Bank Discount Calculator
Commercial discount, also called bank discount: enter the face value, the rate and the time to maturity to see the discount, the net value you receive and what the operation really costs per year
Your Numbers
Type plain numbers; a decimal point or comma both work. Face value up to 1,000,000,000,000. The discount (rate × time) must stay below 100% of the face value. Your inputs stay in your browser.
Discount = face value × rate × time = 10,000.00 × 6% × 0.25 = 150.00
At the same rate, the rational discount (charged on the amount received instead of the face value) would be 147.78, for a net value of 9,852.22. The commercial discount takes 2.22 more.
| Time before maturity | Discount | Net value |
|---|---|---|
| 1 month(s) | 50.00 | 9,950.00 |
| 2 month(s) | 100.00 | 9,900.00 |
| 3 month(s) | 150.00 | 9,850.00 |
How to use it
- Pick what you want to find: the discount and net value, the face value, the discount rate or the time before maturity.
- Enter the face value, the rate (per year or per month) and the time (years, months or days). If you count in days, set the days in a year to 360 or 365 as your contract or textbook says.
- If the bank also charges a commission, type it as a percentage of the face value in the fees field.
- When you solve for the face value, rate or time, also enter the value you know and say whether it is the discount or the net value received.
- Read the result, the steps with your numbers, the rational-discount comparison and the table. Copy Result keeps the key figures for a message.
Worked example
A note with a face value of 10,000 is discounted 3 months before maturity at 6% per year. Discount = 10,000 × 6% × 0.25 = 150.00, so you receive 9,850.00. The real cost is 150.00 ÷ (9,850.00 × 0.25) = 6.09% a year, a little above the 6% quoted. The rational discount at the same rate would be 147.78, 2.22 less. Reverse it: knowing the net value of 9,850.00, a rate of 6% and 3 months, the face value is 9,850.00 ÷ (1 − 0.06 × 0.25) = 10,000. Counting in days, 90 days at 6% on 10,000 gives 150.00 on a 360-day year and 147.95 on a 365-day year.
Why this tool exists and where its numbers come from
People discount notes, invoices and post-dated checks to get cash before the due date, and the quoted discount rate understates what that really costs. The tool uses the textbook formulas for commercial (bank) discount and their rearrangements. The sources below cover the formulas, the real rate and the day-count conventions, not any particular bank’s terms, which add their own fees, taxes and days.
Sources
- Financial Mathematics in Economics (OPENBOOK@UMS): Bank Discount
- Université Paul-Valéry Montpellier 3: escompte (French, PDF)
- OpenCourseWare (ocw.uc3m.es): Matemáticas Financieras, tema 3 (Spanish, PDF)
- Cursa: Matemática Financeira, descontos (Portuguese)
For the full method, see the Methodology section just below.
Methodology
The formulas. Commercial (bank) discount is charged on the face value N, for the time t in years, at the discount rate d: D = N × d × t. The holder receives A = N − D = N × (1 − d × t). Because the discount comes off the face value but the holder gets only A, the real cost per year is higher than d: i = D ÷ (A × t) = d ÷ (1 − d × t). The rational discount applies the rate to the amount received instead: A = N ÷ (1 + r × t). A monthly rate is multiplied by 12, time in months is divided by 12 and time in days by the days in a year you choose. Fees, when entered, come off the face value too and are included in the real cost.
Sources and documentation
The commercial-discount formula comes from the first and third entries, the real rate from the fourth and sixth, the rational discount from the third and sixth, the treatment of fees from the seventh and eighth, and the day-count conventions from the second to the eighth. Pages were consulted in October 2026. Entries three to eight are in Portuguese, French, German and Spanish.
- Financial Mathematics in Economics (OPENBOOK@UMS): Bank DiscountD = S·d·t, proceeds P = S − D = S(1 − d·t).
- Business and Financial Mathematics (eCampusOntario): Simple InterestDays divided by a 365-day year in its worked examples.
- Cursa: Matemática Financeira, descontos (Portuguese)Commercial discount D = N·d·n and A = N(1 − d·n); rational discount A = N/(1 + i·n); 360 days as a common bank convention.
- Université Paul-Valéry Montpellier 3: escompte (French, PDF)e = V·t·n/36,000, commercial present value V(1 − t·n/36,000), effective rate t/(1 − t·n/36,000) and the 360-day commercial year.
- Welt der BWL: Diskontkredit (German)Bill amount × [1 − rate × days/360]; 100,000 € at 5% for 90 days pays out 98,750 €.
- OpenCourseWare (ocw.uc3m.es): Matemáticas Financieras, tema 3 (Spanish, PDF)E = N[1 − d·n/360]; rational discount C0 = Ct/(1 + r·t); 8% over 90 days costs about 8.16%.
- Economipedia: Descuento comercial (Spanish)Discount plus commissions on a 365-day year; 10,000 over 60 days at 6% with a 0.5% commission costs 148.63.
- Nexco Expertise: L’escompte commercial (French)Discount on a 360-day year plus commissions and VAT make up the agio; not the same as a commercial price discount.
Where discounting sums go wrong
Each slip below can be reproduced with the tool. The first and third use a note of 10,000 discounted 3 months before maturity at 2% per month.
- Reading the rate as the cost. The discount is 600.00 and you receive 9,400.00, so the real cost is 2.13% a month (25.53% a year), not 2%.
- Mixed units. 90 days is 3 months, or 0.25 of a 360-day year at 24% a year. Multiplying 2% by 90 as if it were months would give 180%, more than the whole note.
- The wrong method. Using the rational discount for a commercial-discount problem gives 566.04 instead of 600.00, a difference of 33.96.
- A term that is too long. At 24% a year, 5 years means rate × time = 120%: the discount would exceed the note, so the tool refuses the numbers.
- The day count. 90 days at 6% on 10,000 is 150.00 with 360 days and 147.95 with 365.
Estimate for information only, not financial advice.
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Frequently asked questions
What is commercial (bank) discount? ▼
It is the amount a bank or buyer deducts for paying a note, invoice or post-dated check before its due date. It is calculated on the face value: discount = face value × rate × time, and you receive the face value minus the discount. It is the kind of discount taught in financial math.
What is the difference between commercial and rational discount? ▼
Commercial discount applies the rate to the face value; rational discount applies it to the amount actually received. For the same rate and time the commercial discount is always larger. For 10,000 at 24% a year for 3 months it is 600.00 against 566.04.
Why is the real cost higher than the discount rate? ▼
Because the discount is taken from the face value, you receive less than you would if the rate were charged on the amount received. Real cost per year = discount ÷ (net value × time). In the example, a 24% discount rate becomes 25.53% a year (2.13% a month).
Should I use 360 or 365 days in a year? ▼
Use what your contract or textbook states. For 90 days at 6% on 10,000 the discount is 150.00 with 360 and 147.95 with 365. Months always count as one twelfth of a year.
Is this the same as a price discount or an early-payment discount? ▼
No. A sale price or an early-payment discount (such as 2/10 net 30) is a percentage taken off an invoice. This tool is for discounting a credit instrument before it matures. For a plain percentage off a price, use the percentage calculator.
Does the result include fees or taxes? ▼
Only the fee percentage you type in. Taxes and bank tariffs differ by country and contract, so add them as a fee if you know them, or ask your bank for the total cost of the operation. The result is an estimate for information, not financial advice.