Bond Dirty Price Calculator

Clean price versus dirty price explained

When you scan bond quotes on a brokerage platform, the price displayed on your screen is almost always the clean price. A bond quoted at 98.50 indicates that the buyer is offering 98.50 percent of face value, or $985.00 for a standard $1,000 par bond. When the trade clears and money changes hands, the actual cash that exits your brokerage account is higher. That settlement amount is known as the dirty price, or the full price.

The difference between the two prices comes down to accrued interest. Bonds pay interest periodically, usually twice each year. If you buy a bond midway between two coupon dates, the issuer will send the entire upcoming coupon payment to you on the next scheduled payment date. You did not own the bond for that whole six-month stretch. The seller owned the security for the first portion of the period. To keep the transaction fair, the buyer pays the seller the interest accrued up to the settlement date.

Dirty price equals clean price plus accrued interest. On the day a coupon payment is distributed, accrued interest resets to zero, making the dirty price equal the clean price. As each day ticks forward toward the subsequent payment date, accrued interest grows, causing the dirty price to climb along a predictable ramp until the next coupon drops it back down.

Day count conventions across bond asset classes

To compute accrued interest accurately, market participants must count how many days elapsed between the prior coupon date and the trade settlement date. Different fixed-income sectors follow distinct day-count rules. Corporate bonds and municipal bonds adhere to the 30/360 convention, whereas United States Treasury bonds and notes follow the Actual/Actual convention. Choosing the wrong convention produces settlement discrepancies on trade confirmations.

Under the 30/360 convention, every month is treated as having exactly 30 days, and every year is assumed to contain 360 days. A semiannual coupon period under 30/360 contains 180 days, regardless of whether February or July falls inside the calendar window. If a trade settles on the 15th day of the third month of a coupon period, exactly 74 days of interest have accrued under the 30/360 formula.

Under the Actual/Actual convention used by the TreasuryDirect portal, market makers tally the exact number of calendar days between dates. A semiannual period running from May 15 to November 15 contains 184 actual days, whereas a period from November 15 to May 15 contains 181 days (or 182 days in a leap year). The denominator reflects the exact number of days in that specific coupon period.

Mathematical formulas for dirty price and accrued interest

The mathematical relationship governing bond pricing is straightforward. Accrued interest is calculated as a proportion of the periodic coupon payment based on the fraction of the coupon period that has passed prior to settlement. The standard equations appear below:

Periodic Coupon Payment = Par Value * (Annual Coupon Rate / Coupon Frequency)

Accrual Fraction = Days Accrued / Total Days in Coupon Period

Accrued Interest per Bond = Periodic Coupon Payment * Accrual Fraction

Dirty Price per Bond = Quoted Clean Dollar Price + Accrued Interest per Bond

When quotes are stated as a percentage of par value, the dirty price percentage is expressed as:

Dirty Price (% of Par) = Clean Price (%) + [ (Annual Coupon Rate / Coupon Frequency) * (Days Accrued / Days in Period) ]

To arrive at the total cash outlay for an institutional or retail order, multiply the dirty price per bond by the quantity of bonds purchased. In professional bond trading platforms monitored by the Securities and Exchange Commission, trade confirmations always display the clean price, the accrued interest line item, and the final net settlement amount.

Worked example: Corporate bond settlement using 30/360

Consider an investor purchasing an investment-grade corporate bond with a par value of $1,000. The annual coupon rate is 5.00 percent with semiannual disbursements paid on March 15 and September 15. The bond trades at a quoted clean price of 98.50 percent of par, which equals $985.00 per bond. The transaction settles on May 27.

First, determine the periodic coupon payment. A 5.00 percent annual rate on $1,000 par yields $50.00 annually. Dividing by 2 semiannual cycles gives a periodic coupon payment of $25.00.

Second, count accrued days under the 30/360 convention from March 15 to May 27. March contains 15 remaining days (30 - 15 = 15). April provides 30 full days. May provides 27 days. Summing these segments gives: 15 + 30 + 27 = 72 accrued days. The total days in the semiannual period under 30/360 is fixed at 180 days.

Third, calculate accrued interest. The accrual fraction is 72 / 180 = 0.40. Multiplying the $25.00 semiannual coupon by 0.40 yields: 25.00 * 0.40 = 10.00 dollars of accrued interest per bond.

Fourth, calculate dirty price. Adding the clean price of $985.00 and accrued interest of $10.00 produces: 985.00 + 10.00 = 995.00 dollars. If the investor buys a block of 10 bonds, the total cash required at settlement equals: 10 * 995.00 = 9950.00 dollars.

Worked example: US Treasury bond with Actual/Actual count

Now examine a United States Treasury bond traded in the secondary market. The Treasury bond carries a $1,000 par value, a 4.00 percent coupon paid semiannually on May 15 and November 15, and a quoted clean price of 102.25 percent of par, equivalent to $1,022.50 per bond. The trade settles on July 15.

Under the Actual/Actual convention governed by FINRA trade reporting rules, exact calendar days determine both numerator and denominator. The semiannual coupon payment is: 1000 * 0.04 / 2 = 20.00 dollars.

Tallying calendar days between May 15 and July 15: May contributes 16 days (31 minus 15). June contributes 30 days. July contributes 15 days. Summing these produces: 16 + 30 + 15 = 61 accrued calendar days. The full coupon period runs from May 15 to November 15, which spans 184 calendar days (16 in May + 30 in June + 31 in July + 31 in August + 30 in September + 31 in October + 15 in November).

The accrual proportion is 61 / 184 = 0.3315217. Multiplying by the $20.00 coupon payment yields accrued interest of $6.63 per bond. Adding this accrued sum to the clean price gives: 1022.50 + 6.63 = 1029.13 dollars as the dirty settlement price. A position of 20 Treasury bonds demands an aggregate cash outlay of 20 * 1029.13 = 20582.60 dollars.

Why bond markets quote clean prices instead of dirty prices

Beginners often ask why bond exchanges do not quote the dirty price directly. The primary reason is that dirty prices fluctuate every single day due to the calendar, even if market interest rates and issuer credit risk remain completely unchanged. Quoting dirty prices would create misleading price charts resembling erratic sawtooth patterns.

Clean prices strip out the steady buildup of accrued coupon interest. When you observe a clean price chart moving upward, you know that the issuer creditworthiness has improved, benchmark interest rates have dropped, or demand has risen. Isolating accrued interest allows investors to compare bonds of different maturities, coupons, and payment schedules on an apples-to-apples basis.

Below is a comparative breakdown showing how accrued interest alters the settlement cash across differing points within a standard six-month coupon period on a 5.00 percent, $1,000 par bond quoted at 98.50 clean.

Tax reporting rules for accrued interest

Accrued interest carries specific tax reporting implications for both buyers and sellers under federal tax law. When a seller receives payment for accrued interest as part of the dirty price, that portion represents ordinary taxable interest income for the seller, not capital gain. The seller must report this interest on IRS Schedule B for that tax year.

For the buyer, the tax code prevents double taxation. When the bond issuer sends the subsequent full six-month coupon payment, the buyer receives interest for the entire period, including the portion that accrued before purchasing the bond. The buyer reports the full coupon received on Schedule B and then records an accrued interest adjustment to subtract the amount paid to the seller at settlement.

Brokerage tax statements (Form 1099-INT) typically report total interest in Box 1 and accrued interest paid at acquisition in Box 3. Failing to claim the accrued interest deduction causes taxpayers to pay tax on income they never earned. Always check your year-end 1099 statements against trade confirmation sheets to ensure settlement adjustments are recorded properly.

Common pitfalls in bond dirty price calculations

Executing accurate bond pricing requires avoiding recurring operational mistakes. The most frequent pitfall is mixing trade date with settlement date. Interest accrues strictly until the settlement date when legal ownership transfers, not the date the order was placed. In the United States, corporate and municipal securities settle on a T+1 basis (one business day after trade date), matching Treasury securities.

A second common mistake is misidentifying the day-count convention. Applying a 30/360 formula to a Treasury note misstates the cash total by several dollars per position. A third error is treating annual coupon rates as flat dollar amounts without adjusting for semiannual or quarterly payment schedules.

Finally, remember that defaulted bonds trade flat, meaning without accrued interest. When an issuer is in bankruptcy or default, the dirty price equals the clean price because future coupon payments are uncertain. For all performing securities, factoring in accrued interest prevents surprise cash shortages when settling orders.