Business Math Lab

Cash Discount Calculator: Step-by-Step Solution

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

Enter the numbers from your problem and this cash discount calculator writes out every step: the terms such as 2/10, n/30, the discount deadline and net due date, the days between the invoice and the payment, the cash discount, and the amount paid. It handles ordinary, EOM, ROG and proximo dating, freight that is not discounted, and partial payments (credit given).

Leave blank if the whole invoice qualifies.

Type the terms as written in the problem, such as 2/10, n/30. For proximo, the numbers are days of the next month.

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Step-by-step solution

Find the amount paid: invoice $1,500.00, terms 2/10, n/30, invoice dated March 3, paid March 11.

Amount paid

$1,470.00

Cash discount
$30.00
Discount deadline
March 13
Net due date
April 2

  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, March 3.
    • Discount deadline: March 3 + 10 days = March 13
    • Net due date: March 3 + 30 days
    • Days left in March: 31 − 3 = 28
    • 30 − 28 = 2 days remain
    • Day 2 of April: April 2

  4. Count the days from March 3 to March 11

    • March 3 is day 62 of 2027 (31 + 28 + 3)
    • March 11 is day 70 of 2027 (31 + 28 + 11)
    • 70 − 62 = 8 days

  5. Compare the payment date with the discount deadline

    • Payment date: March 11
    • Discount deadline: March 13
    • 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
    • $1,500.00 × 0.02 = $30.00

  7. Subtract the cash discount from the invoice amount

    • $1,500.00 − $30.00 = $1,470.00

What is a cash discount?

A cash discount is a reduction in the invoice amount that a seller offers if the buyer pays early. The offer is written as credit terms. In 2/10, n/30 (“two ten, net thirty”) the buyer may subtract 2% if it pays within 10 days; if it does not, the full net amount is due within 30 days. The 10 days are the discount period and the 30 days are the credit period.

Paying 20 days early to save 2% is equivalent to a simple annual rate of about 2 ÷ 98 × 365 ÷ 20 ≈ 37% on the cash paid out sooner, which is why the discount is worth comparing with the buyer’s cost of borrowing. This page does not calculate that rate; it is shown only to explain why sellers offer cash discounts.

Cash discount formulas

  • Cash discount = Invoice amount × Cash discount rate
  • Amount paid = Invoice amount − Cash discount = Invoice amount × (1 − Rate)
  • Eligible amount = Invoice amount − Freight or tax not eligible for the discount
  • Discount deadline = Start date + Discount days
  • Net due date = Start date + Credit days
  • Credit given (partial payment) = Partial payment ÷ (1 − Cash discount rate)
  • Balance due = Invoice amount − Credit given

The start date is the invoice date for ordinary dating. The other dating methods change it, as described below. Rates are written as decimals in the formulas, so 2% is 0.02 and its complement is 1 − 0.02 = 0.98.

Counting the days

The usual business math rule counts the exact number of days between two dates, and a payment made on the deadline day still earns the discount. For an invoice dated March 3 with terms 2/10, n/30:

  • Discount deadline: March 3 + 10 days = March 13.
  • Net due date: March 3 + 30 days = April 2 (March has 31 days, so 28 days remain after March 3, and 2 more days reach April 2).
  • A payment on March 11 is 8 days after the invoice date, inside the 10-day period. A payment on March 14 is 11 days after, one day late.

To count days across months, number each date by its day of the year and subtract: March 3 is day 62 (31 + 28 + 3) and March 11 is day 70 (31 + 28 + 11) in a year that is not a leap year, so 70 − 62 = 8 days. The calculator shows these lines for the dates you enter and adds February 29 in a leap year.

EOM, ROG and proximo dating

Discount deadline and net due date for an invoice dated March 3 under each dating method
MethodTermsPeriods startDiscount deadlineNet due date
Ordinary2/10, n/30Invoice date, March 3March 13April 2
EOM (end of month)2/10 EOM, n/30 EOMEnd of the invoice month, March 31April 10April 30
ROG (receipt of goods)2/10 ROG, n/30 ROGGoods received March 20March 30April 19
Proximo (next month)2/10 prox, n/25 proxThe month after the invoiceApril 10April 25

EOM starts the periods on the last day of the invoice month, which suits sellers that bill once a month. Many courses add the 26th rule: an invoice dated the 26th or later is treated as dated at the end of the next month, so a March 27 invoice with 2/10 EOM has a May 10 deadline. Check whether your course uses it; the dating box has a separate EOM option for it. ROG starts the periods when the buyer receives the goods, which protects the buyer when shipping is slow. Proximo (“prox”) gives fixed days of the following month: the numbers in 2/10 prox, n/25 prox are the 10th and the 25th of that month, not counts of days.

Partial payments and credit given

When a buyer pays only part of an invoice inside the discount period, the seller credits more than the amount received, because the payment already has the discount taken out. If the payment is 98% of the amount credited, the credit is the payment divided by 0.98. On a $1,500.00 invoice with terms 2/10, n/30 and a $588.00 payment on March 11:

Credit given = $588.00 ÷ 0.98 = $600.00
Cash discount earned = $600.00 − $588.00 = $12.00
Balance due = $1,500.00 − $600.00 = $900.00

A common error is to multiply by 1.02, which gives $599.76, or to take 2% off the payment. The check-my-answer box points out these slips. If the payment arrives after the discount deadline, the credit equals the payment.

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 trade discounts
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 inside the discount period

When a problem has both, find the net price with the trade discount calculator first, then take the cash discount from that net price. Example 10 does this with an EOM cash discount. A cash discount is usually calculated on the merchandise amount after returns and trade discounts; freight and sales tax are normally left out, which is why the calculator has a box for amounts that are not eligible. Follow your course’s rule if it says otherwise.

Rounding rules used on this page

  • Interim values 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 cash discount is rounded first and then subtracted from the invoice, so the discount and the amount paid add back to the invoice amount.
  • The credit given for a partial payment is the rounded quotient; the calculator then checks it by multiplying back.

Common mistakes

  • Reporting the discount as the amount paid. The amount paid is what is left after the discount.
  • Counting the wrong number of days. Use the exact days between the dates, not 30-day months. Payment on the deadline day still qualifies.
  • Taking the discount on freight or tax. Only the eligible amount is discounted.
  • Taking the cash discount from the list price. Apply trade discounts first.
  • Multiplying a partial payment by 1.02. Divide by 0.98 to find the credit given.
  • Reading proximo days as a count. 2/10 prox means the 10th of next month.

Assumptions and limits

The calculator uses the textbook day-counting rules above and assumes the discount applies when the payment is dated on or before the deadline. Real contracts vary: some start the clock on a different date, some exclude weekends or holidays, and some suppliers set their own late-payment rules. It does not model interest on late payments, returns, sales tax rules, or accounting entries. Amounts can have up to four decimal places and the discount rate must be more than 0% and less than 100%. Dates must fall between the years 1900 and 2200.

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 (Lyryx Learning, CC BY-NC-SA), and the credit-terms conventions 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, and automated tests compare the solver with hand-worked answers for every problem on the examples page and the worksheet. Dates are checked against Python’s calendar.

Frequently asked questions

What does 2/10, n/30 mean?

It is read “two ten, net thirty”. The buyer may subtract 2% from the invoice if it pays within 10 days of the invoice date. If it misses that window, the full amount is due within 30 days. On a $1,500.00 invoice, paying inside the discount period saves $30.00 and costs $1,470.00.

How do you calculate a cash discount?

Cash discount = Invoice amount × Cash discount rate, and Amount paid = Invoice amount − Cash discount. Most business math courses figure the discount on the merchandise amount after any trade discount and returns, and leave out freight and sales tax. Follow your course’s rule if it differs.

How do you count the days in the discount period?

Add the discount days to the invoice date. An invoice dated March 3 with terms 2/10, n/30 has a discount deadline of March 13 and a net due date of April 2, and a payment made on March 13 still earns the discount. To count the days between two dates, number each date as its day of the year (March 3 is day 62 in a year that is not a leap year) and subtract.

How is a partial payment credited?

A payment made inside the discount period is credited for more than its face value: Credit given = Partial payment ÷ (1 − Cash discount rate). A $588.00 payment on 2/10, n/30 terms is credited as $588.00 ÷ 0.98 = $600.00, which includes a $12.00 discount, and the balance due falls by $600.00.

What do EOM, ROG and proximo mean?

EOM (end of month) counts the discount and net periods from the last day of the invoice month. ROG (receipt of goods) counts them from the day the goods arrive. Proximo (prox) sets the deadlines on fixed days of the month after the invoice. Some courses add a “26th rule” to EOM: an invoice dated the 26th or later starts its periods at the end of the following month.

Is the cash discount taken before or after the trade discount?

After. Take the trade discount first to get the net price on the invoice, then apply the cash discount to that net price. A cash discount rewards early payment; a trade discount reflects who the buyer is.

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