Accrued Interest: Clean and Dirty Price
Why do you pay extra when you buy a bond between coupon dates? Understand accrued interest and you can tell the quoted clean price from the dirty price you actually pay.
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Text version · Bonds & Fixed Income, lesson 7: “Accrued Interest: Clean and Dirty Price”
Why do you pay extra when you buy a bond between coupon dates? Understand accrued interest and you can tell the quoted clean price from the dirty price you actually pay.
Coupons build up day by day
Coupons are only paid once a year, but they “build up” day by day. The part built up since the last coupon that hasn't been paid yet is accrued interest, which resets to zero on the coupon date.
The buyer first pays the seller for the coupon built up so far
On the next coupon date, the full coupon goes to whoever holds the bond that day. The seller has already held it for a while, so the buyer pays accrued interest on top, handing the seller their share of the coupon in advance.
Quoted clean, paid dirty
dirty price = clean price + accrued interest. On each coupon date the dirty price suddenly drops by a full coupon, while the clean price stays smooth, which is why trading apps and quotes usually show the clean price.
Key takeaways
- Accrued interest = annual coupon × the fraction of time since the last coupon (this lesson counts by month, using the 30/360 convention).
- Dirty price = clean price + accrued interest. The buyer pays the dirty price, and the accrued interest pays the seller back for the coupon they've "built up".
- The dirty price drops by a whole coupon on the payment date, while the clean price moves smoothly, which is why markets usually quote the clean price.
- If yields don't change, a premium bond's clean price slowly drifts toward face value over time.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Click “Example: 4 months after a coupon”: what's the accrued interest? What are the clean and dirty prices? Check that dirty price = clean price + accrued interest.
- Click “1 month before coupon”, then “Coupon date”: how much did the dirty price drop? And the clean price?
- Press ▶ to play a full 3 years and watch the green sawtooth and the cyan curve: which line "drops off a cliff" on each coupon date?
- Drag “Market yield” to 3%, then to 8%: how does the clean price change? Does the accrued interest at the same point in time change?
Quiz and explanations
- 1. A bond has a $1,000 face value and a 6% coupon, paid once a year. Four months have passed since the last coupon. What's the accrued interest?
- Answer: $20.$60 × 4/12 = $20.
- 2. A bond is quoted at a clean price of $985 with $15 of accrued interest. How much does the buyer actually pay?
- Answer: $1,000.Dirty price = clean price + accrued interest = $985 + $15 = $1,000.
- 3. On a coupon payment date, a bond's dirty price usually…
- Answer: Drops by about one coupon, while the clean price barely changes.The coupon is paid to the existing holder, so the dirty price drops. The clean price, which excludes accrued interest, stays continuous.
Terms in this lesson
- accrued interest (Accrued Interest): Coupon interest that has built up day by day since the last payment but hasn't been paid yet; buying between payments, the buyer pays this to the seller first.
- yield (Yield): The annual return you'd earn buying a bond at its current price; the lower the price, the higher the yield.
- clean price (Clean Price): A bond's price without accrued interest, the price normally quoted in the market, which doesn't jump on payment dates.
- dirty price (Dirty Price): Clean price + accrued interest: what the buyer actually pays, equal to the present value of the remaining cash flows.