Business Mathematics: Buying - Trade Discounts

When merchandise is offered for sale, a list price or catalog priceis determined for the item being sold. Often a manufacturer’s suggested retail price is printed on the item’s packaging or in advertisements. These, however, are only suggested prices and are often reduced significantly when the merchandise is actually sold.
 

Trade discounts are commonly used in trade industries. A plumber or electrician, for example, is usually able to purchase supplies at a much lower price than the consumer.

Discounts are frequently given for large quantities of an item purchased or as incentives to sell older merchandise.

The advantage of using discounts is that the manufacturer can print one catalog or price sheet for merchandise being sold to different classes of buyers.

Prices to wholesalers, retailers, and consumers, for example, can be changed by simply adjusting the discount rate.

Discount rates are expressed as decimals or percentages. The dollar amount of the discount is computed by a simple formula. To compute the net price for the item, subtract the discount from the list price of the item.

Amount of discount = discount rate × list price


Example
Compute the discount and net price for a $250 television set offered at a 16% discount rate.

The discount is $40. The net price for the television is $250 – $40 = $210.


Example
A manufacturer of plumbing fixtures labels a sink with a list price of $300. His wholesaler gets a 50% discount, a plumber gets a 40% discount, and a consumer gets a 15% discount. How much will each pay for the sink?

The complement of a discount rate is the discount rate subtracted from 100%. Thus the complement of a 35% discount would be 100% – 35% = 65%. While a discount rate can be viewed as a percentage “off” the price of an item, the complement of a discount rate is viewed as the percentage of the list price actually paid for the item. The net price for the item can be more conveniently computed by the formula
Net price = (100% – discount rate) × list price

Example
Use complements to compute the prices paid for the sink of Example 2.
Amount paid by wholesaler = (100% – 50%) × $300 = 0.50 × $300 = $150
Amount paid by plumber = (100% – 40%) × $300 = 0.60 × $300 = $180
Amount paid by consumer = (100% – 15%) × $300 = 0.85 × $300 = $255

Since amount of discount = discount rate × list price, it follows that

Similarly, since net price = (100% – discount rate) × list price, it follows that


Example
Compute the discount rate for a $450 lamp which is sold for $315. The actual discount is $450 – $315 = $135:

Expressed as a percentage, the discount rate is 30%.

Example
Compute the list price of a telephone assuming that a 25% discount was worth $20:


Example
Compute the list price of a fax machine whose net price is $195 if it sold at a 35% discount:


Solved Problems:

8.1 Compute the discount on an office desk which lists for $240 if a discount of 10% is offered.
 

Solution
Discount = 10% of $240 = 0.10 × $240 = $24.

8.2 Compute the net price for a painting whose list price is $172 and is offered on sale for 20% off.
 

Solution


8.3 A VCR with a list price of $340 went on sale for “25% off.” An extended warranty, which was not on sale, sold for $17. How much did George pay (before tax) when he bought both the VCR and extended warranty?
 

Solution


8.4 A lamp which normally sells for $180 was purchased by a consumer for $120. How much of a discount did the consumer receive?
 

Solution


8.5 Jane spent $150 on a printer on sale for 15% off list price. What was the list price of the printer?
 

Solution

Thus


8.6 Which actually costs less: a $300 coil of 10-gage wire which is offered with a trade discount of 40% or a $450 coil of 12-gage wire which is offered with a trade discount of 65%?
 

Solution