What is the Accrued Interest of US Treasury Note/Bond?

When a Treasury Note/Bond (T-Note/T-Bond) is issued, it will start to earn interest based on its interest rate and interest payment schedule, also called coupon rate and coupon payment schedule.

Accrued Interest represents the interest earned since the last interest payment date. It is proportional to the number of days passed since the last interest payment date over the total number of days in the payment period.

${\displaystyle \frac{\mathrm{Accrued}}{\mathrm{Coupon}}}={\displaystyle \frac{\mathrm{Days}}{\mathrm{Period}}}$
$\mathrm{Accrued}=\text{Accrued interest}$
$\mathrm{Coupon}=\text{Coupon value per period}$
$\mathrm{Days}=\text{Days since the last payment date}$
$\mathrm{Period}=\text{Number of days in the period}$

If you are purchasing a T-Note/T-Bond in middle of a coupon payment period, you need to pay the accrued interest to the previous owner. This accrued interest will be carried over to you as part of the T-Note/T-Bond ownership.

For example, if you purchase $1,000.00 of the 10-year T-Note 91282CLW9 at its 1st reopening auction, you have to pay an accrued interest of $3.63950 as shown in the following auction results report:

Release Date: December 11, 2024 (the 1st reopening auction date)
Term and Type of Security: 9-Year 11-Month Note
CUSIP Number: 91282CLW9
Series: F-2034

Interest Rate: 4-1/4%
High Yield: 4.235% (the highest accepted yield)
Price: 100.114150 (the lowest accepted price)
Accrued Interest per $1,000: $3.63950 

Median Yield: 4.190% (50% accepted at or blow this yield)
Low Yield: 4.080% (5% accepted at or blow this yield)

Issue Date: December 16, 2024 (the settlement date)
Maturity Date: November 15, 2034
Original Issue Date: November 15, 2024
Dated Date: November 15, 2024 

We can use this example to verify our accrued interest formula:

${\displaystyle \frac{\mathrm{Accrued}}{\mathrm{Coupon}}}={\displaystyle \frac{\mathrm{Days}}{\mathrm{Period}}}$
$\mathrm{Accrued}=\mathrm{Coupon}\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Period}}}$
$\mathrm{Accrued}=\mathrm{21.25}\times {\displaystyle \frac{\mathrm{31}}{\mathrm{181}}}=\mathrm{3.6395}$

The output matches well with the auction result:

Accrued = 3.6395 (Accrued Interest)
Interest Rate = 4.25%
Par = 1000.0 (Par value)
Days = 31 ("2024-12-16" - "2024-11-15")
Period = 181 ("2025-05-15" - "2024-11-15")
Coupon = 21.25 (Coupon value = 0.5*Par*(Interest Rate)

⇒ YTM with Fractional Period on US T-Note/T-Bond

⇐ High/Median/Low Yield of US Treasury Note/Bond

⇑ Performance Measurements of US Treasury Notes/Bonds

⇑⇑ US Treasury Securities