Clean price, dirty price: what is accrued interest?

Here is a practical problem the market had to solve. A bond pays its coupon twice a year. You buy it four months after the last payment. Two months later the full coupon lands — in your account, even though the seller held the bond for two thirds of that period.

Should the seller lose four months of interest because of the timing of the trade? Obviously not. The fix is accrued interest, and it produces the two prices every bond quote carries.

Interest accrues by the day

A bond earns interest continuously, day by day, even though it pays only on coupon dates. At any moment, some portion of the next coupon has already been earned by whoever holds the bond.

When you buy, you pay the seller for that earned-but-unpaid portion. You get it back in full when the next coupon arrives. Nobody wins or loses; the interest is simply cut at the right place.

The two prices

• Clean price — the quoted price, with accrued interest stripped out. This is what you see on a screen, and it is what people mean by "the price of the bond."
• Dirty price (also full or invoice price) — clean price plus accrued interest. This is what actually leaves your account on settlement.

Dirty price = clean price + accrued interest.

Why quote the clean price at all?

Because the dirty price is a sawtooth. It climbs every single day as interest accrues, then drops by the full coupon amount the instant the coupon is paid, then starts climbing again. If bonds were quoted dirty, every screen would show a price rising steadily for six months and then falling off a cliff — pure calendar artefact, telling you nothing about the bond.

The clean price strips that sawtooth out, so a change in the clean price means something real: the market repriced this bond. It exists to make prices comparable across the coupon cycle.

The arithmetic

Accrued interest = coupon payment × (days since last coupon ÷ days in the coupon period)

Worked example. A $1,000 bond, 4% coupon, paid semi-annually:

• Each coupon payment: $20 (4% of $1,000, halved)
• Today is 90 days into a coupon period that runs 181 days
• Accrued interest = 20 × (90 ÷ 181) = $9.94

If the bond is quoted at 98.00, then:

• Clean price: 98% of $1,000 = $980.00 (the screen price)
• Accrued interest: $9.94
• Dirty price: $989.94 — the cash you actually pay

Two months later the full $20 coupon arrives in your account. You keep $10.06 (your 91 days of ownership) and the $9.94 you advanced comes back. Clean, in both senses.

Accrued interest is counted to the settlement date, the day cash and bond change hands, which is later than the trade date. US Treasuries settle the next business day (T+1). US corporate and municipal bonds moved to T+1 on 28 May 2024, with the rest of the US securities market. Most euro-denominated bonds settle two business days after the trade (T+2). A trade agreed on a Thursday for T+2 settlement accrues through Monday, three more days of interest; on a $50 million 4% bond that is about $16,700, and an invoice computed to the trade date fails to match the confirmation. The accrued days run to settlement, and the convention belongs to the market the bond trades in.

Day-count conventions

The one wrinkle: markets disagree about how to count days. The convention is written into the bond's terms.

• Actual/actual — real days, real period length. Standard for most government bonds.
• 30/360 — pretend every month has 30 days and every year 360. Common for US corporate and municipal bonds, because it makes every period identical and the arithmetic trivial.
• Actual/360 and actual/365 — common in money markets.

The differences are small in cash terms, but they are exact, they are contractual, and on a $50 million trade "small" is still real money. You do not need to memorise them — you need to know they exist and that the convention is a property of the bond, not a choice you make.

The trap this closes

A beginner sees a bond quoted at 98, computes $980, transfers $980, and finds the trade fails to settle. The invoice was $989.94. The quote is never the payment. Every professional bond system carries both numbers for exactly this reason.

Try it now

1. Compute accrued interest on a $1,000 bond, 6% coupon, semi-annual, sitting 60 days into a 180-day period. (Coupon = $30; accrued = 30 × 60/180 = $10.00.)
2. If that bond is quoted at 101.50, what is the dirty price? (Clean $1,015.00 + $10.00 = $1,025.00.)
3. Say the rule once: "the screen shows clean, the invoice is dirty, and the difference is interest that already belonged to the seller."