Accrued Interest
Accrued interest is the coupon income that has accumulated on a bond since the last coupon payment date but has not yet been paid to the bondholder, representing the seller's claim to compensation when a bond is sold between coupon dates. The buyer compensates the seller for accrued interest at settlement, making the invoice price (dirty price) equal to the quoted price (clean price) plus accrued interest.
Key takeaways
- Dirty Price = Clean Price + Accrued Interest; most bond markets quote clean prices to facilitate comparison across bonds with different coupon payment dates.
- Accrued interest is calculated as: Coupon Rate × (Face Value) × (Days Since Last Coupon / Days in Coupon Period).
- Day count conventions vary by instrument: Actual/Actual for US Treasuries, 30/360 for corporate bonds, Actual/360 for money market instruments.
- In a repo transaction, accrued interest accretes daily and is included in the invoice price at each leg, requiring careful cash flow management for leveraged fixed income portfolios.
- At the time of default, accrued but unpaid interest typically becomes part of the principal claim in bankruptcy, though its recovery rate may differ from principal recovery.
Explanation
Accrued interest solves a fundamental fairness problem in bond markets: coupon bonds pay interest periodically, but ownership changes continuously. Without accrued interest, a buyer who purchases a bond one day before a coupon payment would receive the full coupon despite having held the bond for only one day—an economic windfall at the prior holder's expense. The accrued interest mechanism ensures that each holder receives economic compensation proportional to their holding period.
The mechanics involve two prices. The clean price (also called the flat price or quoted price) is what appears on Bloomberg, in fund NAVs, and in most market quotations. It strips out accrued interest to provide a price that moves primarily with changes in yield rather than the mechanical accrual of coupon income. The dirty price (invoice price, full price) is what the buyer actually pays and what the seller receives. On coupon payment dates, the dirty price equals the clean price; on all other dates, it is higher by the accrued interest amount.
Day count conventions introduce complexity. US Treasury bonds use Actual/Actual (ICMA), counting the actual number of days between coupon dates in both the numerator and denominator. Investment-grade corporate bonds in the US typically use 30/360, which assumes each month has 30 days and each year has 360 days—a simplification that creates minor pricing discrepancies on stub periods. European government bonds often use Actual/Actual (ISMA), while money market instruments (commercial paper, T-bills) use Actual/360. Getting the day count wrong in a fixed income model can produce meaningful pricing errors on large notional positions.
In repo markets, accrued interest compounds the complexity of computing the true carrying cost. When a bond is used as collateral in an overnight repo, the seller-borrower continues to accrue interest economically on the bond; the repo rate represents the cost of that financing. The net carry—coupon income minus repo cost—is a critical metric for leveraged fixed income strategies. If carry turns negative, running a leveraged long position costs money even if prices are stable.
Formula
Accrued Interest = (Coupon Rate / Coupon Frequency) × Face Value × (Days Since Last Coupon / Days in Coupon Period) Dirty Price = Clean Price + Accrued Interest
Example
An investor purchases a 4.50% coupon US corporate bond (face value $1,000,000) with a clean price of 98.50 on a date that is 47 days after the last semiannual coupon payment, with 183 days in the full coupon period. Using the 30/360 convention: Accrued Interest = 4.50% × $1,000,000 × (47/180) = $11,750 (noting 30/360 rounds months). The invoice price = $985,000 (clean) + $11,750 (accrued) = $996,750. The buyer pays $996,750 at settlement but will receive the full $22,500 coupon at the next payment date, effectively recovering the $11,750 paid to the seller as compensation for the prior ownership period.
Related terms
Bond Cheapest To Deliver Clean Price Commercial Paper Corporate Bond Dirty Price Face Value Fallen Angel Repo Repurchase Agreement Settlement Strips