How Treasury bills are priced
By Jude Wallis
A Treasury bill pays no coupon. It is bought at a discount and redeemed at face. On $10,000 face, a 5 percent discount for 180 days on a 360-day year prices the bill at $9,750. The $250 gap is the discount earned if held to maturity.
Price today
$1,000.00
$25.00 per coupon, twice a year, then $1,000.00 back at maturity. It trades at par.
- Coupon per payment
- $25.00
- Coupon rate, on face value
- 5.00%
- Current yield, on price
- 5.00%
- Premium or discount
- $0.00
What the issuer repays at maturity. Coupons are quoted on this, never on the price.
The annual rate, fixed when the bond is issued, so this one does not move. It is split across the coupons in a year.
What buyers want today on the same risk and maturity. This is the yield to maturity, quoted as an annual rate and split the same way.
Priced on a coupon date, so this leaves a whole number of coupons still to come.
On this page
In short
- T-bill price on this sheet is face minus face times the discount rate times days over 360.
- $10,000 face at a 5 percent discount for 180 days prices at $9,750. The discount is $250.
- $10,000 face at a 4 percent discount for 90 days prices at $9,900. The discount is $100.
- The discount rate is not a coupon and not a bond-equivalent yield. Those are different identities.
No coupon, a discount to face
A Treasury bill is a short-term United States Treasury security. It does not pay a periodic coupon. The holder buys it below face and receives face at maturity. On this teaching sheet the bank-discount price is
On face of $10,000, a discount rate of 0.05, and 180 days, the discount is $250 and the price is $9,750.
How bonds work is the coupon-and-principal package. A T-bill is the short end of that family without the coupon.
A shorter bill, a smaller discount
Keep face at $10,000. Cut the discount rate to 4 percent and the days to 90. The discount is $100 and the price is $9,900. Less time and a lower discount rate both shrink the gap between price and face.
The bond price calculator on this page is a coupon bond's present value. A T-bill has no coupon, so this sheet's identity is the discount formula rather than that calculator's coupon sum. The calculator is still the nearest working tool for how Treasuries are valued.
How TIPS work is a longer inflation-linked Treasury. Principal on a T-bill is the face paid at maturity.
Discount rate is not the holding-period yield
The discount rate is quoted on face, using a 360-day year, not on the amount invested. The holding-period return on the $9,750 price is $250 over $9,750, which is a different percent than 5. Bond-equivalent and effective yields annualise that return. This page stops at price and the dollar discount.
How yield to maturity works is the coupon-bond cousin of that yield. How money market funds work is a fund that often holds bills.
Scope of this sheet
The two teaching rows are $10,000 face at 5 percent for 180 days (price $9,750, discount $250) and at 4 percent for 90 days (price $9,900, discount $100). They are not a coupon, not a bond-equivalent yield, and not an auction stop-out. This is educational material, not financial advice.
Worked examples
\$10,000 face at 5 percent for 180 days
Face is $10,000. The discount rate is 5 percent. Days to maturity are 180 on a 360-day year. What are the discount and the price?
- Discount is , so $250.
- Price is $10,000 minus $250, which is $9,750.
The discount is $250. The price is $9,750 on $10,000 of face.
\$10,000 face at 4 percent for 90 days
Face is still $10,000. The discount rate is 4 percent. Days to maturity are 90 on a 360-day year. What are the discount and the price?
- Discount is , so $100.
- Price is $10,000 minus $100, which is $9,900.
The discount is $100. The price is $9,900 on $10,000 of face.
Common questions
Why divide days by 360 rather than 365?
The bank-discount quote for bills uses a 360-day year by market convention. A money-market yield on the price invested uses a different day count. This sheet is the discount quote.
Does a T-bill pay a coupon?
No. The return is the gap between the discounted purchase price and face at maturity.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.