Discount Calculator

How to calculate discount?

To find the discount, use D = Price × (discount% ÷ 100). The final price then follows from Final Price = Price − D.

Suppose $250 with a 15% discount: D = 250 × 0.15 = $37.50, so the final price comes to $212.50.

Commercial discount and rational discount

In financial mathematics, when you pay off a future obligation early (face value N) ahead of its due date by time t at rate i, there are two different ways to run the numbers. Commercial discount (the "by outside" method) takes the rebate off the face value: D = N·i·t, with present value A = N(1 − i·t). Rational discount (the "by inside" method) charges simple interest on the present value instead: D = N·i·t / (1 + i·t), with present value A = N / (1 + i·t). At the same nominal rate the commercial model always costs the debtor more.

Take a duplicata with N = R$ 1,000 paid off 3 months early at 2% per month. Under the commercial method, D = 1,000 · 0.02 · 3 = R$ 60 and A = R$ 940. Under the rational method, D = 60 / 1.06 ≈ R$ 56.60 and A ≈ R$ 943.40.

Practical context in Brazil

Most of the time Brazilian banks reach for commercial discount. You see it in desconto de duplicatas, factoring, cheques pré-datados and discounting promissory notes. Since the upfront rebate is bigger, the company ends up paying an effective rate higher than the nominal one would suggest. Rational discount shows up mainly in academic financial-math exercises, and in some court calculations where simple interest on the present value is the legal benchmark. Retail "discounts" on sticker prices are a different animal altogether: they apply a flat percentage off, not these formulas.

FAQ

Why is commercial discount more expensive? It charges the rate against the face value, a larger base, whereas rational discount charges it against the present value, a smaller one. Same numerator, but a bigger denominator in the present-value formula.

Which one do Brazilian banks use? Almost always commercial discount, particularly in desconto de duplicatas and short-term receivables anticipation.

Can the commercial discount equal the face value? Yes. Once i·t ≥ 1, the formula returns A ≤ 0, which makes no economic sense. So a given rate effectively caps how far ahead you can anticipate a payment.

Is "store discount" the same thing? No. Knocking 15% off a sticker price uses P_final = P · (1 − d), a flat percentage with no time involved. That is exactly what the calculator above does.