Question

A firm offers credit terms of 3/12, net 45. What is the effective annual rate on the credit extended if a customer foregoes the discount on a $10,000 purchase? (Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit the % sign in your response. For example, an answer of 15.39% should be entered as 15.39.)

Answer 1

Solution :

The formula for calculating the effective annual rate of forgoing the discount is

= [ ( 1 + [Discount rate / (1 – Discount Rate )] ) ⁿ ] – 1

Where n= No. of days in a year / ( Total payment Period – period for which discount has been

offered)

As per the information given in the question we have

Discount rate = 3 % = 0.03   ; No. of days in a year = 365 days ;

Total payment Period = 45 days ; Period for which discount has been offered = 12 days ;

Total payment Period – period for which discount has been offered = 45 - 12 = 33 days

Applying the above values in the formula we have

= [ ( 1 + ( 0.03 / (1 – 0.03 )) ^{( 365/33 )} ] - 1                         

= [ ( 1 + ( 0.03 / 0.97 )) ^{( 365 / 33 )} ] - 1                                

= [ ( 1 + 0.030928 ) ^{( 11.060606 )} ] - 1                                   

= [ ( 1.030928 ) ^{(11.060606 )} ] - 1

= 1.400595 – 1 = 0.400595

= 40.0595 %                                                                            

= 40.06 % ( when rounded off to two decimal places )    

Thus the effective annual rate of forgoing the discount is = 40.06 %      

Note : ( 1.030928 ) ^{( 11.060606 )}   is calculated using the excel formula =POWER(Number,Power)

=POWER(1.030928,11.060606) = 1.400595