Business Math Lab

Cash Discount Examples with Solutions

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

Ten cash 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, including the day count. They start with terms such as 2/10, n/30, then cover discount deadlines, freight that is not discounted, partial payments, EOM and ROG dating, and a trade discount followed by a cash discount.

Formulas used in these examples

  • Cash discount = Eligible amount × Rate; Amount paid = Invoice amount − Cash discount
  • Discount deadline = Start date + Discount days; Net due date = Start date + Credit days
  • Days between two dates = Day of the year of the later date − Day of the year of the earlier date
  • Credit given = Partial payment ÷ (1 − Rate); Balance due = Invoice amount − Credit given

Start date: the invoice date (ordinary), the end of the invoice month (EOM), or the date the goods are received (ROG). A payment on the deadline day still earns the discount. Rounding: interim values stay exact; money is rounded to the nearest cent at the end.

Example 1 · Basic

Pay inside the discount period

Northfield Tool Supply bills a contractor $2,400 for merchandise on an invoice dated June 8 with terms 2/10, n/30. The contractor pays on June 16. How much does the contractor pay?

Invoice amount
$2,400.00
Terms
2/10, n/30
Invoice date
June 8
Payment date
June 16
Find
Cash discount and amount paid

Solution

  1. Write the formulas

    • Cash discount = Invoice amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 2/10, n/30 means 2% off if paid within 10 days of the invoice date; the full amount is due within 30 days of the invoice date.

  3. Find the discount deadline and the net due date

    • Counting starts on the invoice date, June 8.
    • Discount deadline: June 8 + 10 days = June 18
    • Net due date: June 8 + 30 days
    • Days left in June: 30 − 8 = 22
    • 30 − 22 = 8 days remain
    • Day 8 of July: July 8

  4. Count the days from June 8 to June 16

    • June 8 is day 159 of 2027 (31 + 28 + 31 + 30 + 31 + 8)
    • June 16 is day 167 of 2027 (31 + 28 + 31 + 30 + 31 + 16)
    • 167 − 159 = 8 days

  5. Compare the payment date with the discount deadline

    • Payment date: June 16
    • Discount deadline: June 18
    • 8 days is within the 10-day discount period.
    • The payment is on or before the deadline, so the cash discount applies.

  6. Find the cash discount

    • 2% = 2 ÷ 100 = 0.02
    • $2,400.00 × 0.02 = $48.00

  7. Subtract the cash discount from the invoice amount

    • $2,400.00 − $48.00 = $2,352.00

Answer: June 16 is 8 days after June 8, inside the 10-day period. Cash discount = $48.00; amount paid = $2,352.00.

Open this problem in the solver

Example 2 · Basic

Pay after the discount period

A print shop receives an invoice for $860 dated October 4 with terms 3/10, n/30 and pays it on October 17. Does the shop get the discount? How much does it pay?

Invoice amount
$860.00
Terms
3/10, n/30
Invoice date
October 4
Payment date
October 17
Find
Amount paid

Solution

  1. Write the formulas

    • Cash discount = Invoice amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 3/10, n/30 means 3% off if paid within 10 days of the invoice date; the full amount is due within 30 days of the invoice date.

  3. Find the discount deadline and the net due date

    • Counting starts on the invoice date, October 4.
    • Discount deadline: October 4 + 10 days = October 14
    • Net due date: October 4 + 30 days
    • Days left in October: 31 − 4 = 27
    • 30 − 27 = 3 days remain
    • Day 3 of November: November 3

  4. Count the days from October 4 to October 17

    • October 4 is day 277 of 2027 (31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 4)
    • October 17 is day 290 of 2027 (31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 17)
    • 290 − 277 = 13 days

  5. Compare the payment date with the discount deadline

    • Payment date: October 17
    • Discount deadline: October 14
    • 13 days is more than the 10-day discount period.
    • The payment is after the deadline, so there is no cash discount.

  6. Pay the full invoice amount

    • With no cash discount, the buyer pays the full invoice amount: $860.00

Answer: October 17 is 13 days after October 4, past the October 14 deadline, so there is no discount. The shop pays the full $860.00, which is due by November 3.

Open this problem in the solver

Example 3 · Basic

Find the discount deadline and the due date

An invoice is dated July 19 with terms 2/10, n/30. Find the last day on which the buyer can still take the cash discount and the day the full amount is due.

Terms
2/10, n/30
Invoice date
July 19
Find
Discount deadline and net due date

Solution

  1. Read the credit terms

    • 2/10, n/30 means 2% off if paid within 10 days of the invoice date; the full amount is due within 30 days of the invoice date.

  2. Find the discount deadline and the net due date

    • Counting starts on the invoice date, July 19.
    • Discount deadline: July 19 + 10 days = July 29
    • Net due date: July 19 + 30 days
    • Days left in July: 31 − 19 = 12
    • 30 − 12 = 18 days remain
    • Day 18 of August: August 18

Answer: The discount deadline is July 29 and the net amount is due on August 18.

Open this problem in the solver

Example 4 · Intermediate

Count the days across two months

Ridgeview Paper invoices a retailer $1,275 on January 24 with terms 2/15, n/45. The retailer pays on February 7. Count the days and find the amount paid.

Invoice amount
$1,275.00
Terms
2/15, n/45
Invoice date
January 24
Payment date
February 7
Find
Days elapsed and amount paid

Solution

  1. Write the formulas

    • Cash discount = Invoice amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 2/15, n/45 means 2% off if paid within 15 days of the invoice date; the full amount is due within 45 days of the invoice date.

  3. Find the discount deadline and the net due date

    • Counting starts on the invoice date, January 24.
    • Discount deadline: January 24 + 15 days
    • Days left in January: 31 − 24 = 7
    • 15 − 7 = 8 days remain
    • Day 8 of February: February 8
    • Net due date: January 24 + 45 days
    • Days left in January: 31 − 24 = 7
    • 45 − 7 = 38 days remain
    • February has 28 days: 38 − 28 = 10 days remain
    • Day 10 of March: March 10

  4. Count the days from January 24 to February 7

    • January 24 is day 24 of 2027
    • February 7 is day 38 of 2027 (31 + 7)
    • 38 − 24 = 14 days

  5. Compare the payment date with the discount deadline

    • Payment date: February 7
    • Discount deadline: February 8
    • 14 days is within the 15-day discount period.
    • The payment is on or before the deadline, so the cash discount applies.

  6. Find the cash discount

    • 2% = 2 ÷ 100 = 0.02
    • $1,275.00 × 0.02 = $25.50

  7. Subtract the cash discount from the invoice amount

    • $1,275.00 − $25.50 = $1,249.50

Answer: The payment comes 14 days after the invoice date, inside the 15-day period. Cash discount = $25.50; amount paid = $1,249.50.

Open this problem in the solver

Example 5 · Intermediate

Freight is not discounted

A $3,150 invoice for restaurant equipment includes $150 of freight. The invoice is dated May 2 with terms 2/10, n/30, and the buyer pays on May 11. The cash discount does not apply to freight. How much does the buyer pay?

Invoice amount
$3,150.00
Freight (not eligible)
$150.00
Terms
2/10, n/30
Invoice date
May 2
Payment date
May 11
Find
Amount paid

Solution

  1. Write the formulas

    • Eligible amount = Invoice amount − Amount not eligible for the discount
    • Cash discount = Eligible amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 2/10, n/30 means 2% off if paid within 10 days of the invoice date; the full amount is due within 30 days of the invoice date.

  3. Find the discount deadline and the net due date

    • Counting starts on the invoice date, May 2.
    • Discount deadline: May 2 + 10 days = May 12
    • Net due date: May 2 + 30 days
    • Days left in May: 31 − 2 = 29
    • 30 − 29 = 1 days remain
    • Day 1 of June: June 1

  4. Count the days from May 2 to May 11

    • May 2 is day 122 of 2027 (31 + 28 + 31 + 30 + 2)
    • May 11 is day 131 of 2027 (31 + 28 + 31 + 30 + 11)
    • 131 − 122 = 9 days

  5. Compare the payment date with the discount deadline

    • Payment date: May 11
    • Discount deadline: May 12
    • 9 days is within the 10-day discount period.
    • The payment is on or before the deadline, so the cash discount applies.

  6. Find the amount eligible for the discount

    • $3,150.00 − $150.00 = $3,000.00

  7. Find the cash discount

    • 2% = 2 ÷ 100 = 0.02
    • $3,000.00 × 0.02 = $60.00

  8. Subtract the cash discount from the invoice amount

    • $3,150.00 − $60.00 = $3,090.00

Answer: Eligible amount = $3,000.00; cash discount = $60.00; amount paid = $3,150.00 − $60.00 = $3,090.00.

Open this problem in the solver

Example 6 · Intermediate

Partial payment: credit given and balance due

A $4,000 invoice is dated August 5 with terms 2/10, n/30. On August 12 the buyer sends a partial payment of $1,960. How much credit does the buyer receive, and what is the balance due?

Invoice amount
$4,000.00
Terms
2/10, n/30
Invoice date
August 5
Partial payment
$1,960.00
Payment date
August 12
Find
Credit given and balance due

Solution

  1. Write the formulas

    • Credit given = Partial payment ÷ (1 − Cash discount rate)
    • Cash discount earned = Credit given − Partial payment
    • Balance due = Invoice amount − Credit given

  2. Read the credit terms

    • 2/10, n/30 means 2% off if paid within 10 days of the invoice date; the full amount is due within 30 days of the invoice date.

  3. Find the discount deadline and the net due date

    • Counting starts on the invoice date, August 5.
    • Discount deadline: August 5 + 10 days = August 15
    • Net due date: August 5 + 30 days
    • Days left in August: 31 − 5 = 26
    • 30 − 26 = 4 days remain
    • Day 4 of September: September 4

  4. Count the days from August 5 to August 12

    • August 5 is day 217 of 2027 (31 + 28 + 31 + 30 + 31 + 30 + 31 + 5)
    • August 12 is day 224 of 2027 (31 + 28 + 31 + 30 + 31 + 30 + 31 + 12)
    • 224 − 217 = 7 days

  5. Compare the payment date with the discount deadline

    • Payment date: August 12
    • Discount deadline: August 15
    • 7 days is within the 10-day discount period.
    • The payment is on or before the deadline, so the cash discount applies.

  6. Find the complement of the discount rate

    • 100% − 2% = 98% = 0.98

  7. Divide the payment by the complement to find the credit given

    • $1,960.00 ÷ 0.98 = $2,000.00

  8. Find the cash discount earned

    • $2,000.00 − $1,960.00 = $40.00

  9. Find the balance due

    • $4,000.00 − $2,000.00 = $2,000.00

  10. Check the answer

    • $2,000.00 × 0.98 = $1,960.00
    • This matches the payment, $1,960.00.

Answer: Credit given = $2,000.00 (a $40.00 discount on the $1,960.00 paid); balance due = $2,000.00.

Open this problem in the solver

Example 7 · Intermediate

EOM dating

An invoice for $5,280 is dated April 13 with terms 2/10, n/30 EOM. The buyer pays on May 9. Find the discount deadline, the due date and the amount paid.

Invoice amount
$5,280.00
Terms
2/10, n/30 EOM
Invoice date
April 13
Payment date
May 9
Find
Discount deadline, due date and amount paid

Solution

  1. Write the formulas

    • Cash discount = Invoice amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 2/10, n/30 EOM means 2% off if paid within 10 days after the end of the invoice month; the full amount is due within 30 days after the end of the invoice month.

  3. Find the discount deadline and the net due date

    • EOM: the periods start on the last day of the invoice month.
    • Last day of April: April 30
    • Discount deadline: April 30 + 10 days
    • April 30 is the last day of April, so no days are left in it
    • Day 10 of May: May 10
    • Net due date: April 30 + 30 days
    • April 30 is the last day of April, so no days are left in it
    • Day 30 of May: May 30

  4. Count the days from April 30 to May 9

    • April 30 is day 120 of 2027 (31 + 28 + 31 + 30)
    • May 9 is day 129 of 2027 (31 + 28 + 31 + 30 + 9)
    • 129 − 120 = 9 days

  5. Compare the payment date with the discount deadline

    • Payment date: May 9
    • Discount deadline: May 10
    • 9 days is within the 10-day discount period.
    • The payment is on or before the deadline, so the cash discount applies.

  6. Find the cash discount

    • 2% = 2 ÷ 100 = 0.02
    • $5,280.00 × 0.02 = $105.60

  7. Subtract the cash discount from the invoice amount

    • $5,280.00 − $105.60 = $5,174.40

Answer: The periods start on April 30. Discount deadline = May 10; due date = May 30. Cash discount = $105.60; amount paid = $5,174.40.

Open this problem in the solver

Example 8 · Intermediate

ROG dating

A distributor invoices a store for $7,900 on September 15 with terms 3/10, n/30 ROG. The goods arrive on October 2, and the store pays on October 11. How much does the store pay?

Invoice amount
$7,900.00
Terms
3/10, n/30 ROG
Invoice date
September 15
Goods received
October 2
Payment date
October 11
Find
Amount paid

Solution

  1. Write the formulas

    • Cash discount = Invoice amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 3/10, n/30 ROG means 3% off if paid within 10 days of receiving the goods; the full amount is due within 30 days of receiving the goods.

  3. Find the discount deadline and the net due date

    • ROG: counting starts on the day the goods were received, October 2.
    • Discount deadline: October 2 + 10 days = October 12
    • Net due date: October 2 + 30 days
    • Days left in October: 31 − 2 = 29
    • 30 − 29 = 1 days remain
    • Day 1 of November: November 1

  4. Count the days from October 2 to October 11

    • October 2 is day 275 of 2027 (31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 2)
    • October 11 is day 284 of 2027 (31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 11)
    • 284 − 275 = 9 days

  5. Compare the payment date with the discount deadline

    • Payment date: October 11
    • Discount deadline: October 12
    • 9 days is within the 10-day discount period.
    • The payment is on or before the deadline, so the cash discount applies.

  6. Find the cash discount

    • 3% = 3 ÷ 100 = 0.03
    • $7,900.00 × 0.03 = $237.00

  7. Subtract the cash discount from the invoice amount

    • $7,900.00 − $237.00 = $7,663.00

Answer: The periods start on October 2, the day the goods were received. Discount deadline = October 12; due date = November 1. Cash discount = $237.00; amount paid = $7,663.00.

Open this problem in the solver

Example 9 · Exam-style

Proximo dating

A $2,750 invoice dated February 17 carries terms 2/10 prox, n/25 prox. The buyer pays on March 9. Find the discount deadline, the due date and the amount paid.

Invoice amount
$2,750.00
Terms
2/10 prox, n/25 prox
Invoice date
February 17
Payment date
March 9
Find
Discount deadline, due date and amount paid

Solution

  1. Write the formulas

    • Cash discount = Invoice amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 2/10 prox, n/25 prox means 2% off if paid by day 10 of the month after the invoice month; the full amount is due by day 25 of that month.

  3. Find the discount deadline and the net due date

    • Proximo: the deadlines are days of the month after the invoice month, March.
    • Discount deadline: day 10 of March = March 10
    • Net due date: day 25 of March = March 25

  4. Compare the payment date with the discount deadline

    • Payment date: March 9
    • Discount deadline: March 10
    • The payment is on or before the deadline, so the cash discount applies.

  5. Find the cash discount

    • 2% = 2 ÷ 100 = 0.02
    • $2,750.00 × 0.02 = $55.00

  6. Subtract the cash discount from the invoice amount

    • $2,750.00 − $55.00 = $2,695.00

Answer: Under proximo dating the deadlines are days of March: discount deadline = March 10; due date = March 25. Cash discount = $55.00; amount paid = $2,695.00.

Open this problem in the solver

Example 10 · Exam-style

Trade discount first, then an EOM cash discount

A catalog lists a commercial refrigerator at $6,800 less a trade discount of 25/10. The invoice is dated May 20 with terms 2/10 EOM, n/30 EOM, and the buyer pays on June 8. How much does the buyer pay?

List price
$6,800.00
Trade discount
25/10
Terms
2/10, n/30 EOM
Invoice date
May 20
Payment date
June 8
Find
Amount paid

Solution

Trade discount first

  1. 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

  2. Find the complement of each discount

    • 100% − 25% = 75% = 0.75
    • 100% − 10% = 90% = 0.9

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

    • 0.75 × 0.9 = 0.675
    • Net price equivalent rate = 0.675 (the buyer pays 67.5% of the list price)

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

    • $6,800.00 × 0.675 = $4,590.00

  5. Find the single equivalent discount rate

    • 1 − 0.675 = 0.325
    • 0.325 = 32.5%

  6. Find the trade discount amount

    • $6,800.00 − $4,590.00 = $2,210.00

  7. Why the discounts are not added

    • 25% + 10% = 35%, but the real discount is 32.5%: each discount is taken from the price that is left after the one before it.

Then the cash discount

  1. Write the formulas

    • Cash discount = Invoice amount × Cash discount rate
    • Amount paid = Invoice amount − Cash discount

  2. Read the credit terms

    • 2/10, n/30 EOM means 2% off if paid within 10 days after the end of the invoice month; the full amount is due within 30 days after the end of the invoice month.

  3. Find the discount deadline and the net due date

    • EOM: the periods start on the last day of the invoice month.
    • Last day of May: May 31
    • Discount deadline: May 31 + 10 days
    • May 31 is the last day of May, so no days are left in it
    • Day 10 of June: June 10
    • Net due date: May 31 + 30 days
    • May 31 is the last day of May, so no days are left in it
    • Day 30 of June: June 30

  4. Count the days from May 31 to June 8

    • May 31 is day 151 of 2027 (31 + 28 + 31 + 30 + 31)
    • June 8 is day 159 of 2027 (31 + 28 + 31 + 30 + 31 + 8)
    • 159 − 151 = 8 days

  5. Compare the payment date with the discount deadline

    • Payment date: June 8
    • Discount deadline: June 10
    • 8 days is within the 10-day discount period.
    • The payment is on or before the deadline, so the cash discount applies.

  6. Find the cash discount

    • 2% = 2 ÷ 100 = 0.02
    • $4,590.00 × 0.02 = $91.80

  7. Subtract the cash discount from the invoice amount

    • $4,590.00 − $91.80 = $4,498.20

Answer: Net price after the trade discount = $4,590.00. The EOM periods start on May 31, so the discount deadline is June 10 and June 8 qualifies. Cash discount = $91.80; amount paid = $4,498.20.

Open Trade discount first in the solver · Open Then the cash discount in the solver

Practice on your own

Problems and businesses on this page are original practice problems written for Business Math Lab. Answers are checked by automated tests against the solver.