Accrued Interest Meaning and Formula

What is accrued interest

Accrued interest is the interest a bond has earned since its last coupon payment but has not yet paid out.

A coupon is the regular interest payment on a bond (see Coupon (bond)). Interest builds up every day, but the issuer pays it only on coupon dates. When a bond changes hands between those dates, the buyer pays the seller the interest earned so far. On the next coupon date the buyer receives the full coupon.

Accrued interest formula

Accrued interest = C × d / D

C is the coupon for one period: face value × annual coupon rate ÷ number of coupon payments per year. Face value is the amount repaid at maturity (see Face value).
d is the number of days from the last coupon date to the settlement date.
D is the number of days in the coupon period.

How d and D are counted depends on the day-count convention set in the bond's terms. Some conventions count actual calendar days. Others treat every month as the same length. The same trade can show slightly different accrued interest under different conventions.

Worked example (hypothetical)

Take a hypothetical bond with face value F, annual coupon rate r and k coupon payments a year.

Coupon per period: C = F × r ÷ k.
You buy the bond for settlement d days after the last coupon date. The period has D days.
Accrued interest owed to the seller: C × d / D.
You pay the quoted clean price plus this accrued interest. That total is the dirty price, also called the full price.
On the next coupon date you receive the full C. Your own interest income is C minus the accrued interest you paid. The seller has already received the rest through the purchase price.

Each side gets interest only for the days it held the bond.

Where you see the term

Bond quotes and news: prices are usually quoted clean. Reports may mention "plus accrued".
Contract notes and statements: a bond trade usually shows the principal, the accrued interest and the total as separate lines (see Account statement).
Settlement: accrued interest is calculated to the settlement date, not the trade date (see Clearing and settlement).
CFD platforms: bond or rate CFDs do not pay coupons. Holding a position overnight is usually charged or credited through a swap instead (see Swap fees). Leveraged CFD trading can lose money fast.

Precise definition and edge cases

Formally, accrued interest is the pro-rata share of the current coupon that has been earned from the last coupon date up to the settlement date, under the bond's day-count convention.

Ex-coupon period: some markets set a record date before the coupon date. A buyer who settles after that date does not receive the next coupon, so accrued interest can be negative and the seller compensates the buyer.
Zero-coupon bonds and discount bills: these pay no coupons, so there is no accrued interest in this sense. The return comes from the gap between the purchase price and face value.
Floating-rate notes: interest accrues at the rate fixed for the current period, so the amount depends on the latest reset.
Defaulted bonds: these often trade "flat", meaning without accrued interest, because the coupon may never be paid (see Default).
Sukuk: these pay profit instead of interest. Accrued profit is often handled in a similar way, but the terms of each issue decide (see Islamic finance).

Frequent questions

What is accrued interest in simple words?

It is the interest a bond has earned since its last coupon date but not yet paid. A buyer pays it to the seller at settlement.

Is the quoted bond price clean or dirty?

Most bond markets quote the clean price. You pay the clean price plus accrued interest, which together make the dirty price.

Who pays accrued interest?

The buyer pays it to the seller. The buyer then receives the full coupon on the next payment date.

Can accrued interest be negative?

Yes. If a bond settles during an ex-coupon period, the seller still receives the next coupon. The buyer is compensated through negative accrued interest.

Does a CFD position earn accrued interest?

No. CFDs do not pay coupons. Overnight holding costs or credits come through swaps, which you should check in the instrument specification.