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Bank Discounts Calculator

Bank discount equals maturity value times discount rate times time

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Bank Discount Equation

A bank discount is interest deducted upfront from a loan or note. The borrower receives less than the face value, and the difference is the bank’s profit. This method is common with Treasury bills and commercial paper.

D = S × d × t

Bank Proceeds Equation

The proceeds equation gives the actual cash the borrower receives after the discount is subtracted from the maturity value.

Pb = S − D

How It Works

A bank discount is interest deducted upfront from a loan or note, rather than charged at maturity. The borrower receives less than the face value, and the difference is the bank’s profit. This method is common with Treasury bills and commercial paper. Two equations apply: the discount equation D = S × d × t calculates how much the bank withholds, while the proceeds equation Pb = S − D gives the actual cash the borrower receives.

Example Problem

A $10,000 note is discounted at 6% for 90 days (0.25 years). How much does the borrower receive?

  1. Bank discount: D = $10,000 × 0.06 × 0.25 = $150
  2. Proceeds: Pb = $10,000 − $150 = $9,850

The borrower receives $9,850 today and repays $10,000 at maturity.

When to Use Each Variable

  • Solve for Bank Discount (D) — when you know the maturity value, discount rate, and time and need to find how much interest the bank deducts upfront, e.g., pricing a commercial note.
  • Solve for Maturity Value (S) — when you know the discount amount, rate, and time and need the face value of the note, e.g., structuring a promissory note.
  • Solve for Discount Rate (d) — when you know the discount, maturity value, and time and need the implied rate, e.g., comparing T-bill yields.
  • Solve for Time (t) — when you know the discount, maturity value, and rate and need the term, e.g., determining how long until a note matures.
  • Solve for Bank Proceeds (Pb) — when you know the maturity value and discount and need the cash the borrower receives, e.g., calculating net funds from a discounted loan.
  • Solve for Maturity Value from Proceeds — when you know the proceeds and discount and need the face value, e.g., reverse-engineering the note amount from cash received.
  • Solve for Discount from Proceeds — when you know the maturity value and proceeds and need the discount amount, e.g., verifying bank charges on a discounted note.

Key Concepts

A bank discount deducts interest at the time of loan origination rather than at maturity. The effective interest rate is always higher than the stated discount rate because the borrower receives less than the face value but repays the full amount. The proceeds equation (Pb = S - D) shows the actual cash disbursed. This mechanism is standard for Treasury bills, commercial paper, and banker's acceptances.

Applications

  • Treasury bill pricing: calculating the purchase price and yield of short-term government securities
  • Commercial lending: determining upfront interest deductions on short-term business notes
  • Trade finance: pricing banker's acceptances used in international import/export transactions
  • Money market analysis: comparing effective yields between discount instruments and interest-bearing alternatives

Common Mistakes

  • Expressing time in days but forgetting to convert to years — the formula uses time in years, so 90 days must be entered as 90/360 = 0.25, not 90
  • Comparing the bank discount rate directly to a simple interest rate — the effective rate on a discount instrument is higher because you earn interest on less principal; always compute the effective rate for fair comparison
  • Confusing maturity value with proceeds — the maturity value is what the borrower repays, not what they receive; the proceeds are always less by the discount amount

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.

Reference: Kellison, Stephen G. The Theory of Interest. McGraw-Hill Education.

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