Share:
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?
- Bank discount: D = $10,000 × 0.06 × 0.25 = $150
- Proceeds: Pb = $10,000 − $150 = $9,850
The borrower receives $9,850 today and repays $10,000 at maturity.
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.
Related Calculators
- Interest Rate Calculator — compute simple and compound interest.
- Compounding & Discount Factors Calculator — time value of money calculations.
- Present Worth Calculator — discount future cash flows to present value.
- Loan Calculator — compute monthly payments and amortization schedules.
Reference: Kellison, Stephen G. The Theory of Interest. McGraw-Hill Education.