There’s nothing unsanitary about a bond’s “dirty” price. This price is simply the full price you pay to buy a bond. It equals the quoted price plus accrued interest. The price you see quoted in newspapers and other media outlets is typically a bond’s “clean” price, which excludes accrued interest. A bond pays interest periodically, such as every six months, but the meter’s always running: The bond still accumulates interest between payments. The dirty price compensates the seller for the accrued interest she’s earned but not yet received.
TL;DR (Too Long; Didn't Read)
To calculate a bond's "dirty" price, simply add the quoted price and the accrued interest, which is another calculation altogether.
Determine the Bond's Quoted Price
Find out a bond’s quoted price without interest, its face value, its annual coupon rate and the number of days since its last interest payment from your broker. A bond’s price is typically quoted as a percentage of its face value. For example, assume a corporate bond has a price of 97.534, a $1,000 par value and a 6 percent annual coupon rate. Assume it’s been 15 days since its last interest payment.
Calculate Annual Interest
Divide the bond’s quoted price by 100 and multiply your result by its face value to determine its clean price in dollars. In this example, divide 97.534 by 100 to get 0.97534. Multiply 0.97534 by $1,000 to get a clean price of $975.34. Multiply the bond’s annual coupon rate by its face value to figure its annual coupon -- or interest -- payment. In this example, multiply 6 percent, or 0.06, by $1,000 to get $60 in annual interest.
Determine Dirty Price
Divide the number of days since the last interest payment by 360 if the bond is a corporate or municipal bond. Alternatively, divide the number of days since the last payment by 365 if it’s a government bond, such as a Treasury bond. In this example, divide 15 by 360 to get 0.0417. Multiply your result by the annual interest payment to determine the accrued interest. In this example, multiply 0.0417 by $60 to get $2.50 in accrued interest. Add the accrued interest to the bond’s clean price to calculate its dirty price. Concluding the example, add $2.50 and $975.34 to get a dirty price of $977.84.
In general, a bond trades for less than its face value when its annual coupon rate is less than the market interest rate. A bond trades for more than face value when its coupon rate exceeds the current market rates.