Question

A firm offers credit terms of 3/10, net 35. What is the effective annual rate on the credit extended if a customer foregoes the discount on a $10,000 purchase? Assume that there are 365 days in one year. (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 = 35 days ; Period for which discount has been offered = 10 days ;

Total payment Period – period for which discount has been offered = 35 - 10 = 25 days ;

Applying the above values in the formula we have

= ( 1 + ( 0.03 / (1 – 0.03 )) ^{( 365 / 25)}   - 1                         

= ( 1 + ( 0.03 / 0.97 )) ^{( 365 / 25 )}   - 1                                

= ( 1 + 0.030928 ) ^{( 14.60 )}   - 1                                   

= ( 1.030928 ) ^{(14.60 )}   - 1

= 1.560029 – 1 = 0.560029

= 56.0029 %                                                                            

= 56.00 % ( when rounded off to two decimal places )    

Thus the effective annual rate on the credit extended if the customer forgoes the discount is = 56.00 %      

Note : ( 1.030928 ) ^{( 14.60 )}   is calculated using the excel formula =POWER(Number,Power)

=POWER(1.030928,14.60) = 1.560029