Eleven trade discount problems with full solutions, written the way they appear on
business math homework and exams. Each one lists what is given and what to find,
then works every step. They start with a single discount and build up to chain
discounts, working backward to the list price, comparing suppliers, and a trade
discount followed by a cash discount.
Formulas used in these examples
Trade discount = List price × Rate; Net price = List price − Trade discount
Rate = Trade discount ÷ List price
Net price equivalent rate = (1 − d₁) × (1 − d₂) × …; Net price = List price × Net price equivalent rate
Single equivalent discount rate = 1 − Net price equivalent rate
List price = Net price ÷ Net price equivalent rate
Rounding: interim values stay exact; money is rounded to the nearest cent at the end.
Example 1 · Basic
Find the trade discount and net price
Harbor Office Supply lists an ergonomic desk chair at $360. Office furniture dealers receive a 30% trade discount. Find the trade discount and the net price a dealer pays.
List price
$360.00
Trade discount rate
30%
Find
Trade discount and net price
Solution
Write the formulas
Trade discount = List price × Trade discount rate
Net price = List price − Trade discount
Change the rate to a decimal
30% = 30 ÷ 100 = 0.3
Find the trade discount
$360.00 × 0.3 = $108.00
Subtract the trade discount from the list price
$360.00 − $108.00 = $252.00
Check with the complement method
Complement of the rate: 100% − 30% = 70% = 0.7
$360.00 × 0.7 = $252.00
Same net price: $252.00
Answer: Trade discount = $108.00; net price = $252.00.
A lighting wholesaler's catalog lists a pack of LED shop lights at $240. An electrical contractor's invoice for the pack shows a net price of $186. What trade discount rate did the contractor get?
List price
$240.00
Net price
$186.00
Find
Trade discount rate
Solution
Write the formulas
Trade discount = List price − Net price
Trade discount rate = Trade discount ÷ List price
Find the trade discount
$240.00 − $186.00 = $54.00
Divide the trade discount by the list price
$54.00 ÷ $240.00 = 0.225
Change the decimal to a percent
0.225 × 100 = 22.5%
Answer: The trade discount is $54.00, so the rate is 22.5%.
The list price of a commercial blender is $1,150. A café owner buying through a restaurant supply account gets a trade discount of $230. Find the trade discount rate and the net price.
List price
$1,150.00
Trade discount
$230.00
Find
Trade discount rate and net price
Solution
Write the formula
Trade discount rate = Trade discount ÷ List price
Divide the trade discount by the list price
$230.00 ÷ $1,150.00 = 0.2
Change the decimal to a percent
0.2 × 100 = 20%
Find the net price
$1,150.00 − $230.00 = $920.00
Answer: Trade discount rate = 20%; net price = $920.00.
A paint distributor sells a pallet of exterior paint to hardware stores at a list price of $2,450 less a chain discount of 20/10. Find the net price, the trade discount and the single equivalent discount rate.
List price
$2,450.00
Chain discount
20/10
Find
Net price, trade discount, single equivalent discount rate
Solution
Write the formulas
Net price equivalent rate = (1 − d₁) × (1 − d₂)
Net price = List price × Net price equivalent rate
Single equivalent discount rate = 1 − Net price equivalent rate
Find the complement of each discount
100% − 20% = 80% = 0.8
100% − 10% = 90% = 0.9
Multiply the complements to get the net price equivalent rate
0.8 × 0.9 = 0.72
Net price equivalent rate = 0.72 (the buyer pays 72% of the list price)
Multiply the list price by the net price equivalent rate
$2,450.00 × 0.72 = $1,764.00
Find the single equivalent discount rate
1 − 0.72 = 0.28
0.28 = 28%
Find the trade discount amount
$2,450.00 − $1,764.00 = $686.00
Why the discounts are not added
20% + 10% = 30%, but the real discount is 28%: each discount is taken from the price that is left after the one before it.
Answer: Net price = $1,764.00; trade discount = $686.00; single equivalent discount rate = 28%.
A manufacturer offers distributors a chain discount of 30/20/10. A new buyer assumes this is the same as 60% off. Using a list price of $500, show that it is not, and find the single equivalent discount rate.
Net price = List price × Net price equivalent rate
Single equivalent discount rate = 1 − Net price equivalent rate
Find the complement of each discount
100% − 30% = 70% = 0.7
100% − 20% = 80% = 0.8
100% − 10% = 90% = 0.9
Multiply the complements to get the net price equivalent rate
0.7 × 0.8 = 0.56
0.56 × 0.9 = 0.504
Net price equivalent rate = 0.504 (the buyer pays 50.4% of the list price)
Multiply the list price by the net price equivalent rate
$500.00 × 0.504 = $252.00
Find the single equivalent discount rate
1 − 0.504 = 0.496
0.496 = 49.6%
Find the trade discount amount
$500.00 − $252.00 = $248.00
Why the discounts are not added
30% + 20% + 10% = 60%, but the real discount is 49.6%: each discount is taken from the price that is left after the one before it.
Answer: Net price = $252.00, so the real discount is $248.00, a single equivalent discount rate of 49.6%. A flat 60% off would have left a net price of $200.00.
Find the list price from the discount amount (20/15)
An auto parts wholesaler's invoice shows a total trade discount of $543.20 on an order sold at a chain discount of 20/15. Find the list price and the net price of the order.
Supplier A sells an office printer at a list price of $780 less 25/15. Supplier B lists the same printer at $750 less 20/10/5. Which supplier has the lower net price, and by how much?
Supplier A
$780.00 less 25/15
Supplier B
$750.00 less 20/10/5
Find
The lower net price and the difference
Solution
Supplier A
Write the formulas
Net price equivalent rate = (1 − d₁) × (1 − d₂)
Net price = List price × Net price equivalent rate
Single equivalent discount rate = 1 − Net price equivalent rate
Find the complement of each discount
100% − 25% = 75% = 0.75
100% − 15% = 85% = 0.85
Multiply the complements to get the net price equivalent rate
0.75 × 0.85 = 0.6375
Net price equivalent rate = 0.6375 (the buyer pays 63.75% of the list price)
Multiply the list price by the net price equivalent rate
$780.00 × 0.6375 = $497.25
Find the single equivalent discount rate
1 − 0.6375 = 0.3625
0.3625 = 36.25%
Find the trade discount amount
$780.00 − $497.25 = $282.75
Why the discounts are not added
25% + 15% = 40%, but the real discount is 36.25%: each discount is taken from the price that is left after the one before it.
A furniture store orders sofas with a list price of $4,200 less 20/10. The invoice is dated March 3 with terms 2/10, n/30, and the store pays on March 11. How much does the store pay?
List price
$4,200.00
Chain discount
20/10
Terms
2/10, n/30; invoice March 3, paid March 11
Find
Amount paid
Solution
Trade discount first
Write the formulas
Net price equivalent rate = (1 − d₁) × (1 − d₂)
Net price = List price × Net price equivalent rate
Single equivalent discount rate = 1 − Net price equivalent rate
Find the complement of each discount
100% − 20% = 80% = 0.8
100% − 10% = 90% = 0.9
Multiply the complements to get the net price equivalent rate
0.8 × 0.9 = 0.72
Net price equivalent rate = 0.72 (the buyer pays 72% of the list price)
Multiply the list price by the net price equivalent rate
$4,200.00 × 0.72 = $3,024.00
Find the single equivalent discount rate
1 − 0.72 = 0.28
0.28 = 28%
Find the trade discount amount
$4,200.00 − $3,024.00 = $1,176.00
Why the discounts are not added
20% + 10% = 30%, but the real discount is 28%: each discount is taken from the price that is left after the one before it.
Subtract the cash discount from the invoice amount
$3,024.00 − $60.48 = $2,963.52
March 11 is 8 days after March 3, inside the 10-day discount period, so the 2% cash discount applies. The cash discount is taken from the net price after the trade discount, never from the list price.
Answer: The store pays $2,963.52 (net price $3,024.00 less a $60.48 cash discount).
Problems and businesses on this page are original practice problems written for
Business Math Lab. Answers are checked by automated tests against the solver.