An overdraft is available at a quoted rate of 12% per annum with interest charged on a monthly basis. What is the annual effective rate?

Select one:

a. 10.64%

b. 12.68%

c. 12.00%

d. 24.13%

Solution :

As per the information given in the question we have

Annual rate of Interest on the overdraft = 12 %

Thus the Monthly rate of Interest on the overdraft = 12 % / 12

= 1 % = 0.01

The formula for calculating the annual effective rate is

AER = ( 1 + m ) ¹² - 1

Where

m = Monthly Interest rate of the loan = 1 % = 0.01 ; n = No. of months in a year =12

Applying the available information in the formula we have Annual effective rate as

AER = ( 1 + 0.01 ) ¹² – 1

= ( 1.01 ) ¹² – 1

= 1.126825 – 1

= 0.126825

= 12.6825 %

= 12.68 % ( when rounded off to two decimals )

Thus the annual Effective Rate of the loan = 12.68 %

The solution is option b.12.68 %

Note: ( 1.01 ) ^{( 12)}   is calculated using the excel function =POWER(Number,Power)

=POWER(1.01,12) = 1.126825