Business Mathematics: Buying - Cash Discounts

Cash discounts are discounts applied to bills which are paid within a specified period of time. They are given by large companies as an inducement to pay bills quickly.

Cash discounts are often listed under the heading terms on a bill or invoice.

For example, 2/10, net 30 (sometimes written 2/10, n/30) means that the customer is entitled to receive a 2% discount if the bill is paid within 10 days; otherwise the customer has 30 days to pay the bill at the invoice price.

After that there may be a late charge or interest may be imposed on the past due balance.

Delivery charges and other special fees are seldom included in a cash discount.

Example
An invoice of $520 dated April 1 has terms 2/10, net 30. What is the discount if the bill is paid on or before April 11? How much should the customer pay?

Discount = 2% of $520 = 0.02 × 520 = $10.40
The customer should pay $520.00 – $10.40 = $509.60. If the bill is paid between April 12 and May 1, the full $520 must be paid.
Sometimes a company will offer several different payment options. These must be clearly stated on the bill.

Example
Budget Press received a $720 bill from its paper supplier, dated August 1, with terms 3/10, 2/20,1/30, net/60. How much should Budget Press pay their supplier?

(a)  If the bill is paid on before August 11, the discount is 3% × $720 = $21.60. Budget Press should pay $720.00 – $21.60 = $698.40.
(b)  If the bill is paid between August 12 and 21, the discount is 2% × $720 = $14.40. They should pay $720.00 – $14.40 = $705.60.
(c)  If the bill is paid between August 22 and 31, the discount is 1% × $720 = $7.20. In this case $720 – $7.20 = $712.80 must be paid.
(d)  If the bill is paid between September 1 and 30, the full $720 is due.

Discount periods do not always start on the invoice date.

There are additional ways of stating the time a bill is due:


Example
An invoice for $5,000 in merchandise is dated July 27 and has credit terms 3/10,1/20, net 30 EOM. How much money should be paid if payment is received on (a) August 1? (b) August 15? (c) August 25?

(a)  Since the invoice is labeled EOM, the buyer has until August 10 to receive a 3% discount: 3% of $5,000 = 0.03 × $5,000 = $150; $5,000 – $150 = $4,850.
(b)  Since August 15 falls within 20 days of the end of July, the buyer is entitled to a 1% discount: 1% of $5,000 = $50; $5,000 – $50 = $4,950.
(c)  Since August 25 falls after the 20–day period starting on July 31, there is no discount. The buyer must pay the full invoice of $5,000.

Example
The list price of a meat-slicing machine is $780 with a trade discount of 22%. If the terms of the invoice are 2/10, net 30 ROG, how much should the butcher remit if he pays his bill within 10 days of receipt of the machine?

The butcher’s trade discount is 22%:
22% of $780 = 0.22 × 780 = $171.60
so he must pay
$780 – $171.60 = $608.40.

His discount for prompt payment is
2% of $608.40 = $12.17
so he must pay
$608.40 – $12.17 = $596.23.

It is a bit more convenient to think of this as a chain discount: 22% followed by 2%. His final payment is then computed:
(100% – 22%) × (100% – 2%) × $780 = 0.78 × 0.98 × $780 = $596.23

Solved Problems:

8.13   ABC Supply Company receives a bill for $7,200, dated June 15, with terms 5/10, net 30. How much must they pay if payment is made June 20?
 

Solution
Since June 20 is within 10 days of the invoice date, they are entitled to a 5% discount:
(100% – 5%) × $7,200 = 0.95 × $7,200 = $6,840

8.14   Jemco Plumbing Supply receives an invoice of $7,500 for copper pipe. Terms are 2/10,1/15, net 25. How much should Jemco pay if they send payment immediately on receipt of the invoice?
 

Solution
Since they send payment well before 10 days have elapsed, they are entitled to a 2% discount: (100% – 2%) × $7,500 = 0.98 × $7,500 = $7,350

8.15 Jacob’s Hardware received an invoice for $1,475 dated October 23 for nails and screws. The price included $25 for delivery. Terms were 4/10, 2/15, 1/20, net 30 EOM. How much should Jacob pay if his payment is received on (a) November 9 and (b) November 19?
 

Solution
(a)  Although November 9 is more than 10 days past the invoice date, EOM indicates that he has until November 10 to receive a 4% discount.

Delivery price is not included in the discount:
(100% – 4%) × $1,450 = 0.96 × $1,450 = $1,392
$1,392 + $25 = $1,417 (payment should be $1,417)
(b)  Since November 19 is within 20 days of the end of October, but more than 15 days, Jacob is entitled to a 1% discount:
(100% – 1%) × $1,450 = 0.99 × $1,450 = $1,435.50
$1,435.50 + $25 = $1,460.50 (payment should be $1,460.50)

8.16   On July 1, AAA Refrigeration Corp. paid two bills dated June 18. The first bill was for $3,000 with terms 3/10, 2/15, net 30 and the second was for $2,500 with terms 2/10, 1/20, net 30. If payment is to be made with one check, what should the payment amount be?
 

Solution
Since there are 30 days in June, the payment date, July 1, is more than 10, but less than 15 days past the invoice date, June 18. The discount on the first bill is 2%:
(100% – 2%) × $3,000 = 0.98 × $3,000 = $2,940

The discount on the second bill is 1%:
(100% – 1%) × $2,500 = 0.99 × $2,500 = $2,475
Payment amount = $2,940 + $2,475 = $5,415.

8.17   A carpeting retailer received an invoice in the amount of $6,875 dated September 15 which included $35 for shipping and $15 for special handling. Terms were 5/10, 2/20, net 30 ROG. If the goods were delivered on September 23, and the retailer pays the bill on October 1, how much should the retailer pay?
 

Solution
Since the payment date of October 1 is within 10 days of delivery, the retailer is entitled to a 5% discount on the cost of the goods only (not shipping or handling). The cost of the goods is $6,875 – $35 – $15 = $6,825:
(100% – 5%) × $6,825 = 0.95 × $6,825 = $6,483.75
The delivery and handling ($50 total) must be added to this amount, so the retailer must pay a total of $6,533.75.

8.18   ICT Computer Corp. ordered 15 computers with a list price of $990 each. They are entitled to a trade discount of 15% and an additional discount of 10% for quantity. They receive an invoice dated June 15 with terms 3/15, net 30. How much should they pay if their payment is made before July 1?
 

Solution
The total price of the order is 15 × $990 = $14,850. The two discounts, applied successively, bring their invoice total to
(100% – 15%) × (100% – 10%) × $14,850 = 0.85 × 0.90 × $14,850 = $11,360.25
Because they pay their bill within 15 days, they are entitled to an additional 3% discount:
(100% – 3%) × $11,360.25 = 0.97 × $11,360.25 = $11,019.44