Accrued Interest
With bond pricing mechanics covered, the next question is: what happens when a bond is bought or sold between coupon payments? The answer is accrued interest: the mechanism that ensures both buyer and seller receive fair compensation for the time they held the bond.
Definition and Settlement Convention
- Accrued interest is the interest that has accumulated on a bond since the last coupon payment date up to (but not including) the settlement date
- The buyer pays the seller accrued interest at settlement
- The buyer then receives the full coupon at the next payment date
- The buyer is made whole because the full coupon reimburses the accrued interest paid to the seller
How it works in practice:
- Seller held the bond for part of a coupon period and earned interest during that time
- At settlement, the buyer pays the market price plus accrued interest
- On the next coupon date, the buyer receives the full coupon payment
- The net effect: each party earns interest only for the days they held the bond
Day-Count Conventions
Different types of bonds use different methods to calculate the number of days of accrued interest:
| Security Type | Day-Count Convention | Method |
|---|---|---|
| Corporate bonds | 30/360 | Each month = 30 days; year = 360 days |
| Municipal bonds | 30/360 | Each month = 30 days; year = 360 days |
| U.S. government bonds | Actual/actual | Actual days in month; actual days in year |
30/360 Method (Corporate and Municipal Bonds)
- Count each full month as 30 days regardless of the calendar month
- Partial months use actual days (capped at 30 per month)
- The full year equals 360 days (12 months x 30 days)
Actual/Actual Method (Government Bonds)
- Count the exact calendar days between the last coupon date and the settlement date
- February counts as 28 or 29 days, months with 31 days count as 31
Exam Tip: Gotchas
The exam may give you a date range and ask you to calculate accrued interest. If you apply the wrong day-count method for the security type, the answer will be slightly off - and that wrong answer will likely be one of the choices.
Memory Aid: Corporate and Municipal use 30/360. Government uses actual/actual.
Accrued Interest Formula
Accrued Interest = (Annual Coupon / Periods per Year) x (Days Since Last Coupon / Days in Period)
Example (30/360 Method):
A semiannual corporate bond pays $60/year ($30 every 6 months). If 90 days have passed since the last coupon:
- Semiannual coupon = $30
- Days since last coupon = 90
- Days in period = 180 (using 30/360)
- Accrued interest = $30 x (90/180) = $15.00
The buyer pays the seller the market price plus $15.00 in accrued interest.
Bonds Trading Flat (Without Accrued Interest)
Some bonds trade flat - meaning the buyer does not pay accrued interest to the seller. This applies to:
- Bonds in default - If the issuer has missed interest payments, there is no accrued interest to pay
- Income bonds (adjustment bonds) - Interest is paid only if the issuer has sufficient earnings, so accrual is uncertain
- Zero-coupon bonds - There is no coupon to accrue (the return comes entirely from the discount)
Exam Tip: Gotchas
Zero-coupon bonds do NOT have accrued interest for settlement purposes (no periodic coupon). However, for tax purposes, the imputed interest (OID accretion) is taxed annually. Settlement accrued interest and OID tax treatment are separate concepts: a common mix-up on the exam.