Question

Compute the cost of not taking the following trade discounts: (Use 365 days in a year. Round the intermediate calculations to 4 decimal places. Round the final answer to 2 decimal places.)

a. 2/13, net 50.

Cost of lost discount             %

b. 2/20, net 50.

Cost of lost discount              %

c. 3/18, net 65.

  

Cost of lost discount             %

d. 3/18, net 150.

  

Cost of lost discount             %

Answer 1

Solution :

a. 2/13, net 50           

The formula for calculating the cost of not taking the trade discount is

= [ Discount % / ( 100 – Discount % ) ] * [ 365 / ( Days allowed for payment - Discount period ) ]

As per the information given in the question we have

Discount % = 2 % ; Discount period = 13 ; Days allowed for payment = 50 days   ;

Applying the above values in the formula we have

= [ 2 / ( 100 – 2 ) ] * [ 365 / ( 50 – 13 ) ]

= ( 2 / 98 ) * (365 / 37 )

= 0.020408 * 9.864865 = 0.201324

= 0.201324 * 100 = 20.1324 %

= 20.13 % ( when rounded off to two decimal places )

Thus the cost of lost discount is = 20.13 %

b. 2/20, net 50

The formula for calculating the cost of not taking the trade discount is

= [ Discount % / ( 100 – Discount % ) ] * [ 365 / ( Days allowed for payment - Discount period ) ]

As per the information given in the question we have

Discount % = 2 % ; Discount period = 20 ; Days allowed for payment = 50 days   ;

Applying the above values in the formula we have

= [ 2 / ( 100 – 2 ) ] * [ 365 / ( 50 – 20 ) ]

= ( 2 / 98 ) * (365 / 30 )

= 0.020408 * 12.166667 = 0.248299

= 0.248299 * 100 = 24.8299 %

= 24.83 % ( when rounded off to two decimal places )

Thus the cost of lost discount is = 24.83 %

c. 3/18, net 65

The formula for calculating the cost of not taking the trade discount is

= [ Discount % / ( 100 – Discount % ) ] * [ 365 / ( Days allowed for payment - Discount period ) ]

As per the information given in the question we have

Discount % = 3 % ; Discount period = 18 ; Days allowed for payment = 65 days   ;

Applying the above values in the formula we have

= [ 3 / ( 100 – 3 ) ] * [ 365 / ( 65 – 18 ) ]

= ( 3 / 97 ) * (365 / 47 )

= 0.030928 * 7.765957 = 0.240184

= 0.240184 * 100 = 24.0184 %

= 24.02 % ( when rounded off to two decimal places )

Thus the cost of lost discount is = 24.02 %

d. 3/18, net 150

The formula for calculating the cost of not taking the trade discount is

= [ Discount % / ( 100 – Discount % ) ] * [ 365 / ( Days allowed for payment - Discount period ) ]

As per the information given in the question we have

Discount % = 3 % ; Discount period = 18 ; Days allowed for payment =150 days   ;

Applying the above values in the formula we have

= [ 3 / ( 100 – 3 ) ] * [ 365 / ( 150 – 18 ) ]

= ( 3 / 97 ) * (365 / 132 )

= 0.030928 * 2.765152 = 0.085520

= 0.085520 * 100 = 8.5520 %

= 8.55 % ( when rounded off to two decimal places )

Thus the cost of lost discount is = 8.55 %

Thus we have

a. 2/13, net 50.

Cost of lost discount = 20.13  %

b. 2/20, net 50.

Cost of lost discount = 24.83 %

c. 3/18, net 65.

Cost of lost discount = 24.02 %

d. 3/18, net 150.

Cost of lost discount = 8.55   %