Treasury Bill Yield Calculator

Background.

A Treasury bill yield calculator prices a short-term U.S. Treasury bill from face value, discount rate, and days to maturity, then compares several return measures. Treasury bills are discount securities. The investor pays less than face value and receives face value at maturity. There are no semiannual coupon payments like a Treasury note or Treasury bond. The interest is the difference between what the investor paid and what Treasury pays back at maturity.

The example uses a $10,000 face value bill, a 4.8 percent bank discount rate, and 182 days to maturity. TreasuryDirect's bill pricing formula is price equals face value times one minus discount rate times time divided by 360. Converting 4.8 percent to decimal gives 0.048. The time fraction is 182 divided by 360. Multiplying 0.048 by 182 divided by 360 gives 0.0242666666666666. One minus that value is 0.975733333333333. Multiplying by $10,000 gives a purchase price of $9,757.33333333333.

The discount is the difference between face value and purchase price. In the example, $10,000 minus $9,757.33333333333 equals $242.666666666666. That discount is the investor's dollar interest if the bill is held to maturity, before considering taxes, fees, reinvestment, or secondary-market sale. The price per $100 of face value is $97.5733333333333, which is the purchase price divided by face value and multiplied by 100.

The return measures then separate three ideas that users often confuse. Holding-period return asks how much the investor earned relative to the money paid. The example divides $242.666666666666 by $9,757.33333333333 and multiplies by 100, giving 2.48701831101393 percent for the 182-day holding period. Bank discount yield uses the dollar discount over face value and a 360-day basis. Recomputing it from the example gives 4.79999999999999 percent, which rounds back to the quoted 4.8 percent. Investment yield uses the dollar discount over purchase price and a 365-day annualization basis. In the example, it is 4.98770155780266 percent.

This distinction is the reason the calculator is valuable. A quoted Treasury bill discount rate is not exactly the investor's annual return on cash invested. The quoted discount rate uses face value in the denominator. The investor actually pays less than face value, so a price-denominator yield is usually higher than the bank discount yield for a positive discount. The day-count basis also changes the number. A product that labels all of these as simply yield creates confusion.

For Quanta, the calculator should support two modes. The first mode prices a bill from face value, discount rate, and days. The second mode starts with settlement price or price per $100 and computes the implied discount rate and investment yield. The first release can implement the pricing mode because it maps directly to TreasuryDirect's formula and common auction result pages. Later, the same formula can be rearranged for price-to-yield calculations.

The tool should also include important limitations. Treasury bills can be bought through TreasuryDirect, banks, or brokers, and secondary-market prices can differ from auction pricing. Fees, bid-ask spreads, taxes, settlement timing, and reinvestment assumptions are outside the base formula. The calculator should not promise auction allocation, current rates, or suitability. It should compute transparent arithmetic for users who already know the face value, discount rate, and days to maturity.

What is treasury bill yield calculator?

A Treasury bill yield calculator is a fixed-income arithmetic tool for U.S. Treasury bills. Treasury bills mature in one year or less and are generally sold at a discount from face value. At maturity, the holder receives face value. The difference between purchase price and face value is the interest earned if the bill is held to maturity.

The key terms are face value, purchase price, discount rate, bank discount yield, days to maturity, price per $100, holding-period return, investment yield, auction, maturity, and discount security. Face value is the amount paid at maturity. Purchase price is what the investor pays upfront. Discount dollars are face value minus purchase price. Bank discount yield annualizes the discount using face value and a 360-day basis. Holding-period return uses purchase price as the denominator and does not annualize. Investment yield uses purchase price as the denominator and annualizes on a 365-day basis in this dossier.

The calculator is valid for formula arithmetic on a known bill term and discount rate. It is not a live auction feed, investment recommendation, tax calculator, broker quote, or guarantee of allocation. It should not be used for coupon-bearing Treasury notes or bonds because those securities pay periodic interest and use different pricing mathematics. It is specifically for discount Treasury bills and similar short-term discount-security comparisons.

How to use this calculator.

1. 01Enter the Treasury bill face value.
2. 02Enter the quoted bank discount rate as a percent.
3. 03Enter the number of days to maturity.
4. 04Review the calculated purchase price and dollar discount.
5. 05Compare holding-period return with bank discount yield.
6. 06Review investment yield if you want a price-denominator annualized return.
7. 07Confirm actual auction, broker, tax, and settlement details before investing.

The formula.

The calculator first converts the quoted discount rate from percent to decimal. A 4.8 percent discount rate becomes 0.048. TreasuryDirect's pricing formula for bills is face value times one minus discount rate times time divided by 360. The 360-day denominator is part of the bank discount convention. In the example, the time fraction is 182 divided by 360, and 0.048 times that fraction equals 0.0242666666666666.

One minus the discount fraction equals 0.975733333333333. Multiplying by the $10,000 face value gives $9,757.33333333333. That is the unrounded purchase price from the formula. Treasury systems may round actual dollar amounts to cents according to their rules. The dossier keeps full precision so implementation tests can verify the formula without display-rounding noise.

The dollar discount is face value minus price. Here, $10,000 minus $9,757.33333333333 equals $242.666666666666. Price per $100 is the purchase price divided by face value and multiplied by 100. With the example values, that gives 97.5733333333333 per $100 of face value.

Holding-period return uses the actual cash paid as the denominator. It divides the discount by price and multiplies by 100. The example calculation is $242.666666666666 divided by $9,757.33333333333 times 100, which equals 2.48701831101393 percent. This is the return over 182 days, not a full-year annualized value.

Bank discount yield reverses the discount-rate convention. It divides the discount by face value, multiplies by 360 divided by days to maturity, and then multiplies by 100. Using the example, $242.666666666666 divided by $10,000 times 360 divided by 182 times 100 equals 4.79999999999999 percent, which rounds to the original 4.8 percent.

Investment yield in this dossier uses the price denominator and a 365-day annualization. It divides the discount by price, multiplies by 365 divided by days, and then multiplies by 100. The example gives 4.98770155780266 percent. The product should label this convention because different platforms may use terms such as investment rate, coupon-equivalent yield, or bond-equivalent yield differently. The safe design is to show formulas beside the result labels.

A worked example.

Frequently asked questions.

References& sources.

1. [1]TreasuryDirect (n.d.). Understanding Pricing and Interest Rates. U.S. Department of the Treasury.
2. [2]TreasuryDirect (n.d.). Treasury Bills In Depth. U.S. Department of the Treasury.
3. [3]TreasuryDirect (n.d.). About Treasury Marketable Securities. U.S. Department of the Treasury.
4. [4]TreasuryDirect (n.d.). Auctions In Depth. U.S. Department of the Treasury.
5. [5]TreasuryDirect (n.d.). FAQs about Treasury Marketable Securities. U.S. Department of the Treasury.
6. [6]TreasuryDirect (2024). Investing Directly with the U.S. Treasury. FS Publication 009.