What is the difference between discount rate and bond-equivalent yield?

The bank discount rate measures the gain against face value over 360 days; the bond-equivalent yield measures it against the price you actually paid over 365 days. The bond-equivalent yield is higher and is the right figure for comparing T-bills to other investments.

Why do T-bills use a 360-day year?

It is a long-standing money-market convention dating to manual interest calculations. It makes the quoted discount rate slightly lower than the true annualized return, which is one reason the bond-equivalent yield exists.

How do T-bills pay interest?

They do not pay periodic coupons. Instead you buy them below face value and receive the full face value at maturity; the difference is your interest. This is called a discount security.

What maturities do T-bills come in?

Common maturities are 4, 8, 13, 17, 26, and 52 weeks. Shorter bills have less interest-rate risk; the days-to-maturity you enter should match the specific bill you are evaluating.

Are T-bill returns taxable?

T-bill interest is subject to federal income tax but exempt from state and local income taxes — an advantage in high-tax states. This calculator shows pre-tax yields.

What is the difference between discount rate and bond-equivalent yield?

The bank discount rate measures the gain against face value over 360 days; the bond-equivalent yield measures it against the price you actually paid over 365 days. The bond-equivalent yield is higher and is the right figure for comparing T-bills to other investments.

Why do T-bills use a 360-day year?

It is a long-standing money-market convention dating to manual interest calculations. It makes the quoted discount rate slightly lower than the true annualized return, which is one reason the bond-equivalent yield exists.

How do T-bills pay interest?

They do not pay periodic coupons. Instead you buy them below face value and receive the full face value at maturity; the difference is your interest. This is called a discount security.

What maturities do T-bills come in?

Common maturities are 4, 8, 13, 17, 26, and 52 weeks. Shorter bills have less interest-rate risk; the days-to-maturity you enter should match the specific bill you are evaluating.

Are T-bill returns taxable?

T-bill interest is subject to federal income tax but exempt from state and local income taxes — an advantage in high-tax states. This calculator shows pre-tax yields.

Treasury Bill Discount Rate Calculator

Compute a T-bill’s bank discount rate and bond-equivalent yield from its face value, purchase price, and days to maturity.

Result

Bank discount rate

4.9451%

bond-equivalent yield 5.1423%

Discount (Face − Price)$250.00
Bank discount rate (360-day)4.9451%
Bond-equivalent yield (365-day)5.1423%
Holding-period return2.5641%
Annualized (simple, 365)5.1423%

Source: Bank discount rate = (Face − Price)/Face × 360/days. Bond-equivalent yield (investment yield) = (Face − Price)/Price × 365/days.

Not financial advice — T-bills are quoted on a bank-discount basis (360-day year, against face value), which understates the true return. The bond-equivalent yield (365-day year, against price paid) is the better measure for comparing to other investments.

Step-by-step

Discount = face − price = $10,000.00 − $9,750.00 = $250.00.
Bank discount rate = discount/face × 360/days = 2.500% × (360/182) = 4.9451%.
Bond-equivalent yield = discount/price × 365/days = 5.1423% — the truer comparison yield.

How to use this calculator

Enter the T-bill’s face value (what you receive at maturity).
Enter the purchase price (what you pay today).
Enter the days to maturity.
Read the bank discount rate and the more meaningful bond-equivalent yield.

About this calculator

Treasury bills (T-bills) are short-term U.S. government securities sold at a discount to their face value; you pay less than face today and receive the full face value at maturity, with the difference being your return. They are quoted two ways, and the distinction matters. The bank discount rate is the traditional quote: the discount as a fraction of face value, annualized over a 360-day year. But because it measures the gain against face value (not the smaller price you actually paid) and uses a 360-day year, it understates your real return. The bond-equivalent yield (also called the investment yield) corrects both, measuring the gain against the price paid over a 365-day year — making it directly comparable to other investments. This calculator reports both from your face value, purchase price, and days to maturity.

How it works — the formula

Bank discount rate = (Face − Price)/Face × 360/days
Bond-equivalent yield = (Face − Price)/Price × 365/days

The discount rate annualizes the gain against face on a 360-day basis; the bond-equivalent yield annualizes against price on a 365-day basis for true comparison.

Source: TreasuryDirect — Treasury Bills

Worked examples

Example 1

Face $10,000, price $9,750, 182 days

Inputs:: face=10000, price=9750, days=182
Output:: discount 4.945%, BEY 5.142%

Example 2

Face $10,000, price $9,900, 91 days

Inputs:: face=10000, price=9900, days=91
Output:: discount ~3.96%, BEY ~4.05%

Example 3

Face $1,000, price $980, 52 weeks

Inputs:: face=1000, price=980, days=364
Output:: discount ~2.02%, BEY ~2.05%

Limitations

Bank discount rate understates true return (use BEY to compare).
Simple annualization; does not compound.
Pre-tax yields; state-tax exemption not modeled.

Quoting conventions per TreasuryDirect; not investment advice.

Frequently asked

The bank discount rate = (face value − price) ÷ face value × (360 ÷ days to maturity). It expresses the discount as an annualized percentage of face value using a 360-day year — the convention for quoting T-bills.