ 1 + ( APR / n) ] ⁿ ] -1

Where

APR = Annual Percentage Return ;   n = No. of compounding periods in one year = 12 months / Compounding period   ;

As per the Information given in the question we have

EAR = 18.75 % = 0.1875

Compounding periods = 1 month ( Since the compounding is monthly )

n = 12 / 1 = 12 ;

Applying the above values in the formula we have

0.1875 = [ [ 1 + (APR/12 ) ]¹² ] -1     

0.1875 + 1 = [ [ 1 + (APR/ 12) ] ¹² ]

1.1875 = [ 1 + (APR/ 12) ] ¹²

( 1.1875 ) ^1/12 = 1 + (APR/ 12)

( 1.1875 ) ^0.083333 = 1 + (APR/ 12)

1.014424 = 1 + (APR/ 12)

1.014424 - 1 = (APR/ 12)

0.014424 = (APR/ 12)

APR / 12 = 0.014424

APR = 0.014424 * 12

APR = 0.173087

APR = 17.3087 %

APR = 17.31 % (when rounded off to two decimal places )

Thus the APR = 17.31 % when the EAR is 18.75 % with monthly compounding.

Note : ( 1.1875 ) ^0.083333 is calculated using the excel function =POWER(Number,Power)

= POWER(1.1875,0.083333) = 1.014424