WealthWiseGuys Practical Mathematics

Chapter 7

Trade Discounts, Cash Discounts, and Purchasing

From a supplier list price to the actual cost of an order

A low advertised price is only one part of a purchasing decision. Learn to read discount terms, account for returns and freight, and compare complete orders. All vendors, prices, dates, and terms are hypothetical; round each monetary discount and tax to cents, with a half cent rounded up.

7.1

Trade Discounts and Discount Series

Learning objectives

After this section you will be able to:

  1. Find a net price after a trade discount.
  2. Apply a series of trade discounts in order.
  3. Calculate a single equivalent discount.

Real-life situation

A club buys event supplies

Use this hypothetical Philadelphia-area scenario to connect the calculation to a decision. All people, businesses, amounts, and rates in this chapter are invented; tax and payroll rules are teaching assumptions, not current law.

A club buys event supplies

  • Supplier list price: $800.00
  • Trade discounts: 25%, then 10%
  • Net merchandise price: $540.00
Figure 7.1 A club buys event supplies (hypothetical)

The concept

A trade discount reduces a supplier list price before the invoice amount is established. It may reflect a buyer category or order arrangement. A list price is a reference price, not necessarily the amount that any particular buyer pays.

For one discount, multiply list price by the discount rate and subtract that amount. The complementary rate, 1 minus the decimal discount rate, is the net price factor. Multiplying by this factor gives the same result before any rounding differences.

A discount series applies each discount to the price remaining after the previous discount. A 25% and 10% series does not mean 35% off. The second discount has a smaller base. On an $800 order, the discounts are $200 and $60, not $200 and $80.

The product of the net price factors gives the series net factor. Subtract it from 1 to find an equivalent single discount. This equivalent rate compares offers clearly, but actual invoices should follow the stated cent-rounding procedure for each discount. Freight and tax remain separate unless the contract says otherwise.

Successive discounts use a changing base

List price$ 800
After 25% off$ 600
After another 10% off$ 540

Bars share a zero baseline.

Figure 7.1.V Successive discounts use a changing base. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • invoice

    A document listing goods or services sold and the amount owed.

  • payment terms

    The rules in an agreement about when a bill must be paid and any discounts for paying early.

  • discount

    An amount taken off a regular price.

Key terms

List price
Supplier reference price before trade discounts.
Trade discount
Price reduction used to establish the merchandise invoice price.
Net price
Merchandise amount remaining after trade discounts.
Net price factor
Fraction of a price left after discounts.
Equivalent discount
One discount rate matching a discount series before rounding.

Formulas & rules

  • Single discount

    Net price = list price × (1 − decimal discount rate)

  • Series factor

    Net factor = (1 − d1) × (1 − d2)

  • Equivalent discount

    Equivalent decimal discount = 1 − net factor

Worked examples

Example 1One trade discount

A $600 supply order receives a 20% trade discount. Find its net merchandise price.

Solution

  1. 1Convert 20% to 0.20.
  2. 2Discount: 600 × 0.20 = $120.00.
  3. 3Net price: 600 − 120 = $480.00.

Answer: Net merchandise price: $480.00.

Example 2A discount series

An $800 list-price order receives 25% and 10% trade discounts. Find its net price and equivalent discount.

Solution

  1. 1First discount: 800 × 0.25 = $200.00; remaining price = $600.00.
  2. 2Second discount: 600 × 0.10 = $60.00; net price = $540.00.
  3. 3Net factor: 0.75 × 0.90 = 0.675.
  4. 4Equivalent discount: 1 − 0.675 = 0.325 = 32.5%.

Answer: Net price $540.00; equivalent discount 32.5%.

Practice exercises 7.1

  1. Find the net price of a $250 order with a 12% trade discount.
  2. Apply 20% and 5% trade discounts to $1,000.
  3. Find the equivalent discount for 20% and 5%.
  4. A $400 net price follows a 20% trade discount. Find list price.
  5. Which costs less on a $500 list: 30% off or 20% then 15% off?

Recap quiz 7.1

1. A 15% trade discount on $200 leaves:
2. The net factor for 10% then 20% off is:
3. Why are series discounts not added?

Section 7.1 recap

  • Apply each trade discount to the remaining merchandise price.
  • Use net factors to compare discount series.
Answer key with explanations: Section 7.1

Practice exercises

  1. Discount = 250 × 0.12 = $30.00; net = $220.00.
  2. First net = 1000 × 0.80 = $800.00; second discount = $40.00; final net = $760.00.
  3. Net factor = 0.80 × 0.95 = 0.76; equivalent discount = 1 − 0.76 = 24%.
  4. Net factor = 0.80; list price = 400 ÷ 0.80 = $500.00.
  5. Single discount leaves 500 × 0.70 = $350.00. Series leaves 500 × 0.80 × 0.85 = $340.00, so the series saves $10.00 more.

Recap quiz

  1. $170: 200 − 200 × 0.15 = $170.
  2. 0.72: 0.90 × 0.80 = 0.72.
  3. Each uses a new base: The second discount is based on the reduced price, not the original list price.
7.2

Cash Discounts and Invoice Terms

Learning objectives

After this section you will be able to:

  1. Interpret cash discount and net payment terms.
  2. Determine eligibility using a stated counting convention.
  3. Separate discount-eligible merchandise from excluded charges.

Real-life situation

A supplier offers prompt-payment terms

Use this hypothetical Philadelphia-area scenario to connect the calculation to a decision. All people, businesses, amounts, and rates in this chapter are invented; tax and payroll rules are teaching assumptions, not current law.

A supplier offers prompt-payment terms

  • Invoice: April 3
  • Terms: 2/10, n/30
  • Day after invoice is day 1
  • Discount deadline: April 13; net deadline: May 3
Figure 7.2 A supplier offers prompt-payment terms (hypothetical)

The concept

A cash discount rewards payment within an early-payment window. Terms 2/10, n/30 mean a 2% discount if payment meets the 10-day deadline; otherwise the full net amount is due within 30 days. This is different from a trade discount, which determines the invoice merchandise price before payment timing is considered.

For every example here, count the day after the invoice date as day 1, use calendar days, and assume payment is received on the stated date. Holidays and weekends do not extend deadlines in these hypothetical contracts. Real contracts may define receipt, mailing, or electronic settlement differently.

The discount base is the eligible merchandise balance after applicable returns and allowances. In these examples, freight is excluded from the cash discount and tax is omitted unless a problem explicitly supplies it. Apply the discount only to the eligible amount, then add the excluded charges.

Paying early reduces the amount paid but also uses cash sooner. A buyer should check that funds are actually available and compare any borrowing cost with the savings; a discount does not automatically justify borrowing. If payment misses the discount deadline, use the undiscounted balance rather than a partial discount.

Invoice deadlines

  1. 1

    Invoice date

    April 3

  2. 2

    Discount deadline

    April 13

  3. 3

    Net deadline

    May 3

Figure 7.2.V Invoice deadlines. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • markdown

    A reduction from the regular selling price, often to clear out inventory.

  • wholesale

    The price or market for buying goods in bulk, usually from a supplier.

  • retail

    The price or market for selling goods to the public, usually in small amounts.

Key terms

Cash discount
Reduction for meeting an early-payment condition.
Discount period
Number of days in which discounted payment is permitted.
Net period
Time allowed for full payment without a cash discount.
Eligible balance
Amount to which a cash discount applies.
Invoice date
Starting reference date specified on the bill.

Formulas & rules

  • Cash discount

    Cash discount = eligible balance × decimal cash discount rate

  • Early payment

    Payment = eligible balance − cash discount + excluded charges

  • Full payment

    Full payment = eligible balance + excluded charges

Worked examples

Example 1Read the calendar

An April 3 invoice for $1,000 has terms 2/10, n/30. Payment is received April 12. Find deadlines and payment.

Solution

  1. 1Count April 4 as day 1; day 10 is April 13.
  2. 2Day 30 is May 3; April 12 is inside the discount period.
  3. 3Discount: 1000 × 0.02 = $20.00.
  4. 4Payment: 1000 − 20 = $980.00.

Answer: Pay $980.00; the discount deadline is April 13 and the net deadline is May 3.

Example 2Exclude freight

An invoice has $600 eligible merchandise and $40 freight, terms 3/10, n/30. Timely payment qualifies for the discount. Find the payment.

Solution

  1. 1Eligible base is $600.00, not $640.00.
  2. 2Discount: 600 × 0.03 = $18.00.
  3. 3Payment: 600 − 18 + 40 = $622.00.

Answer: The timely payment is $622.00.

Practice exercises 7.2

  1. Pay an $800 eligible invoice within terms 2/10, n/30. No other charges apply.
  2. Pay that same $800 invoice on day 15.
  3. A June 10 invoice has a 10-day discount window under this section's convention. What is the deadline?
  4. Find early payment on $900 eligible merchandise plus $50 excluded freight with a 1% discount.
  5. A timely payment of $490 settled merchandise only under a 2% cash discount. Find the eligible invoice balance.

Recap quiz 7.2

1. Terms 1/10, n/30 offer which discount?
2. A $500 eligible balance receives 2% off. Payment is:
3. Under the stated convention, day 1 after a July 6 invoice is:

Section 7.2 recap

  • Read both the discount deadline and the full-payment deadline.
  • Do not discount excluded freight or other excluded charges.
Answer key with explanations: Section 7.2

Practice exercises

  1. Discount = 800 × 0.02 = $16.00; payment = $784.00.
  2. Day 15 is outside the 10-day discount period, so no discount applies: payment = $800.00.
  3. June 11 is day 1; add 10 calendar days to June 10 to get June 20.
  4. Discount = 900 × 0.01 = $9.00; payment = 900 − 9 + 50 = $941.00.
  5. Payment is 98% of the balance; 490 ÷ 0.98 = $500.00.

Recap quiz

  1. 1% within 10 days: The first number is the percent and the second is the discount window.
  2. $490: Discount = 500 × 0.02 = $10; payment = $490.
  3. July 7: Counting begins the calendar day after the invoice date.
7.3

Returns, Freight, and Total Purchasing Cost

Learning objectives

After this section you will be able to:

  1. Adjust an invoice for returns and allowances.
  2. Calculate the complete delivered cost of an order.
  3. Compare suppliers on cost per usable unit.

Real-life situation

The club checks a delivery

Use this hypothetical Philadelphia-area scenario to connect the calculation to a decision. All people, businesses, amounts, and rates in this chapter are invented; tax and payroll rules are teaching assumptions, not current law.

The club checks a delivery

  • 20 supply kits at $12.00: $240.00
  • Return 2 kits: credit $24.00
  • Remaining merchandise: $216.00
  • Freight: $18.00; total: $234.00
Figure 7.3 The club checks a delivery (hypothetical)

The concept

A purchase return removes merchandise from an order and creates a credit for its agreed invoice value. An allowance reduces the price of goods the buyer keeps, perhaps because of minor damage. Subtract these credits before calculating a cash discount when the contract makes only the adjusted balance eligible.

Freight is part of acquiring goods even when it is not eligible for a cash discount. For these problems, delivered cost means adjusted merchandise minus any qualifying cash discount plus freight and any stated tax. No tax is assumed when it is not supplied.

Purchasing comparisons should use the same quantity and quality. Cost per usable unit divides complete delivered cost by units actually retained and usable. Returned or unusable units do not belong in that denominator, even if the original order was larger.

The lowest unit cost is a mathematical comparison, not the entire purchasing decision. Delivery reliability, storage capacity, quality, and the cash needed for a large order also matter. State which costs and assumptions the comparison includes rather than presenting a low sticker price as the complete answer.

Purchasing cost bridge

  1. 1

    20 kits

    $240

  2. 2

    Return 2 kits

    Subtract $24

  3. 3

    Freight

    Add $18 → total $234

Figure 7.3.V Purchasing cost bridge. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • vendor

    A company or person that supplies goods or services to a business.

  • cost

    The amount paid to make or buy an item before it is sold.

  • inventory

    The stock of goods a business holds ready to sell.

Key terms

Return
Goods sent back for a credit.
Allowance
Price reduction on goods retained.
Freight
Charge for transporting goods.
Delivered cost
Purchase cost including the specified delivery-related charges.
Usable unit cost
Total delivered cost divided by usable units retained.

Formulas & rules

  • Adjusted merchandise

    Adjusted merchandise = invoice merchandise − returns − allowances

  • Delivered cost

    Delivered cost = adjusted merchandise − cash discount + freight + stated tax

  • Unit cost

    Cost per usable unit = delivered cost ÷ usable units

Worked examples

Example 1Return before paying

A club receives 20 kits at $12 each, returns 2 for full credit, and pays $18 freight. No discounts or tax apply. Find delivered cost per retained kit.

Solution

  1. 1Original merchandise: 20 × 12 = $240.00.
  2. 2Return credit: 2 × 12 = $24.00; adjusted merchandise = $216.00.
  3. 3Delivered cost: 216 + 18 = $234.00.
  4. 4Usable kits: 20 − 2 = 18; 234 ÷ 18 = $13.00 per kit.

Answer: Delivered cost is $234.00, or $13.00 per retained kit.

Example 2Compare delivered offers

Vendor A offers 50 identical notebooks for $100 plus $15 freight. Vendor B offers 50 for $110 with free freight. No tax or discounts apply. Which costs less?

Solution

  1. 1A delivered cost: 100 + 15 = $115.00.
  2. 2B delivered cost: 110 + 0 = $110.00.
  3. 3Unit costs: 115 ÷ 50 = $2.30; 110 ÷ 50 = $2.20.
  4. 4Difference: 115 − 110 = $5.00.

Answer: Vendor B costs $5.00 less overall, or $0.10 less per notebook.

Practice exercises 7.3

  1. Adjust $700 merchandise for an $80 return and a $20 allowance.
  2. Apply a timely 2% cash discount to that $600 adjusted balance and add $30 excluded freight.
  3. Thirty usable items cost $162 delivered. Find cost per unit.
  4. Compare 40 identical items at $180 plus $20 freight with 40 at $196 delivered.
  5. A $300 shipment contains 25 items, but 5 unusable items receive no credit. Find cost per usable item with no other charges.

Recap quiz 7.3

1. A $400 invoice less a $50 return has an adjusted merchandise balance of:
2. Which belongs in delivered cost under the stated model?
3. $144 delivered for 24 usable units costs how much per unit?

Section 7.3 recap

  • Adjust merchandise before applying a qualifying cash discount.
  • Compare full delivered costs using usable quantities.
Answer key with explanations: Section 7.3

Practice exercises

  1. 700 − 80 − 20 = $600.00 adjusted merchandise.
  2. Discount = 600 × 0.02 = $12.00; delivered payment = 600 − 12 + 30 = $618.00.
  3. 162 ÷ 30 = $5.40 per usable item.
  4. First offer totals $200.00, or $5.00 each; second is $196.00, or $4.90 each. The second saves $4.00.
  5. Usable units = 25 − 5 = 20; 300 ÷ 20 = $15.00, not 300 ÷ 25 = $12.00.

Recap quiz

  1. $350: 400 − 50 = $350.
  2. Merchandise and specified freight: Delivery charges must be included along with adjusted merchandise and any other stated costs.
  3. $6: 144 ÷ 24 = $6 per unit.

Chapter 7 Organizer and Review

Chapter Organizer

Every section at a glance: key formulas, key terms, and the main idea.

  • 7.1 Trade Discounts and Discount Series

    Key formulas

    • Single discount: Net price = list price × (1 − decimal discount rate)
    • Series factor: Net factor = (1 − d1) × (1 − d2)
    • Equivalent discount: Equivalent decimal discount = 1 − net factor

    Key terms

    List price, Trade discount, Net price, Net price factor, Equivalent discount

    Remember

    Apply each trade discount to the remaining merchandise price.

  • 7.2 Cash Discounts and Invoice Terms

    Key formulas

    • Cash discount: Cash discount = eligible balance × decimal cash discount rate
    • Early payment: Payment = eligible balance − cash discount + excluded charges
    • Full payment: Full payment = eligible balance + excluded charges

    Key terms

    Cash discount, Discount period, Net period, Eligible balance, Invoice date

    Remember

    Read both the discount deadline and the full-payment deadline.

  • 7.3 Returns, Freight, and Total Purchasing Cost

    Key formulas

    • Adjusted merchandise: Adjusted merchandise = invoice merchandise − returns − allowances
    • Delivered cost: Delivered cost = adjusted merchandise − cash discount + freight + stated tax
    • Unit cost: Cost per usable unit = delivered cost ÷ usable units

    Key terms

    Return, Allowance, Freight, Delivered cost, Usable unit cost

    Remember

    Adjust merchandise before applying a qualifying cash discount.

Cumulative Review

Mixed practice from this chapter and the two chapters before it.

  1. Section 7.1

    Which costs less on a $500 list: 30% off or 20% then 15% off?

    Show answer

    Single discount leaves 500 × 0.70 = $350.00. Series leaves 500 × 0.80 × 0.85 = $340.00, so the series saves $10.00 more.

  2. Section 7.2

    A timely payment of $490 settled merchandise only under a 2% cash discount. Find the eligible invoice balance.

    Show answer

    Payment is 98% of the balance; 490 ÷ 0.98 = $500.00.

  3. Section 7.3

    A $300 shipment contains 25 items, but 5 unusable items receive no credit. Find cost per usable item with no other charges.

    Show answer

    Usable units = 25 − 5 = 20; 300 ÷ 20 = $15.00, not 300 ÷ 25 = $12.00.

  4. Review of Section 5.3

    A number plus 18 is 47. Find the number.

    Show answer

    n + 18 = 47 → 29

  5. Review of Section 6.3

    Find the price of a $90 jacket after 30% off, before tax.

    Show answer

    Discount = 90 × 0.30 = $27.00; sale price = 90 − 27 = $63.00.

All prices, stores, people, and accounts in this chapter are hypothetical and for teaching only. Product references are generic categories; no brand endorses or is endorsed by this textbook.