🏛️ T-Bill Calculator

Enter the face value, purchase price, and term of a Treasury bill to calculate the discount amount, bank discount yield, and investment yield (bond-equivalent yield).

Discount Amount

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Discount Amount — Bank Discount Yield — Investment Yield (BEY) — Total Return —

Yield Breakdown

Metric	Formula	Value

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What Is a Treasury Bill (T-Bill)?

A Treasury bill, or T-bill, is a short-term debt obligation issued by the U.S. Department of the Treasury with maturities of 4, 8, 13, 17, 26, or 52 weeks. Unlike bonds that pay periodic coupon interest, T-bills are sold at a discount to their face (par) value and pay the full face value at maturity the difference between what you pay and what you receive at maturity is your return. For example, you might pay $9,800 for a bill with a $10,000 face value maturing in 13 weeks, earning a $200 discount over that period. T-bills are considered one of the safest investments available because they are backed by the full faith and credit of the U.S. government, and they are highly liquid, tradable in a deep secondary market before maturity through TreasuryDirect or a brokerage.

Bank Discount Yield Explained

The bank discount yield (sometimes just called the "discount rate") is the traditional method used to quote T-bill yields and is calculated as the discount amount divided by the face value, annualized using a 360-day year: Bank Discount Yield = (Discount / Face Value) x (360 / Days to Maturity). Using a $10,000 face value bill purchased for $9,800 with 91 days to maturity (13 weeks), the discount is $200, giving a bank discount yield of ($200/$10,000) x (360/91) = 7.912%. This method understates the true return in two ways: it divides by face value rather than the actual amount invested (the purchase price), and it uses a 360-day year instead of a 365-day year. Despite these quirks, the bank discount yield remains the standard convention quoted at Treasury auctions and by TreasuryDirect.

Investment Yield (Bond-Equivalent Yield) Explained

Because the bank discount yield understates real returns, most investors compare T-bills to other investments using the investment yield, also called the coupon-equivalent yield or bond-equivalent yield (BEY). For bills maturing in 182 days or less, BEY = (Discount / Purchase Price) x (365 / Days to Maturity), which correctly divides by the amount actually invested and uses a 365-day year. On the same $10,000/$9,800/91-day example, BEY = ($200/$9,800) x (365/91) = 8.186% noticeably higher than the 7.912% bank discount yield for the identical bill. For bills with more than 182 days to maturity (the 52-week bill), the U.S. Treasury uses a more complex semiannual-compounding formula because a full year of a discount instrument technically involves compounding, and a simple linear annualization would understate the yield.

The Long-Maturity BEY Formula for 52-Week Bills

For Treasury bills with a term longer than 182 days (the 52-week/364-day bill), the Treasury applies a formula that accounts for semiannual compounding: BEY = [-2y + 2 x sqrt(y^2 - (2y-1) x (D/P))] / (2y-1), where y = days/365, D is the discount amount, and P is the purchase price. This quadratic-style formula exists because a bill held longer than half a year, if it were a coupon-bearing instrument, would compound semiannually, and the BEY is designed to make T-bill yields directly comparable to Treasury notes and bonds that do compound. This calculator automatically applies the correct formula based on your selected term short terms (up to 26 weeks) use the simple linear formula, while the 52-week term uses this semiannual-compounding version.

T-Bills vs CDs vs Money Market Funds

T-bills compete with certificates of deposit (see our CD Ladder Calculator) and money market funds as short-term, low-risk places to park cash. The key advantage of T-bills is that their interest income is exempt from state and local income taxes, though it is still subject to federal income tax an important consideration for residents of high-tax states like California or New York, where the after-tax yield on a T-bill can exceed a similarly priced CD. T-bills also settle and can be purchased directly with no fees through TreasuryDirect.gov in denominations as low as $100, and they can be sold before maturity on the secondary market, though CDs are generally not liquid before maturity without an early withdrawal penalty. Money market funds offer daily liquidity and diversification across short-term instruments (including T-bills) but layer on a small expense ratio and do not offer the same state-tax exemption as a direct T-bill holding.

How to Buy Treasury Bills

Individual investors can buy T-bills directly and commission-free through TreasuryDirect.gov, either at a scheduled auction (competitive or noncompetitive bidding) or on the secondary market through a brokerage account. At auction, a noncompetitive bid guarantees you receive the full amount you request at the yield determined by the auction, which is the simplest approach for most retail investors. Auctions for 4, 8, 13, 17, 26, and 52-week bills occur on a regular weekly or monthly schedule published by the Treasury. Many investors also ladder T-bills similarly to CDs, purchasing bills of different maturities so that a portion of the portfolio matures and becomes available on a rolling basis; this calculator, alongside our CD Ladder Calculator, can help you compare the yields and structure of each approach.

Taxes on Treasury Bill Interest

The full discount (face value minus purchase price) realized on a T-bill is treated as interest income for federal tax purposes in the year the bill matures or is sold, even though no periodic coupon payments are made. This income is reported on Form 1099-INT and must be included in federal taxable income, but it is exempt from state and local income taxes in all 50 states, which can meaningfully improve the after-tax yield compared to a bank CD paying a similar nominal rate, especially for residents of states with high income tax rates. As with any investment decision, consult a tax professional regarding your specific situation, and remember that this calculator provides estimates only.

常見問題

Why is my T-bill yield higher than the discount rate I saw quoted?

The quoted "discount rate" at auction is the bank discount yield, which divides by face value and uses a 360-day year. The investment yield (BEY) shown by this calculator divides by the actual purchase price and uses a 365-day year, which is always a higher, more accurate representation of your real annualized return.

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

Bank discount yield = (Discount / Face Value) x (360 / Days). Investment yield (BEY) = (Discount / Purchase Price) x (365 / Days) for terms of 182 days or less, or a semiannual-compounding formula for the 52-week bill. Investment yield better reflects your actual percentage return on the money you invested.

T-Bill 是安全的投資嗎？

是。T-Bill 由美國政府的完整信用背書，普遍被視為最安全的短期投資之一。不過，和所有固定收益工具一樣，一旦買入後，若市場利率上升，其殖利率不會隨之調整。

T-Bill 利息需要繳州所得稅嗎？

不用。美國國庫券的利息免徵州與地方所得稅，但仍需繳納聯邦所得稅。

T-Bill 可以在到期前賣出嗎？

可以。T-Bill 可透過券商帳戶在到期前於次級市場賣出，不過你拿到的價格會取決於賣出當時的現行利率，可能高於或低於你的原始買入價格。

這個工具算是理財建議嗎？

不算。這個計算器僅供教育與估算用途，不構成財務、投資或稅務建議。實際拍賣結果、交割日期與殖利率都會不同；在做決定前，請參考 TreasuryDirect.gov 或諮詢持牌理財顧問。