Accrued Interest

Accrued interest builds linearly across a coupon period. The amount owed equals the coupon payment for that period multiplied by the fraction of the period that has elapsed: days from the last coupon date up to the settlement date, divided by the total number of days in the current coupon period. Settlement date, not trade date, is what matters, so a T+1 or T+2 convention shifts the accrual by a day or two and changes the invoice amount.

The seller is compensated because the issuer pays the entire coupon to whoever holds the bond on the next payment date. Without the adjustment, a buyer settling one day before a coupon date would capture six months of income for one day of ownership. The accrual mechanism splits the coupon economically along the holding period while leaving the issuer's payment schedule untouched.

The elapsed fraction depends entirely on how a market counts days. Actual/actual, standard for US Treasury notes and bonds, uses the true calendar days elapsed over the true days in the semiannual period, so the denominator varies between roughly 181 and 184. The 30/360 convention, typical for US corporate, agency and municipal bonds, treats every month as thirty days and every year as 360, producing a smooth, formulaic accrual regardless of the calendar. Money market instruments frequently use actual/360 or actual/365.

Because the conventions differ, two bonds with identical coupons and identical settlement dates can carry visibly different accrued amounts. Candidates should be able to state which convention a given instrument type uses and apply it without hesitation, since the exam supplies the settlement date and expects the correct day count to follow.

In valuation, the present value of a bond's remaining cash flows discounted to the settlement date is the full price, also called the dirty or invoice price. Subtracting accrued interest from that figure gives the flat or clean price, which is what dealers quote. The standard exam route is to value the bond at the last coupon date, compound that value forward by the elapsed fraction of a period at the periodic yield, then strip out accrued interest to reach the quoted price.

Quoting flat exists for a reason. The full price rises mechanically each day as interest accrues, then drops by the coupon amount on the payment date, tracing a sawtooth that has nothing to do with changes in credit quality or interest rates. The flat price removes that predictable component, so movements in the quote reflect genuine repricing.

On a trade confirmation, accrued interest is a separate line beneath the quoted price, and the two sum to the cash the buyer wires. Bond funds and dealers carry it on the balance sheet as interest receivable, and issuers accrue the mirror-image interest payable between payment dates under accrual accounting. Repo transactions, index calculations and total-return measures all work from full prices for the same reason.

Some instruments trade flat, meaning no accrued interest changes hands. Bonds in default are the classic case, since the coupon is not expected to be paid, and zero-coupon bonds have no coupon to accrue at all. Certain markets also apply an ex-coupon period shortly before payment, during which the buyer does not receive the coming coupon and accrued interest is computed as a negative adjustment against the seller.