✂️ Bill Discount Calculator

What does a bill discount calculation show?

A bill discount calculation estimates how much a future nominal amount is worth today under a chosen annual rate and time-to-maturity assumption. The nominal value is the amount written on the bill at maturity; the present cash value is the amount after applying the selected discount method.

This calculator returns the present value, the discount amount, the method used, the rate, and the duration. It supports three methods — simple outer discount, simple inner discount, and compound inner discount for longer maturities with multiple compounding periods — and you can enter either the nominal value or the present value, whichever you know. It is designed for commercial-finance discounting of bills or notes, not for retail price discounts on products.

Inner discount and outer discount

In Turkish commercial-finance terminology, dış iskonto calculates the discount amount directly on the nominal value. This is commonly mapped to outer discount or bank discount in English explanations. Because the deduction is taken from the full nominal value, the present value can drop sharply when rate and time are large.

İç iskonto calculates the present value first and then takes the difference between nominal and present value as the discount. This is commonly mapped to inner discount or true discount. For the same nominal value, annual rate, and duration, inner discount and outer discount can produce different present values.

• Outer discount: discount is calculated on the nominal value.
• Inner discount: present value is calculated first, then the discount is the difference from nominal value.
• Both depend entirely on user-entered rate and duration.
• Neither method includes bank commissions, tax, or actual transaction terms.

How the formulas work

The calculator first converts the duration into days: entered directly if you chose days, ×30 if you chose months, ×360 if you chose years, or, if you enter a maturity date and a discount date instead, by splitting the span into whole months plus leftover days and applying the same 30-day month — not the real calendar day count. The rate can be entered as a daily, monthly, or annual percentage; for the simple methods it is converted to an annual equivalent for the calculation.

1. Duration is converted to days: direct, ×30 for months, ×360 for years; for two dates, whole months × 30 plus the leftover days.
2. Simple outer discount uses: discount = nominal value × annual rate × (days / 360).
3. Outer present value is nominal value minus the discount amount.
4. Simple inner discount uses: present value = nominal value / (1 + annual rate × (days / 360)).
5. Compound inner discount uses: present value = nominal value / (1 + period rate) ^ number of periods, where the compounding period is chosen with a separate "Compounding Frequency" control (daily, monthly, or annual), independently of the rate's own unit.
6. If you enter the present value instead of the nominal value, the same formulas are applied in reverse to solve for the nominal value.

Worked example: 100,000 nominal, 45% annual rate, 90 days

Suppose the nominal value is 100,000, the annual discount rate is 45%, and the time to maturity is 90 days. The time factor is 90 / 360 = 0.25 years.

1. Simple outer discount: 100,000 × 0.45 × 90 / 360 = 11,250.00 discount.
2. Simple outer present value: 100,000 − 11,250.00 = 88,750.00.
3. Simple inner present value: 100,000 / (1 + 0.45 × 90 / 360) ≈ 89,887.64.
4. Simple inner discount amount: 100,000 − 89,887.64 ≈ 10,112.36.

The example shows why choosing the method matters. Outer discount takes the deduction from the nominal amount, while inner discount discounts the maturity value back to a present value. Compound inner discount only diverges from simple inner discount once there is more than one compounding period.

When this calculator is the right tool

Use this page when your question is about the present cash value of a bill, note, or dated receivable. It is not a shopping discount calculator, even though both contexts use the word discount.

• Use this calculator for inner/outer discount on a bill or promissory note.
• Use an interest calculator when you want a simple interest amount rather than a bill discount value.
• Use an average-maturity calculator when several payments with different due dates must be summarized into one maturity.
• Use purchasing-power or inflation-related tools when the issue is the value of money over time, not bill discounting.

Limitations and trust notes

• Outer discount can become meaningless if annual rate × time is too large and the present value becomes zero or negative.
• Duration can be entered directly (days/months/years) or as a maturity date and a discount date.
• It does not include commissions, taxes, bank fees, BSMV-style charges, or real institution terms.
• It uses a 360-day-year convention for the simple methods; other conventions (such as 365 days) are not offered in this version.