Accrued Interest and Full vs. Clean Price

Understanding Accrued Interest

Let’s start with a simple question: Have you ever bought something partway through its “useful life”—like purchasing a season ticket halfway through the season? In that case, you might pay a bit extra to compensate the seller for the portion of the season you didn’t attend but the ticket was still valid. Bonds work similarly with something called accrued interest.

In bond markets, accrued interest is the interest that has accumulated since the last coupon payment but hasn’t yet been paid out. If someone buys a bond “today,” and the last coupon was paid 45 days ago, the seller is entitled to the interest earned during those 45 days. Because the seller won’t be around to receive the next coupon in full, an extra payment—i.e., the accrued interest—makes sure the seller is fairly compensated.

Key Points

• Accrued interest belongs to the seller, who held the bond for part of the coupon period.
• It’s added to the quoted bond price at settlement.
• The concept is universal in fixed income: if you hop in mid-stream, you pay the portion of the coupon that’s effectively “already earned.”

Mathematically, you might see it expressed like this:

$$ \text{Accrued Interest} = \text{Coupon Payment} \times \frac{\text{Days from last coupon date to settlement date}} {\text{Days in the coupon period}}, $$

with the day count convention determining exactly how you measure those “Days.”

Below is a simplified timeline showing the relevant dates:

    flowchart LR
	    A["Last Coupon Date <br/> (LC)"] --> B["Settlement Date <br/> (S)"]
	    B["Settlement Date <br/> (S)"] --> C["Next Coupon Date <br/> (NC)"]

• LC: Last coupon payment date.
• S: Settlement date when the bond is purchased or sold.
• NC: Next coupon date (when the coupon is actually paid).

The fraction from LC to S is used to calculate accrued interest owed to the seller.

Clean Price vs. Full (Dirty) Price

You might notice two different prices quoted for bonds: a “clean price” and a “full (or dirty) price.” Don’t worry; this has nothing to do with a bond’s moral character.

• The clean price is what you see quoted on Bloomberg, trade platforms, or financial news. It excludes accrued interest. It’s considered “clean” because it focuses purely on the present value of the bond’s future cash flows.

• The full (dirty) price is the actual price paid by the buyer and received by the seller at settlement. It includes both the clean price and the accrued interest. That might surprise folks the first time they buy a bond: “Wait, I thought the price was 99.50, so why am I paying 100.20?” The difference is the accrued interest portion.

The relationship is straightforward:

$$ \text{Full (Dirty) Price} = \text{Clean Price} + \text{Accrued Interest}. $$

In everyday market dialogue, professionals often talk about “the price of the bond” without specifying whether they mean clean or full. By convention, it’s usually the clean price. But on exam day (and trust me, I’ve been there), watch carefully. If the question or the vignette is describing a “settlement amount,” you’re dealing with the full (dirty) price.

Day Count Conventions

Now, how do we figure out that fraction in the accrued interest calculation? After all, not all months have 30 days, and we have leap years, half months, and all sorts of partial periods.

That’s where day count conventions come in. They’re standardized rules for counting days. Different bond markets and regions can use different conventions, so it’s important to know which one you’re dealing with:

Here’s the thing: it may sound small, but using the wrong day count can lead to errors in accrued interest, yield calculations, or price quotes. If you’re 5 or 6 days off on your day count for a large bond position, that can add up to a real difference in payments—especially if interest rates are high or the trade involves big principal amounts.

Real-World Relevance

You might wonder, “Am I ever going to face this in reality?” Absolutely. In secondary bond markets, almost every transaction includes the concept of accrued interest. Traders pay close attention to upcoming coupon dates, because ironically, right after a coupon is paid, the accrued interest resets to zero. Some investors try to schedule purchases around coupon payment dates to manage cash flows and to minimize or maximize the accrued interest “hit.” Others simply factor the cost into their yield-based strategies.

Moreover, day count conventions can vary between domestic and international markets. A bond denominated in different currencies can have different day count assumptions. If you’re dealing with cross-border trades or analyzing global bond funds, it’s crucial to nail these details.

Exam Tips and Pitfalls

• Be sure to track whether the exam question uses clean or full prices. Many times, an item set will give you a “quoted price” but the actual settlement cost is higher because you need to add accrued interest.
• Double-check day count details. The vignette might drop a subtle mention: “Bond X uses a 30/360 convention.” Don’t ignore that line!
• When calculating yield, keep in mind that the yield is typically derived off the clean price, while the actual cost is the dirty price. This can be a sneaky source of confusion.
• The difference between the day count from the last coupon to settlement (for accrued interest) vs. the day count for the entire coupon period (for yield) might trip you up if you’re not paying attention.

I’ll share a personal confession: early in my career, I seized an “amazing” bond deal at 99.00, only to be caught off guard at settlement paying an unexpected chunk of accrued interest. I guess I learned the “dirty” side of bond pricing the hard way.

Putting It All Together: A Quick Example

Imagine we have a semi-annual coupon bond with a 6% annual coupon (3% every six months), and it pays coupons on January 1 and July 1. Suppose you’re buying this bond on March 1, having missed two months of coupon accrual. Let’s assume we have a simple 30/360 day count:

• Time from last coupon (Jan 1) to purchase date (Mar 1): 60 days (using 30/360 logic: January = 30 days, February = 30 days if we’re ignoring actual days).
• Length of coupon period in 30/360 terms: 180 days for six months.

Accrued interest for that 60-day portion:

$$ \text{AI} = \left( \frac{6% \times $1{,}000 \text{ par}}{2} \right) \times \frac{60}{180} = $1.00. $$

(The coupon for six months is $30 on $1,000 par: 6% of $1,000 = $60 per year → $30 every six months. Then we take 60/180 = 1/3 of $30 = $10, sorry let’s walk carefully here.)

Let’s break that down carefully to avoid the dreaded slip:

• Annual coupon = 6% × $1,000 = $60 per year.
• Semiannual coupon = $30.
• Fraction of coupon period passed = 60/180 = 1/3.
• Accrued interest = $30 × 1/3 = $10.

So if the clean price is $975, the full price is $975 + $10 = $985. And that’s what changes hands when you settle the trade.

Diagram: Simplified Accrued Interest Calculation

Sometimes, it’s helpful to visualize the computation flow. Here’s a quick diagram linking day counts, coupon amounts, and the final settlement:

    flowchart LR
	    A["Identify:<br/>Coupon Payment"] --> B["Determine Days<br/>in Period (N)"]
	    B --> C["Count Days from <br/>Last Coupon to <br/>Settlement (d)"]
	    C --> D["Accrued Interest = <br/>(Coupon × d/N)"]
	    D --> E["Total Settlement = <br/>Clean Price + Accrued Interest"]

Summary

• Accrued interest represents the slice of coupon interest earned between coupon dates.
• Clean prices exclude accrued interest, while full (dirty) prices include it.
• Day count conventions (30/360, Actual/Actual, Actual/365, etc.) define how we measure the fraction of the coupon period.
• On the exam, always confirm whether the question wants the clean or full price and watch those day counts.

If you can master these basics, you’ll glide through many of the bond pricing and yield-related item sets with confidence. Trust me, ignoring accrued interest is a classic “gotcha,” and the exam writers know it!

References and Recommended Readings

• CFA Institute. (2025). CFA® Program Curriculum Level II, Volume 6: Fixed Income.
• International Capital Market Association (ICMA). “Accrued Interest Calculations” for Eurobond Market.
• Khan Academy – Bonds and Accrued Interest.
• Our discussion in Chapter 2.1 on Types of Bonds and coupon structures, for additional background on coupons.

Bond Pricing and Accrued Interest Quiz