1 Treasury Bills
Treasury bills (T-bills) are zero-coupon instruments — they pay no periodic interest. Instead, they are issued at a discount and redeemed at par. In the secondary market T-bills are quoted as a discount yield \(y_d\).
Worked Example
Security: 26-week T-bill maturing August 6, 2026
Trade date: February 5, 2026 → Settlement date: February 6, 2026 (T + 1)
Discount yield: \(y_d = 4.210\%\)
Step 1 — Count actual days from settlement to maturity
| Period | Days |
|---|---|
| Feb 6 → Feb 28 | 22 |
| March | 31 |
| April | 30 |
| May | 31 |
| June | 30 |
| July | 31 |
| Aug 1 → Aug 6 | 6 |
| Total | 181 |
Step 2 — Compute the price
\[ P = 100 \times \Bigl(1 - 0.04210 \times \frac{181}{360}\Bigr) = 100 \times \bigl(1 - 0.02116\bigr) = \$97.8833 \]
2 Treasury Notes and Bonds
- Coupon: 4.000% (semi-annual; pays May 15 and Nov 15)
- Issued: November 17, 2025
- Maturity: November 15, 2030
- Par value: $100
Part A — Price Quotes and Clean Prices
Treasury note and bond prices are quoted in points (dollars) and 32nds of a point. A quote of 102-25 means 102 points plus 25/32nds. For additional precision, sub-32nd increments are used:
- A trailing "+" adds 1/64 of a point (i.e., half a 32nd).
- A trailing fraction (e.g., 3/4) represents fractional 32nds — so 10 3/4 means \(\tfrac{10.75}{32}\).
The clean price (or flat price) is the dollar price per $100 par obtained by converting the quote.
Example A
Trade date: February 10, 2026 → Settlement: February 11, 2026
Quote: 102-25+
Clean Price \(= 102 + \dfrac{25}{32} + \dfrac{1}{64} = 102 + 0.78125 + 0.015625 = \$102.7969\)
Example B
Trade date: September 15, 2026 → Settlement: September 16, 2026
Quote: 101-10 3/4
Clean Price \(= 101 + \dfrac{10.75}{32} = 101 + 0.335938 = \$101.3359\)
Part B — Accrued Interest and the Dirty Price
Between coupon dates the buyer must compensate the seller for interest that has accumulated since the last coupon payment. This compensation is called accrued interest.
The dirty price (or full price, invoice price) is the actual dollar amount the buyer pays the seller.
Calculating Accrued Interest & the Dirty Price — Example A Continued
Settlement: February 11, 2026
Previous coupon: November 15, 2025 | Next coupon: May 15, 2026
| Period | Days |
|---|---|
| Nov 15 – Nov 30 | 16 |
| Dec 1 – Dec 31 | 31 |
| Jan 1 – Jan 31 | 31 |
| Feb 1 – Feb 10 | 10 |
| Accrued Days | 88 |
Nov 15 is the last coupon date. We count from Nov 15 (inclusive) to Feb 11 (exclusive), which gives 16 + 31 + 31 + 10 = 88 days. That is, we count Nov 15, 16, …, Nov 30 (16 days), all of December (31), all of January (31), and Feb 1 through Feb 10 (10 days).
\[ \text{Coupon} = \frac{4\%}{2} \times \$100 = \$2.00 \]
\[ \text{AI} = \$2.00 \times \frac{88}{181} = \$0.9724 \]
\[ \text{Dirty Price} = \$102.7969 + \$0.9724 = \$103.7693 \]
| Clean Price (from quote 102-25+) | $102.7969 |
| + Accrued Interest (88 / 181 × $2.00) | $0.9724 |
| = Dirty Price (what the buyer pays) | $103.7693 |