T-Bill Calculator

The T-Bill Calculator works out the discount purchase price, dollar return, and yield of a U.S. Treasury bill. Because a T-bill pays no coupon — you buy it below face value and collect par at maturity — its quoted "discount rate" is not the same as the return you actually earn. This tool untangles all three yardsticks (the bank discount rate, the coupon-equivalent investment yield, and the effective annual yield/APY) and, because T-bill interest is exempt from state and local income tax, shows the tax-equivalent yield a taxable CD would have to beat.

What is a Treasury Bill?

A Treasury bill (T-bill) is a short-term debt obligation backed by the U.S. government with a maturity of one year or less. T-bills are sold at a discount to their face (par) value and pay no periodic interest. When the bill matures, the Treasury pays you the full face value; the gap between your discounted purchase price and that face value is your return. They are considered among the safest investments available because they are backed by the full faith and credit of the U.S. government.

T-Bill Formulas

Three short formulas connect the price to the rates. Note that the discount rate uses a 360-day year and the face value, while the investment yield uses a 365-day year and the price you actually paid.

Where F is the face value, P is the purchase price, d is the discount rate, t is days to maturity, and i is the investment (coupon-equivalent) yield. For bills longer than 182 days — such as the 52-week bill — the Treasury uses a compounding-aware quadratic formula for the investment yield, which this calculator applies automatically.

Standard T-Bill Terms

Discount Rate vs Investment Yield vs APY

These three numbers describe the same bill but answer different questions, which is why a T-bill quote can look confusing:

• Bank discount rate — the headline number used at auction. It divides the discount by the face value and assumes a 360-day year, so it is always the lowest of the three and understates your true return.
• Investment (coupon-equivalent) yield — divides the return by the price you actually paid and uses a 365-day year. This is the fairest "apples-to-apples" number for comparing a T-bill with a bond or CD.
• Effective annual yield (APY) — compounds the return over a full year, so it is the most directly comparable to a savings account or money-market APY.

The State-Tax Advantage

Interest earned on Treasury bills is subject to federal income tax but exempt from state and local income taxes. For an investor in a high-tax state, that exemption can make a T-bill meaningfully more valuable than a CD or savings account paying the same headline rate. The tax-equivalent yield grosses up the T-bill's yield to show what a fully taxable alternative would need to pay:

Where i is the T-bill investment yield and s is your combined state and local marginal income tax rate (as a decimal). For example, a 5.20% T-bill yield for an investor facing a 9.3% state tax rate is equivalent to a taxable CD yielding about 5.73%.

What Affects Your T-Bill Return?

How to Use This Calculator

1. Enter the face value and term: The face value defaults to $1,000. Choose a standard term (4 to 52 weeks) or enter a custom number of days.
2. Choose your known input: Select whether you know the discount rate or the purchase price, then enter that value.
3. Add your state tax rate (optional): Enter your combined state and local rate to see the tax-equivalent yield.
4. Click Calculate: Review the purchase price, dollar return, the three yields, the tax-equivalent comparison, and a full step-by-step breakdown.

Frequently Asked Questions

What is a Treasury bill (T-bill)?

A Treasury bill is a short-term U.S. government debt security that matures in one year or less. It pays no periodic interest. Instead you buy it at a discount to its face value and receive the full face value at maturity, and the difference is your return.

How is the price of a T-bill calculated?

Price = Face value × (1 − the discount rate × days to maturity ÷ 360). For example, a $1,000, 91-day bill quoted at a 5.10% discount rate costs about $987.11.

What is the difference between the discount rate and the investment yield?

The bank discount rate is based on the face value and a 360-day year, so it understates your true return. The investment yield, also called the coupon-equivalent or bond-equivalent yield, is based on the price you actually paid and a 365-day year, so it is higher and reflects what you really earn.

Are Treasury bills exempt from taxes?

T-bill interest is subject to federal income tax but is exempt from state and local income taxes. That exemption can make a T-bill's after-tax return higher than a CD paying the same headline rate, especially in high-tax states. This calculator shows the tax-equivalent yield a taxable CD would need to match.

What is the tax-equivalent yield of a T-bill?

The tax-equivalent yield is the T-bill's investment yield divided by one minus your state and local tax rate. It tells you the yield a fully taxable investment, such as a bank CD, would have to pay to leave you with the same after-tax return.

What terms do Treasury bills come in?

The Treasury regularly auctions bills with terms of 4, 8, 13, 17, 26, and 52 weeks, which correspond to 28, 56, 91, 119, 182, and 364 days. This calculator also accepts any custom number of days up to one year.

Additional Resources

• United States Treasury Security - Wikipedia
• Treasury Bills - TreasuryDirect