Accrued Interest on Government and Agency Securities
When government and agency securities trade between coupon payment dates, accrued interest must be calculated. The day-count convention determines how that calculation works.
Day-Count Conventions
Different security types use different methods to count the number of days for accrued interest calculations:
| Security Type | Day-Count Basis | How It Works |
|---|---|---|
| Treasury notes and bonds | Actual/actual | Actual days elapsed / actual days in the coupon period |
| Agency debt and mortgage-backed securities (MBS) | 30/360 | Assumes 30-day months and 360-day year |
| Collateralized mortgage obligations (CMOs) | 30/360 | Same as agency debt |
| Treasury bills | N/A | No coupon interest (sold at discount) |
| Corporate bonds | 30/360 | For comparison - same convention as agencies |
| Municipal bonds | 30/360 | For comparison - same convention as agencies |
Exam Tip: Gotchas
- T-bills have NO accrued interest. They are discount instruments with no coupon, so there is nothing to accrue.
How Accrued Interest Works
When a bond trades between coupon payment dates:
- The buyer pays the seller accrued interest from the last coupon date up to (but not including) the settlement date
- The buyer then receives the full next coupon payment
- This effectively reimburses the buyer for the accrued interest paid at purchase
Why this system exists: The seller held the bond and earned interest during the accrual period but will not be around to collect the next coupon. The buyer compensates the seller for that earned-but-not-yet-received interest.
Exam Tip: Gotchas
- The buyer is NOT giving the seller a gift. The buyer pays accrued interest at settlement, then collects the full next coupon. The net effect is the buyer only keeps interest for the days they actually held the bond.
Actual/Actual vs. 30/360
Actual/Actual (Treasuries):
- Count the exact number of days the seller held the bond since the last coupon
- Divide by the exact number of days in the full coupon period
- More precise but varies by month (February has fewer days than July)
30/360 (Agencies, CMOs, corporates, munis):
- Assumes every month has exactly 30 days
- Assumes the year has exactly 360 days
- Simpler to calculate and standardized
Exam Tip: Gotchas
- Treasuries are the exception. Treasury notes and bonds use actual/actual day-count. Everything else (agencies, corporates, munis, CMOs) uses 30/360. The exam may ask which convention applies to a specific security type.