The dirty price represents the total amount you actually pay when you buy a bond. It combines two things: the bond’s quoted market price (called the clean price) and the accrued interest that has built up since the last coupon payment. If you’re buying a bond on the secondary market, the dirty price is your real cash outflow at settlement.
Why Bonds Have Two Prices
Bonds are quoted in the market at their clean price, which strips out accrued interest entirely. This makes it easy to compare bonds across different dates. Two investors looking at the same bond on different days see the same clean price, unaffected by where the bond sits in its coupon cycle. But when money actually changes hands, the settlement happens at the dirty price. The formula is straightforward: dirty price equals clean price plus accrued interest.
This two-price system exists to keep things fair between buyers and sellers. If you buy a bond halfway through a coupon period, the seller held that bond for months and earned interest during that time. When the next coupon payment arrives, it goes entirely to you as the new owner. To compensate the seller for the interest they earned but won’t receive, you reimburse them through the accrued interest portion of the dirty price. You then collect the full coupon on the next payment date, which effectively nets out.
How Accrued Interest Builds Up
Accrued interest grows a little bit every day between coupon payments. The basic calculation takes the coupon payment for the period and multiplies it by the fraction of the period that has elapsed since the last coupon date. For a bond with a 10% annual coupon paying semiannually (so $5 per $100 of face value every six months), if 120 out of 180 days have passed since the last payment, the accrued interest would be $5 × (120/180), or $3.33 per $100 of par value.
On a coupon payment date, accrued interest resets to zero. The dirty price and clean price are identical at that moment. Then, as each day passes, accrued interest starts accumulating again, and the dirty price gradually climbs above the clean price until the next coupon date, when it drops back down. This creates a sawtooth pattern over time: a slow daily rise followed by a sharp drop on each payment date.
Day Count Conventions Matter
The tricky part of calculating accrued interest is that different bond markets count days differently. The two most common methods are “actual/actual” and “30/360.”
- Actual/actual uses the real number of days in each month and the real number of days in the coupon period. Between June 17 and October 1, for example, that’s 106 days: 13 in June, 31 in July, 31 in August, 30 in September, and 1 in October.
- 30/360 treats every month as having 30 days and every year as having 360 days. The same June 17 to October 1 span becomes 104 days under this convention. The Eurobond market commonly uses a version of this approach.
The convention you use changes the accrued interest figure slightly, which means the dirty price varies depending on which market’s rules apply. U.S. Treasury bonds typically use actual/actual, while many corporate bonds use 30/360.
A Worked Example
Consider a bond with a 10% coupon rate, paying interest every six months, with a clean price of 111.2891 per $100 of face value. The settlement date is July 1, and the next coupon date is September 1, which is 60 days away in a 180-day coupon period. That means 120 days of the period have already passed.
The accrued interest is $5 × (1 − 60/180) = $3.3333 per $100 of par value. So the dirty price, what you’d actually pay, is 111.2891 + 3.3333 = 114.6224 per $100 of face value. The clean price of 111.29 is what you’d see quoted on a trading screen. The 114.62 is what leaves your account.
Why It Matters for Yield Calculations
The dirty price is the number that matters for calculating yield to maturity. Since it represents the actual amount you invest, it’s the starting point for figuring out your real return. A bond’s present value, computed by discounting all future coupon payments and the principal repayment back to today, equals the dirty price. The clean price is just a quoting convenience.
The running yield on a bond (the simplest measure of annual return) is the coupon divided by the dirty price, not the clean price. Using the clean price would overstate your yield because it ignores the accrued interest you paid upfront. For any practical investment decision about what a bond will actually earn you, the dirty price is the relevant number.
When Dirty and Clean Prices Converge
There are two situations where the dirty price and clean price are the same. The first is on any coupon payment date, when accrued interest resets to zero. The second is when you buy a newly issued bond at its initial offering, since no interest has accumulated yet. In every other scenario, the dirty price exceeds the clean price by the amount of interest that has accrued since the last payment.
For most individual investors, this distinction shows up automatically. Your broker calculates the accrued interest and adds it to the trade, so the total settlement amount on your confirmation reflects the dirty price even if the bond’s listed price showed only the clean figure. Understanding the difference helps you avoid surprise when the amount debited from your account is higher than the price you thought you were paying.