Clean Price vs Dirty Price (Accrued Interest)

What you quote versus what you actually pay — and why those two numbers are never the same between coupon dates.

When you look up a bond on any data terminal or run it through a bond pricing calculator, the number you see is the clean price. When the trade settles and cash moves, you pay something higher: the dirty price, also called the invoice price or full price. The difference is accrued interest — the slice of the next coupon that has already been earned by the seller but hasn't been paid yet. Understanding the clean vs dirty bond price distinction is not an accounting technicality; it is what separates a correct settlement from an expensive surprise.

Dirty price = clean price + accrued interest

The relationship is exact and additive:

Dirty Price = Clean Price + Accrued Interest

The dirty price is the economically correct value of the bond on any given day. It is the present value of all remaining cash flows — coupons and principal — discounted at the yield. The clean price is derived from the dirty price by stripping out the accrued interest that has accumulated since the last coupon payment. Neither number is "wrong"; they answer different questions. The dirty price is what you pay. The clean price is what you use to compare bonds across their coupon calendars.

Think about pricing a bond mid-period. A holder who bought the bond immediately after the last coupon has been accruing the right to a portion of the next coupon with every passing day. If the bond changes hands, the seller is owed that portion — but the issuer will pay the full coupon to whoever holds the bond on the coupon date. The dirty price embeds that compensation automatically. The buyer pays the clean price plus the seller's accrued interest, receives the full coupon on the coupon date, and is made whole.

Why bonds are quoted clean

Without the clean/dirty convention, bond prices would follow a sawtooth pattern purely as an artifact of the coupon calendar. Between coupon payments, accrued interest builds daily — so the dirty price rises steadily, even when yield is unchanged. The moment a coupon is paid, the dirty price drops by exactly the coupon amount and the cycle restarts. A chart of dirty prices would look like a shark fin: gradual ascent, vertical drop, repeat. That pattern communicates nothing about yield or relative value.

Quoting clean removes the sawtooth. Because the clean price subtracts whatever interest has accrued, it stays roughly flat when yield is flat, rises when yield falls, and falls when yield rises — exactly the intuitive relationship you want from a price. This is why every major bond market — US Treasuries, UK Gilts, European government bonds, investment-grade corporate debt — quotes clean and settles dirty.

Calculating accrued interest

Accrued interest depends on three things: the coupon rate, the face value, and the day-count fraction — the ratio of days elapsed since the last coupon to the total days in the coupon period. The formula is:

Accrued Interest = (Annual Coupon / Periods per Year) × (Days Since Last Coupon / Days in Period)

The numerator is the full periodic coupon payment. The fraction is the day-count. Where it gets precise is in how you count days, which depends on the day-count convention governing that bond:

• 30/360 — Every month is treated as 30 days, every year as 360. Common in US corporate bonds and agency debt. Simple to compute, slightly artificial at month-ends.
• Actual/Actual (ICMA) — Counts the actual calendar days elapsed and the actual days in the coupon period. Standard for US Treasuries and most government bond markets. More precise, slightly more arithmetic.
• Actual/360 — Actual days elapsed divided by 360. Common in money markets and floating-rate notes rather than fixed coupon bonds.

Using the wrong convention produces the wrong accrued interest, which produces the wrong settlement amount. Always confirm the convention from the bond's term sheet or the relevant market standard before calculating.

Worked example

Take a US corporate bond with the following terms:

• Face value: $1,000
• Annual coupon: 5.00% — $50 per year, paid semi-annually as $25 every six months
• Day-count: 30/360
• Last coupon date: 1 March 2026
• Settlement date: 10 June 2026
• Clean price: 98.50 (i.e., $985.00 per $1,000 face)

Under 30/360, count the days from 1 March to 10 June as follows: March has 30 days remaining from the 1st (days 1 through 30, so 29 days from March 1 to March 30 plus 1 = 30, but from March 1 we count March as 29 remaining days), giving us the 30/360 formula: (30 − D1) + 30×(M2 − M1 − 1) + D2. Plugging in M1=3, D1=1, M2=6, D2=10: (30 − 1) + 30×(6 − 3 − 1) + 10 = 29 + 60 + 10 = 99 days elapsed. The semi-annual period under 30/360 is always 180 days.

Accrued Interest = $25 × (99 / 180) = $25 × 0.5500 = $13.75

Dirty Price = $985.00 + $13.75 = $998.75

The buyer pays $998.75 per bond, not $985.00. On 1 September 2026 — the next coupon date — the buyer receives the full $25 coupon. Of that $25, $13.75 reimburses the accrued interest paid to the seller; the remaining $11.25 is compensation for holding the bond from settlement to the coupon date.

Settlement always uses the dirty price

The clean price is a quotation convention, not a payment mechanism. Every bond trade settles on the dirty price. Custodians, clearinghouses, and prime brokers all compute settlement amounts on the full price including accrued interest. In fixed income portfolio accounting, positions are typically carried at dirty price for P&L purposes — though some systems mark the "price" field clean and accrue interest separately on the balance sheet.

There is one exception worth noting: bonds trading at or near default — so-called distressed bonds or bonds trading "flat" — are sometimes quoted dirty, because there is genuine uncertainty about whether the next coupon will be paid at all. In that regime, quoting clean would imply a certainty of payment that the market does not accept. The convention shifts to reflect the credit reality.

For all investment-grade and most high-yield bonds in normal conditions, the rule holds: quote clean, settle dirty, and always verify the day-count before signing off on the accrued interest figure.