Treasury Bill Yield Calculator

A Treasury bill (T-bill) yield calculator converts between the purchase price of a Treasury bill and its equivalent annualised yield, or vice versa. It is used by cash investors, money market fund managers, and anyone comparing short-term government securities to other cash instruments. T-bills are issued at a discount to face value and mature at par, making yield calculations slightly different from standard interest-bearing bonds.

How to Use the Treasury Bill Yield Calculator

1. Enter the face value (par value) of the T-bill, typically £1,000 or $1,000 per bill.
2. Input the purchase price (the discounted price you pay today).
3. Enter the days to maturity (T-bills commonly have maturities of 4, 8, 13, 26, or 52 weeks).
4. Select whether you want the discount yield, the bond-equivalent yield (BEY), or the money market yield.
5. The calculator outputs the relevant yield figure and the expected return at maturity.

The Formula

T-bills use a discount yield convention, not the standard compound interest formula.

Discount Yield (also called bank discount yield): Discount Yield = ((Face Value minus Purchase Price) divided by Face Value) multiplied by (360 divided by Days to Maturity) multiplied by 100

Bond Equivalent Yield (BEY), which uses a 365-day year and is more comparable to coupon bond yields: BEY = ((Face Value minus Purchase Price) divided by Purchase Price) multiplied by (365 divided by Days to Maturity) multiplied by 100

The BEY is generally the preferred yield for direct comparison to other fixed income instruments because it uses the actual investment (purchase price) as the base rather than face value, and uses a 365-day year.

Real-World Example

A 91-day (approximately 13-week) UK gilt bill with a face value of £1,000 is purchased for £988.50.

Discount: £1,000 minus £988.50 = £11.50

Discount Yield = (£11.50 divided by £1,000) multiplied by (360 divided by 91) multiplied by 100 = 0.0115 multiplied by 3.956 multiplied by 100 = 4.55%

Bond Equivalent Yield = (£11.50 divided by £988.50) multiplied by (365 divided by 91) multiplied by 100 = 0.01163 multiplied by 4.011 multiplied by 100 = 4.67%

The BEY of 4.67% is slightly higher than the discount yield of 4.55%. This difference occurs because the BEY uses the purchase price (£988.50) rather than face value as the denominator, and uses a 365-day year rather than 360 days. When comparing T-bill yields to savings account rates or bond yields, always use the BEY for like-for-like comparison.

T-Bills vs Other Cash Instruments

T-bills are among the safest investments available because they are backed by the full credit of the government issuing them. They are used as the "risk-free rate" in financial modelling precisely because default risk is considered negligible.

Compared to savings accounts, T-bills may offer higher yields in some market environments, particularly when central banks have raised interest rates. They are also more liquid than fixed-term deposits, as they can be sold in secondary markets before maturity.

Money market funds invest heavily in T-bills and other short-term government securities, effectively packaging the T-bill yield into a daily-accessible product. The yield on money market funds often closely tracks the current T-bill rate minus a small management fee.

UK equivalents include UK Treasury bills issued by the Debt Management Office, while in the US they are issued directly by the Department of the Treasury. Both are auctioned regularly to institutional and retail investors.

One important distinction is that T-bill income may be exempt from state or local tax in the US, though it is subject to federal income tax. In the UK, gilt income is subject to income tax but exempt from capital gains tax if the gilt was purchased at or above par.

Frequently Asked Questions

How is the T-bill yield related to the base interest rate? T-bill yields closely track the central bank's policy rate (the Bank of England base rate or the Federal Reserve funds rate). When central banks raise rates, T-bill yields rise with them. T-bills typically yield slightly less than the policy rate for short maturities, reflecting their exceptional liquidity and safety premium.

Can individual investors buy Treasury bills directly? In the US, individuals can purchase T-bills directly through TreasuryDirect.gov with a minimum purchase of $100. In the UK, retail investors cannot purchase government Treasury bills directly but can access gilts (including short-dated gilts that behave like T-bills) through brokers or the NS&I. Short-duration gilt ETFs are also widely available and provide similar exposure with daily liquidity.

Why do T-bills use a 360-day year in the discount yield formula? The 360-day convention dates back to pre-computer era banking practices when calculations were done manually and a 360-day year simplified the arithmetic. It remains embedded in US money market conventions. The 365-day bond-equivalent yield is considered more accurate and is preferable for comparative purposes.

What is the difference between a T-bill and a T-note or T-bond? T-bills (Treasury bills) have maturities of up to one year and are issued at a discount to face value. T-notes (Treasury notes) have maturities of 2 to 10 years and pay regular coupon interest. T-bonds (Treasury bonds) have maturities of 20 to 30 years and also pay coupons. The key distinction is maturity and whether the instrument pays periodic coupon interest or is purchased at a discount.

The four figures the calculator reports

The bond equivalent yield is the headline number, and four supporting figures sit underneath it. They answer different questions about the same trade.

| Figure | Formula | Basis | Value for the 91-day example | | Bank discount rate | (Face less price) / face x 360 / days | Face value, 360-day year | 4.550% | | Holding period return | (Face less price) / price | The 91 days held | 1.163% | | Bond equivalent yield | Holding period return x 365 / days | Purchase price, 365-day year | 4.666% | | Effective annual yield | (1 + holding period return) ^ (365 / days) - 1 | Purchase price, compounded | 4.749% |

The dollar gain printed alongside them is the discount itself: 1,000.00 minus 988.50 gives 11.50.

The gap between 4.550 and 4.666 percent explains itself once the two denominators are compared. The discount rate charges the 11.50 against the face value of 1,000. The bond equivalent yield charges the same 11.50 against the 988.50 actually paid. The money at risk is smaller, so the return on it is larger. The 360-day year widens the gap further, and the 364-day bill shows the widest divergence of the maturities in common issue because the annualisation factor is largest there.

The effective annual yield is the only one of the four that accounts for compounding inside the year. On a 91-day bill the step from 4.666 to 4.749 percent is what compounding three further 91-day periods adds.

The same discount across five maturities

Holding the discount at 11.50 and varying the days to maturity separates the annualisation from the return:

| Days to maturity | Weeks | Bank discount rate | Money market yield | Bond equivalent yield | | 28 | 4 | 14.786% | 14.958% | 15.165% | | 56 | 8 | 7.393% | 7.479% | 7.583% | | 91 | 13 | 4.549% | 4.602% | 4.666% | | 182 | 26 | 2.275% | 2.301% | 2.333% | | 364 | 52 | 1.137% | 1.151% | 1.167% |

Every row is the same 11.50 of discount on the same 1,000 of face value. The 4-week bill reports a yield more than twelve times the 52-week bill while returning identical cash, which is the whole content of the annualisation. The money market yield sits between the other two on every row, because it uses the 360-day year of the discount rate and the purchase price base of the bond equivalent yield.

The Treasury's own price formula

Everything above converts a price into a yield. The US Treasury publishes the reverse conversion in 31 CFR Part 356, Appendix B: the price per 100 equals 100 multiplied by (1 minus the discount rate times the days remaining, divided by 360).

The regulation works the formula through two examples. Reading a discount rate off a price:

| Input | Value | | Discount rate | 7.610% | | Days from 24 November 1989 to 22 February 1990 | 90 | | Price per 100 | 98.097500 |

And reading a discount rate from a price:

| Input | Value | | Price per 100 | 95.934567 | | Days from 30 December 1982 to 30 June 1983 | 182 | | Discount rate | 8.042% |

Prices per 100 are rounded to six decimal places. The same appendix is the source of the 360-day convention: the discount rate is expressed in percentage terms on a 360-day year and is also called the bank discount rate.

What the calculation leaves out

The four figures assume the bill is held to maturity and that the issuer pays par on the maturity date. They do not model a sale before maturity, where the realised return depends on the market price on the day, and they do not include dealing costs, custody charges or a broker's spread. A bill bought at auction and held has no such costs beyond the settlement amount, which is why the arithmetic matches the realised return closely in that case and only approximately for a trade in the secondary market.

The days field takes the actual number of days, not weeks or months. Entering 13 for a 13-week bill returns a yield about seven times too high, because the formula annualises whatever number it is given. The tool also requires a price below the face value, since a bill priced above par would produce a negative discount and the formula has no branch for that case.

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