Business Mathematics: Buying - Partial Payments

Situations often occur where a buyer wants to pay a bill early in order to receive a discount, but does not have sufficient funds to pay the bill in its entirety. In this case, the buyer will make a partial payment and receive a discount on a portion of the bill. The buyer’s account will be credited and the difference will be owed.

To determine how much money to credit the account, we must compute how much of the balance is actually paid off by the discounted payment.

Example
An invoice of $4,500 is sent to a buyer on July 5 with terms 3/10, net 30. The buyer, unable to pay the full amount within 10 days, makes a partial payment of $2,500 on July 12. What is the balance due on the account after payment is made?

Since the buyer makes the payment within 10 days of the invoice date, she is entitled to a 3% discount. The amount paid, therefore, represents 97% (100% –3%) of the amount to be credited. If we let x represent the amount to be credited to her account, 97% of x = $2,500:

Thus $2,577.32 is credited to the buyer’s account. The amount owed is $4,500 – $2,577.32 = $1,922.68.

Example
Let us determine how much money the buyer in Example 16 saved by making her partial payment early. Since she paid $2,500 and presumably paid the balance of $1,922.68 within 30 days of the invoice date, she has paid a total of $2,500.00 + $1,922.68 = $4,422.68. She has saved $4,500.00 – $4,422.68 = $77.32.

Solved Problems

8.19   Leonard receives a bill for $3,000 with terms 5/10, net 30. How much credit will he receive if he pays half the bill within 10 days?
 

Solution
Let x represent the credit he will receive. Since he pays $1,500 early, he is entitled to a 5% discount. Since he actually pays 95% (100% – 5%) of x, we have

Leonard receives a credit on his account of $1,578.95.

8.20 Betty’s Dress Shop usually likes to pay its bills early to take advantage of discounts. On July 1, Betty receives a bill from one of her suppliers for $3,700 with terms 3/10, 2/20, net 30. What will her balance be if she makes a partial payment of $2,000 on (a) July 9 and (b) July 15?
 

Solution
(a)  If Betty pays her bill within 10 days, she is entitled to a 3% discount on the amount paid. We let x represent the amount of the balance to be credited to her account. Since she actually pays only 97% of this amount, we have

Her account is credited $2,061.86. Her balance due is $3,700 – $2,061.86 = $1,638.14.
(b)  On July 15, she is only entitled to a 2% discount. Since she pays 98% of the amount due:

Her account is credited $2,040.82. Her balance due is $3,700.00 – $2,040.82 = $1,659.18.

8.21   Peter’s Steak House receives a bill dated April 10, from their meat supplier, in the amount of $4,200. Terms are 4/10, 2/20, net 30. On April 15 Peter pays $1,500 and on April 23 he pays another $1,000. How much must he then pay to clear his debt?
 

Solution
Since he pays the $1,500 before 10 days, he is entitled to a 4% discount. If x represents the credit he will receive on his account, since he pays only 96% of x, we have

His balance due is $4,200 – $1,562.50 = $2,637.50. Now he pays $1,000 but is entitled to only a 2% discount. Let y represent the credit he will receive for that payment:

This further reduces his balance to $2,637.50 – $1,020.41 = $1,617.09. This is the amount due before 30 days.

More Problems:

8.22 (a) Compute the discount on a $275 typewriter offered at a 10% discount rate. (b) What is the sale price?
8.23 What is the trade discount on a prefabricated fireplace which has a list price of $1,700 given a discount rate of 15%?
8.24 A manufacturer of crystal chandeliers offers a 40% discount to interior decorators and a 15% discount to consumers who visit their retail outlet. If a particular chandelier has a list price of $1,300, how much will it cost (a) an interior decorator and (b) a consumer?
8.25 A shipment of books had a list price of $2,140 but was sold to a bookseller for $1,819. What was the trade discount rate?
8.26 A sofa with a list price of $575 is offered to a decorator for $460. What was the discount rate?
8.27 An armoire had a sale price of $280. If it was discounted 30%, what was its original list price?
8.28 Don paid $333.75 for a new VCR and three videotapes. The VCR was on sale at a discount of 15%, but the videotapes were not. If each videotape cost $5.00, what was the list price of the VCR?
8.29 A new automobile has a price of $24,500. Of this amount $2,800 are options which were added on by the dealer. If the dealer discounts the base price of the car by 20%, but not the options, what is the sale price of the automobile?
8.30 Which costs less: a wool suit which lists for $450 but is put on sale at an 18% discount or a cotton blend which lists for $500 but is given a 22% discount?
8.31 Macy’s sells a men’s suit for $450 less 25%. Saks sells the identical suit for $475 less discounts of 20% and 10%. Which store has the suit for a lower price?
8.32 Chicken feed sells for $1.50 a pound. Farmer Gray buys 750 lb of chicken feed. How much must he pay if he is given a 7% farm cooperative discount and a 5% discount for quantity?
8.33 A liquor store discounts its entire stock by 20%. Furthermore, if you buy a case of wine, you receive an additional 10% discount. How much will a case (12 bottles) of Chardonnay, which lists for $12 a bottle, cost?
8.34 What is the net price of a bowling ball which lists for $95, is put on sale for 10% off, and then put on clearance for an additional 20% off?
8.35 A piano originally costs $5,000. It is given successive discounts of 30 and 45%. Verify that the final selling price is the same regardless of the order in which the discounts are taken.
8.36 A snowblower is sold at a discount store at 15% off list price. On March 1, the store manager puts it on sale for an additional 20% off. What is the single equivalent discount for the snowblower?
8.37 Which will lead to a lower price for the consumer?
(a)  A 10% discount followed by a 40% discount
(b)   A 20% discount followed by a 30% discount
(c)  Two successive 25% discounts
8.38 What is the single equivalent discount for a tennis racket which is given successive discounts of 10% and 20%?
8.39 A-l Home Improvements received a delivery of aluminum siding listing for $1,750. The company receives a 15% trade discount and, because they are such a good customer, an additional 10% discount for quantity. Furthermore, they pay their bill within 5 days, so they receive an additional 5% off. How much money should A-l pay their supplier?

8.40 What is the single equivalent discount of successive 10%, 15%, and 20% discounts?

8.41 The Swiss Ski Shop pays $2,422.50 after receiving successive discounts of 15% and 25% for an order of ski equipment. What was the list price of the equipment received?

8.42 An invoice of $470 dated October 17 has terms 2/10,1/20, net 30. How much would a buyer be expected to pay if the bill is paid on (a) October 22 and (b) November 1?

8.43 A delicatessen received a bill for $1,700 from its food supplier dated May 27. Its terms were 4/10, 2/20, net 30 EOM. How much would the owner have to pay if the bill is paid on (a) June 5, (b) June 15, and (c) June 28?

8.44 A shipment of furniture is sent from a North Carolina factory to the Empire Furniture Store on May 10. The invoice of $12,000 with terms 5/10, 3/20, net 30 ROG arrives on May 13, but the furniture is not received until May 20. If the furniture dealer pays the bill on May 25, how much money must he pay the factory?

8.45 A businesswoman decides to pay her bill early and receive a discount only if her discount amounts to $50 or more. She receives a bill for $1,700 with terms , net 30. Should she pay the bill within 10 days?

8.46 A health club buys a new rowing machine which has a list price of $2,500. Because they are a good customer, the club receives a 12% trade discount. The terms of the invoice are 2/15, net 30. How much must the club pay for the machine if they pay the bill within 12 days of receipt?

8.47 An invoice of $7,000 is sent to Beverly’s Beauty Shop on August 1 with terms 5/10, net 30. Beverly pays $3,000 on August 6.
(a)  How much must she pay at the end of the month?
(b)  How much did Beverly save by making an early partial payment?

8.48 Barney is having business trouble, so when he receives a $15,000 bill on July 10 with terms 2/15, net 30, he decides to pay one-third of the bill on July 20 and the balance on July 30. How much must he send on July 30?

8.49 Melissa receives an invoice for $3,000 with terms 2/10, net 30. How much money will Melissa save if she pays $1,200 within 10 days and the balance 20 days later?

8.50 Crazy Harry’s Electronics store receives an invoice on February 1 for $17,000 worth of TVs. Terms are 5/5, 3/15, net 30. Harry makes a payment of $5,000 on February 5 and another $5,000 payment on February 15. If he wants to pay his balance in full on February 28, how much money must he send?

8.51 Which payment sequence is most advantageous for a building supply retailer who receives a bill on April 1 for $60,000 with terms 4/10, 2/15, net 30?
(a)  Pay $30,000 on April 15 and the balance on April 30
(b)  Pay $20,000 on April 10, $20,000 on April 15, and the balance on April 30
(c)  Pay the bill in full on April 15

Answers to Above Problems:

8.22 (a) $27.50, (b) $247.50
8.23 $255
8.24 (a) $780, (b) $1,105
8.25 15%
8.26 20%
8.27 $400
8.28 $375
8.29 $20,160
8.30 The wool suit
8.31 Macy's
8.32 $993.94
8.33 $103.68
8.34 $68.40
8.35 Either way, the price is $1,925
8.36 32%
8.37 (a)
8.38 28%
8.39 $1,271.81
8.40 38.8%
8.41 $3,800
8.42 (a) $460.60, (b) $465.30
8.43 (a) $1,632, (b) $1,666, (c) $1,700
8.44 $11,400
8.45 No; her savings are only $42.50
8.46 $2,156
8.47 (a) $3,842.11, (b) $157.89
8.48 $9,897.96
8.49 $24.49
8.50 $6,582.20
8.51 (b)