Business Math Lab

Trade Discount Calculator: Step-by-Step Solution

Written by Ivan Daniel · Published · Updated · How we check the math

Enter the numbers from your problem and this trade discount calculator writes out every step: the formula, the numbers put into it, each multiplication or subtraction, and the answer rounded to the cent. It handles a single trade discount and series (chain) discounts such as 25/10/5, and it can work backward to the rate or the list price.

One rate, such as 15, or a chain separated by slashes, such as 25/10/5.

Check my answer

Worked it out on paper? Type your answer to compare it with the solution.

Step-by-step solution

Find the net price: list price $1,200.00 less 25/10/5.

Net price

$769.50

Trade discount
$430.50
Single equivalent discount rate
35.875%
Net price equivalent rate
0.64125

  1. Write the formulas

    • Net price equivalent rate = (1 − d₁) × (1 − d₂) × (1 − d₃)
    • Net price = List price × Net price equivalent rate
    • Single equivalent discount rate = 1 − Net price equivalent rate

  2. Find the complement of each discount

    • 100% − 25% = 75% = 0.75
    • 100% − 10% = 90% = 0.9
    • 100% − 5% = 95% = 0.95

  3. Multiply the complements to get the net price equivalent rate

    • 0.75 × 0.9 = 0.675
    • 0.675 × 0.95 = 0.64125
    • Net price equivalent rate = 0.64125 (the buyer pays 64.125% of the list price)

  4. Multiply the list price by the net price equivalent rate

    • $1,200.00 × 0.64125 = $769.50

  5. Find the single equivalent discount rate

    • 1 − 0.64125 = 0.35875
    • 0.35875 = 35.875%

  6. Find the trade discount amount

    • $1,200.00 − $769.50 = $430.50

  7. Why the discounts are not added

    • 25% + 10% + 5% = 40%, but the real discount is 35.875%: each discount is taken from the price that is left after the one before it.

What is a trade discount?

A trade discount is a reduction from the list price (the catalog or suggested price) that a manufacturer or wholesaler gives to business buyers such as retailers, contractors and distributors. The price the buyer actually pays is the net price. Consumers buying for their own use normally pay list price, which is why it is called a trade discount.

When a seller quotes more than one rate, such as 25/10/5, it is a series discount or chain discount: take 25% off the list price, then 10% off what is left, then 5% off what is left after that.

Trade discount formulas

Single trade discount

  • Trade discount = List price × Trade discount rate
  • Net price = List price − Trade discount
  • Net price = List price × (1 − Trade discount rate)
  • Trade discount rate = Trade discount ÷ List price
  • List price = Net price ÷ (1 − Trade discount rate)

Series (chain) discounts

  • Net price equivalent rate = (1 − d₁) × (1 − d₂) × (1 − d₃) …
  • Net price = List price × Net price equivalent rate
  • Single equivalent discount rate = 1 − Net price equivalent rate
  • Trade discount = List price − Net price
  • List price = Net price ÷ Net price equivalent rate

Here d₁, d₂ and d₃ are the discount rates written as decimals, so 25% is 0.25 and its complement is 1 − 0.25 = 0.75. Some textbooks call the net price equivalent rate the net price factor or the net decimal; it is the share of the list price the buyer still pays.

Why chain discounts are not added

It is tempting to read 25/10/5 as 40% off. It is not, because only the first discount is taken from the full list price. On a $1,200.00 list price:

A 25/10/5 chain discount applied one discount at a time to a $1,200.00 list price
DiscountTaken fromDiscount amountPrice left
25%$1,200.00$300.00$900.00
10%$900.00$90.00$810.00
5%$810.00$40.50$769.50

The total discount is $300.00 + $90.00 + $40.50 = $430.50, which is 35.875% of $1,200.00. Adding the rates would have given $1,200.00 × 0.60 = $720.00, which is $49.50 too low. The complement method gets the same $769.50 in one multiplication: $1,200.00 × 0.64125. The order of the discounts does not change the net price.

Trade discount vs cash discount

Differences between a trade discount and a cash discount
Trade discountCash discount
Why it is givenThe buyer is a business in the supply chainThe buyer pays the invoice early
Taken fromThe list priceThe net price on the invoice, after any trade discount
How it is writtenA rate or chain, such as 30% or 25/10/5Credit terms, such as 2/10, n/30
When it appliesBefore the invoice is writtenOnly if payment arrives within the discount period

Terms of 2/10, n/30 mean the buyer may take 2% off if it pays within 10 days of the invoice date; otherwise the full net price is due within 30 days. In a problem that has both, do the trade discount first and take the cash discount from the result with the cash discount calculator, which also counts the days and handles EOM, ROG and partial payments. Example 11 works one through.

In bookkeeping, sellers usually record a sale at the net price after the trade discount, so the trade discount does not appear as its own entry; cash discounts are commonly recorded when the customer takes them. Follow your course or accounting standard for journal entries.

Rounding rules used on this page

  • Interim results such as 0.64125 are kept exact; nothing is rounded halfway through.
  • Money is rounded to the nearest cent only when an amount is reported. Half a cent rounds up.
  • The trade discount is found as list price minus the rounded net price, so the two always add back to the list price.
  • A rate that does not end, such as 33.3333…%, is rounded to four decimal places.

If your instructor rounds the net price equivalent rate before multiplying, your answer may differ by a cent. The check-my-answer box treats a one-cent difference as a rounding difference, not a mistake.

Common mistakes

  • Adding chain discounts. 25/10/5 is 35.875% off, not 40%.
  • Reporting the discount as the net price. The net price is what is left after the discount.
  • Dividing by the net price to find the rate. The rate is always based on the list price.
  • Adding the rate back to find the list price. A $408.00 net price after 15% off is not $408.00 × 1.15 = $469.20; it is $408.00 ÷ 0.85 = $480.00.
  • Taking a cash discount from the list price. Take it from the net price after trade discounts.

Assumptions and limits

The calculator assumes each rate is a percent of the price left after the previous discount, which is how series discounts are quoted in business math courses. It does not handle freight, returns, sales tax, quantity breaks or cash discount dating (see the cash discount calculator); those change the invoice amount in ways a trade discount rate alone cannot capture. Amounts can have up to four decimal places and each rate must be more than 0% and less than 100%.

Sources and method

The formulas and the rounding approach follow the open textbook by Jean-Paul Olivier, Business Math: A Step-by-Step Handbook, section 6.1, “Figuring Out the Cost: Discounts” (Lyryx Learning, CC BY-NC-SA). The names net price equivalent rate and single equivalent discount rate are the terms used in many US business math courses.

Every number in the steps is computed with exact decimal arithmetic, in the browser and on the server, so you will not see results like 0.30000000000000004. Automated tests compare the solver's answers with hand-worked answers for every problem on the examples page and the worksheet.

Frequently asked questions

What is the formula for a trade discount?

Trade discount = List price × Trade discount rate, and Net price = List price − Trade discount. In one step: Net price = List price × (1 − rate). For example, a $480 list price less 15% gives a $72.00 trade discount and a $408.00 net price.

How do I find the trade discount rate?

Divide the trade discount amount by the list price, then multiply by 100. If you only know the net price, first subtract it from the list price to get the trade discount. A $240 list price and a $186 net price give a $54 discount, and $54 ÷ $240 = 0.225, or 22.5%.

Why is a 25/10/5 chain discount not 40% off?

Each discount in a chain is taken from the price left after the one before it, so the later discounts apply to smaller amounts. The buyer pays 0.75 × 0.90 × 0.95 = 0.64125 of the list price, so the single equivalent discount is 35.875%, not 40%.

Does the order of a chain discount matter?

No. Multiplication can be done in any order, so 25/10/5 and 5/10/25 give the same net price. Only the dollar amount of each individual discount changes with the order.

When do I round in trade discount problems?

Keep the net price equivalent rate and other interim results exact, and round money to the nearest cent only when you report an amount. If a percent does not end, round it to four decimal places. Some courses round the factor earlier, which can change the answer by a cent.

Is a trade discount the same as a cash discount?

No. A trade discount lowers the list price for a business buyer before the invoice is written. A cash discount, such as 2/10, n/30, is a reward for paying the invoice early and is taken from the net price after any trade discount.

Practice next