Bank Discount Calculator

What is a Bank Discount?

A bank discount is a method of charging interest on a loan where the interest is deducted upfront from the face value of the note, rather than being paid at maturity. The borrower receives less than the face value (the proceeds), and repays the full face value at maturity. This mechanism is standard for Treasury bills, commercial paper, and banker's acceptances.

The bank discount formula is D = S × d × t, where D is the discount amount withheld upfront, S is the maturity value (face value), d is the annual discount rate (in decimal form), and t is the time in years. The proceeds equation P = S - D gives the actual cash the borrower receives.

How to Use the Bank Discount Calculator

Select the equation type: Bank Discount (D) or Bank Proceeds (P). Then choose what variable to solve for. Enter the known values and the calculator will compute the unknown variable instantly.

Bank Discount Equation

Use this mode when working with the standard bank discount formula D = S × d × t. You can solve for:

Bank Discount (D) — the interest amount withheld upfront given the maturity value, discount rate, and time.
Maturity Value (S) — the face value of the note given the discount, rate, and time.
Discount Rate (d) — the implied annual rate given the discount, maturity value, and time.
Time (t) — the term of the note given the discount, maturity value, and rate.

Bank Proceeds Equation

Use this mode to work with the proceeds identity P = S - D. You can solve for:

Bank Proceeds (P) — the cash the borrower receives given the maturity value and discount.
Maturity Value (S) — the face value given the discount and proceeds.
Discount (D) — the amount withheld given the maturity value and proceeds.

Example: Calculating Bank Discount and Proceeds

A $10,000 note is discounted at 6% for 90 days. Using a 360-day banking year, the time is 90 / 360 = 0.25 years. The bank discount is D = 10,000 × 0.06 × 0.25 = $150. The proceeds are P = 10,000 − 150 = $9,850. The borrower receives $9,850 today and repays the full $10,000 at maturity.

Bank Discount Formulas

Bank discount problems revolve around two relationships:

Bank Discount: D = S × d × t
Bank Proceeds: P = S − D

Where S = maturity value, d = discount rate (decimal), t = time in years, D = bank discount, and P = bank proceeds.

If you're working with interest-bearing instruments, you may also find the Simple Loan Calculator helpful for comparing different lending structures. The Present Value Calculator and APR Calculator provide additional perspectives on the true cost of borrowing and the time value of money, giving you a complete toolkit for financial analysis.

Frequently Asked Questions

What is the difference between a bank discount and simple interest?

With simple interest, interest is paid at maturity and the borrower receives the full principal. With a bank discount, interest is deducted upfront so the borrower receives less than the face value. The effective interest rate on a bank discount is slightly higher than the stated rate.

How are Treasury bills priced using bank discounts?

T-bills are sold at a discount from their face value. A $10,000 T-bill at a 5% discount rate for 182 days would sell for about $9,750. The investor earns $250 when the government pays the full $10,000 at maturity.

What are bank proceeds?

Bank proceeds are the cash the borrower actually receives after the discount is subtracted from the maturity value. If the maturity value is $5,000 and the discount is $200, the proceeds are $4,800.

Why do banks use a 360-day year in discount calculations?

The 360-day year (also called the "banker's year") is a convention that simplifies calculations by treating each month as 30 days. It gives slightly higher interest charges than a 365-day year, which is why banks historically adopted it.

Can bank proceeds ever exceed the maturity value?

No. Proceeds equal maturity value minus the discount. If proceeds appear larger than maturity value, the inputs are inconsistent and should be checked.

How do you solve for the bank discount rate?

Rearrange the discount formula to d = D / (S × t). If the discount is $240 on a $12,000 note for 0.5 years, the rate is 240 / (12,000 × 0.5) = 0.04, or 4%.

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