Treasury Bill Yield Calculator

Background.

A 26-week Treasury bill auctioned at a 4.8% discount rate earns its buyer more than 4.8% a year. The quoted rate is a bank discount rate, which expresses the discount as a share of the face value, not of the money you actually hand over, and it annualises on a 360-day year. Both choices make the quoted figure look smaller than the return on your cash.

Treasury bills pay no coupons. You buy a bill for less than its face value and the Treasury pays you the full face value when it matures; the difference is your interest. TreasuryDirect prices them with one formula, price = face value × (1 − discount rate × days ÷ 360), so a $10,000 bill at 4.8% for 182 days costs $9,757.33 and pays back $10,000, a gain of $242.67.

From those figures come three different percentages, and confusing them is easy. The holding-period return, 2.49% in the example, is what you earn over the life of the bill. The bank discount yield simply restates the 4.8% quote. The investment yield, 4.99% here, divides the gain by the price you paid and annualises over a 365-day year, which makes it the number to set beside a certificate of deposit or a savings account rate. Treasury publishes it on auction results as the investment rate.

Bills come in terms of 4, 6, 8, 13, 17, 26 and 52 weeks, plus cash management bills of variable length, and they are sold in $100 increments with a $100 minimum. The calculator accepts any whole number of days from 1 to 365.

The investment yield follows the method in Treasury's regulations (31 CFR Part 356, Appendix B). For bills of up to half a year it is the simple formula described above. For bills longer than half a year, in practice the 52-week bill, Treasury solves a quadratic formula that comes out somewhat lower than the simple one: a 364-day bill at a 4.8% discount rate has an investment yield of 5.05%, not 5.11%. When the year after a bill's issue date contains 29 February, Treasury annualises over 366 days instead of 365; choose the 366-day investment basis to reproduce that.

What is treasury bill yield calculator?

A Treasury bill is a short-term debt of the US government, maturing in one year or less and sold at a discount to its face value. The bank discount rate is the convention used to quote and auction bills: the dollar discount as a fraction of face value, scaled to a 360-day year. The investment yield, also called the investment rate or coupon-equivalent yield, expresses the same dollar gain as a fraction of the purchase price, scaled to a 365-day year (366 when the year after issue contains 29 February, and by a quadratic formula for bills longer than half a year), so it can be compared with yields on coupon securities and bank deposits. The holding-period return is the unannualised gain over the bill's actual life. All three describe one cash flow; they differ only in the denominator and the length of year. Bills pay their interest only at maturity, and new ones are sold continually: every term except the 52-week bill and cash management bills is auctioned weekly, and the 52-week bill every four weeks.

How to use this calculator.

1. 01Enter the face value in dollars, the amount the Treasury pays at maturity. Bills are sold in multiples of $100. If you start from a sum of cash instead, divide it by the price per $100 and round down to the nearest $100: at the example price, $5,000 buys $5,100 of face value for $4,976.24.
2. 02Enter the bank discount rate as a percentage, the high rate from an auction announcement or the discount quoted by your broker. Zero is allowed, and so are negative rates down to -5%, which put the price above the face value.
3. 03Enter the days to maturity as a whole number, counted from the settlement date to the maturity date. A new 13-week bill has 91 days, a 26-week bill 182 and a 52-week bill 364.
4. 04Leave the discount day-count basis at 360, the US Treasury convention. Switch it to 365 only if the quote you are working from states a 365-day basis.
5. 05Leave the investment yield basis at 365 to match Treasury's investment rate in an ordinary year, and choose 366 when the year after the bill's issue date contains 29 February. The 360 option restates the yield with the simple formula on a money-market footing; it is not part of Treasury's method.
6. 06Read the price and dollar discount first, then compare the investment yield with other cash options.

The formula.

Price P = F × (1 − d × t ÷ B), where F is the face value, d the discount rate as a decimal, t the days to maturity and B the discount basis, 360 by default. The dollar discount is D = F − P, the interest you receive if you hold the bill to maturity. The price per $100 is P ÷ F × 100. The holding-period return is D ÷ P × 100, the percentage gain over t days without annualising. The bank discount yield is D ÷ F × B ÷ t × 100, which by construction always returns the discount rate you entered; it confirms the quote rather than adding information. The investment yield, for a bill of up to half a year (t no more than Y ÷ 2), is D ÷ P × Y ÷ t × 100, with Y = 365 by default; longer bills use the quadratic form described below.

The gap between the discount rate and the investment yield has two sources, and the example separates them neatly. Moving from a 360-day to a 365-day year multiplies 4.8% by 365 ÷ 360, giving 4.8667%. Dividing by the price instead of the face value then divides by 0.9757, giving 4.9877%. The day count adds about 0.0667 percentage points and the smaller denominator about 0.121. Longer bills and higher rates widen the gap, because both deepen the discount. At the same 4.8% discount rate, a 13-week bill (91 days) has an investment yield of 4.93%, the 26-week bill 4.99% and a 364-day bill 5.05% (the 364-day figure uses the quadratic form described below).

The investment yield follows Treasury's investment rate in 31 CFR Part 356, Appendix B. For bills of up to half a year it is a simple yield: it scales the holding-period return up to a year without compounding, so it assumes nothing about reinvesting the proceeds. It matches Treasury's formula exactly whenever the year after issue has 365 days. When that year includes 29 February, Treasury uses 366, which for the example is the 366-day basis and gives 5.0014% instead of 4.9877%. For bills longer than half a year (t greater than Y ÷ 2) Treasury solves the equation P × [1 + (t − Y ÷ 2) × (i ÷ Y)] × (1 + i ÷ 2) = 100, designed to mimic a coupon security paying interest every six months, with the quadratic formula: i = (-b + √(b² - 4ac)) ÷ 2a, where b = t ÷ Y, a = t ÷ 2Y - 0.25 and c = (P - 100) ÷ P, with P as the price per 100. On a 364-day bill at a 4.8% discount rate it gives 5.0513%, against 5.1149% from the simple formula. The 360-day investment basis always uses the simple formula.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Code of Federal Regulations (2026). 31 CFR Part 356, Appendix B, section VI: Computation of Purchase Price, Discount Rate, and Investment Rate (Coupon-Equivalent Yield) for Treasury Bills. eCFR.
2. [2]TreasuryDirect (n.d.). Understanding Pricing and Interest Rates. U.S. Department of the Treasury.
3. [3]TreasuryDirect (n.d.). Treasury Bills In Depth. U.S. Department of the Treasury.
4. [4]TreasuryDirect (n.d.). About Treasury Marketable Securities. U.S. Department of the Treasury.
5. [5]TreasuryDirect (n.d.). Auctions In Depth. U.S. Department of the Treasury.
6. [6]TreasuryDirect (n.d.). FAQs about Treasury Marketable Securities. U.S. Department of the Treasury.
7. [7]TreasuryDirect (2024). Investing Directly with the U.S. Treasury. FS Publication 009.