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Treasury Bill Discount Yield Calculator

Enter the face value, price and days to maturity to find the T-bill yields.

How it is calculated

The tool takes face value F, purchase price P and days to maturity t. The dollar discount is F − P. The bank discount yield is (F − P) ÷ F × 360 ÷ t × 100, which divides by face value and uses a 360-day year. The bond-equivalent yield is (F − P) ÷ P × 365 ÷ t × 100, which divides by the price actually paid and uses a 365-day year, so it is always higher for a positive discount. Yields are shown as percentages to three decimals. Face, price and days must be above zero. The bond-equivalent figure is the simple version, with no compounding adjustment for bills of more than half a year. A price above face gives negative yields; taxes and fees are not included.

Worked example

A bill with a face value of 10,000 is bought for 9,900 and matures in 91 days. Discount = 10,000 − 9,900 = $100.00. Discount yield = 100 ÷ 10,000 × 360 ÷ 91 × 100 = 3.956%. Bond-equivalent yield = 100 ÷ 9,900 × 365 ÷ 91 × 100 = 4.052%. The second figure is higher because you earned the $100 on 9,900 actually invested, not on 10,000.

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Common mistakes

  • Treating the discount yield as what you actually earn. It is a quoting convention based on face value and a 360-day year; the bond-equivalent yield is closer to the real return on the money invested.
  • Entering the discount rate or a price per 100 as the price. The price field is the actual dollar price paid for the stated face value, so 99.00 per 100 on a 10,000 bill is 9,900.
  • Entering the maturity in months or weeks. The field is days to maturity, such as 91 for a 13-week bill.
  • Comparing a bill's discount yield with a bond's coupon yield. For a fair comparison use the bond-equivalent figure.
  • Expecting the result to be after tax or fees, or to compound reinvestment of proceeds.

Sources

About this calculator

Treasury bills are sold at a discount to face value and mature at par, so their return is expressed as a bank discount yield: ((Face Value − Purchase Price) / Face Value) × (360 / Days to Maturity), using a 360-day banker's year. Because this understates the true return (it divides by face value rather than the actual price paid, and uses a 360- instead of 365-day year), a bond-equivalent yield is also calculated to make T-bills comparable to interest-bearing bonds quoted on an actual/365 basis.

Fixed-income traders, Treasury investors and money-market analysts use both figures side by side — the discount yield because it is the quoting convention used in the T-bill market itself, and the bond-equivalent yield to compare a T-bill's return fairly against coupon-paying bonds or other yield-quoted instruments.

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