## What is a 'Clean Price'

Clean price is the price of a coupon bond not including any accrued interest. A clean price is the discounted future cash flows, not including any interest accruing on the next coupon payment date, and immediately following each coupon payment, the clean price will equal the dirty price. The clean price is calculated by subtracting the accrued interest from the dirty price.

Clean Price = Dirty Price - Accrued Interest

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## BREAKING DOWN 'Clean Price'

The country in which the coupon-paying bond is traded will influence how the bond is quoted. In the United States, it is the market convention to quote a bond in terms of its clean price; in other markets, bonds are more commonly quoted in terms of their dirty price.

Bonds are quoted as either a percentage of their par value, or face value, or in dollar terms. For example, if a bond is quoted at 98, this indicates that it is 98% of the bond's par value. Therefore, if the bond's par value is \$1,000, the bond price is \$980. This is the clean price of the bond since it does not reflect the accrued interest on the bond. Although bonds are typically quoted in terms of the clean price, investors pay the dirty price unless the bond is purchased on the coupon payment date.

## Accrued Interest Calculation

On a bond's interest payment date, the accrued interest is reset to zero. If the next coupon payment is not due or the bond has not expired, the accrued interest is added to sale price of the bond. For example, assume a \$1,000 par value bond has a coupon rate of 5%, which is paid quarterly, and 30 days have passed since the last coupon date. Therefore, the accrued interest is calculated to be 0.42, or (5% x (30/90) x (1/4)). 90 days represents the average number of days in a quarter.

## Clean Price Calculation

For example, assume a corporate bond has a par value of \$1,000 and has a coupon rate of 6%, which is paid on a semi-annual basis on Jan. 1 and July 1. The bond is sold for a dirty price of 93, or 93% of par value, on March 2. To calculate the clean price, the number of days between the coupon dates is calculated to be 60 days, excluding the day that the bond was sold. Therefore, the accrued interest is calculated to be 1.00, or (6% x (1/2) x (60/180)). Therefore, the clean price of the bond is calculated to be 92.00, or 93 - 1.00, which is equivalent to \$920.

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