Accrued Interest
Coupon income earned but not yet paid, computed as the periodic coupon scaled by the fraction of the coupon period that has elapsed. Bridges the quoted clean price and the actual settlement (dirty) price.
When to use: Use to settle bond trades between coupon dates. The buyer pays the seller dirty price = clean price + accrued interest, since the seller earned the partial coupon up to the trade date.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Accrued | Accrued Interest | Coupon earned but not yet paid | $ |
| Coupon | Periodic Coupon | Dollar coupon paid each period (F × CR / m) | $ |
| AccruedDays | Days Since Last Coupon | Days elapsed in the current coupon period | integer |
| PeriodDays | Days in Coupon Period | Total days in the current coupon period | integer |
Real-Life Examples
Example 1: 60 Days into a 182-Day Coupon Period
Semi-annual bond paying $25 per period. 60 days have elapsed since the last coupon; the coupon period is 182 days (ACT/ACT).
Given
Step-by-Step
The seller has earned $8.24 of the $25 coupon. The buyer adds $8.24 to the clean price to compensate the seller for the partial coupon period.
Frequently Asked Questions
They affect how AccruedDays and PeriodDays are counted. US Treasuries use ACT/ACT; US corporates and agencies typically use 30/360. The formula itself is unchanged — only the day-count rule for the inputs differs.
Because the coupon is locked in linearly during the period — the issuer "owes" 1/Nth of the coupon for each Nth of the period that has passed, regardless of yield level. Discounting only matters for cash flows in the future.
DirtyPrice = CleanPrice + Accrued. The clean price is what gets quoted; the dirty price is what actually settles. Always add accrued when paying for or receiving a bond between coupon dates.