Accrued Interest in Bonds: How It Works

Accrued interest in a bond is the interest that has accumulated since the bond’s last interest payment date but has not yet been paid. When a bond is bought between payment dates, the buyer generally pays the seller this accrued amount in addition to the bond’s quoted price; the buyer then receives the next full coupon payment.

Why bond interest accrues

Many bonds pay interest, often called a coupon, on a set schedule rather than continuously. A bond might pay twice a year, for example, even though interest builds over the entire period between payments. Accrued interest accounts for the portion of that period during which the seller owned the bond.

The convention makes a between-payment-date sale fairer: the seller is compensated for the interest earned while holding the bond, while the buyer receives the next scheduled coupon. The payment is a settlement adjustment, not an additional coupon or a change to the bond’s stated interest rate.

Not every bond works this way. Zero-coupon bonds do not make regular coupon payments; their value generally reflects interest accumulating through the difference between the purchase price and the amount paid at maturity. Other instruments may have different payment and accrual terms, so check the bond’s documentation.

How accrued interest is calculated

A common simplified calculation is:

Accrued interest = coupon payment for the period × fraction of the period elapsed

For a bond with a fixed annual coupon rate, an equivalent expression is often:

Accrued interest = face value × annual coupon rate × day-count fraction

Face value is the principal amount used to calculate the coupon, not necessarily the bond’s market price. The day-count fraction represents the portion of the coupon period that has elapsed. Its numerator and denominator depend on the bond’s specified day-count convention.

• 30/360: Treats months and years using a standardized 30-day-month, 360-day-year convention, subject to the convention’s detailed rules.
• Actual/actual: Uses the actual number of days elapsed and the actual number of days in the relevant period or year, as defined for the bond.
• Actual/360 or actual/365: Uses actual elapsed days with a fixed 360- or 365-day denominator.

These conventions can produce different accrual amounts for the same dates. The bond’s terms and the transaction’s settlement conventions determine which method applies. A simple days-elapsed calculation is useful for understanding the idea, but it may not reproduce the amount used in an actual trade.

A worked example

Suppose a bond has a face value of $1,000 and a 6% annual coupon paid in two equal installments each year. Each six-month coupon is $30: $1,000 × 0.06 ÷ 2. If 90 days have elapsed in a 180-day coupon period, a simplified proportional calculation gives:

$30 × 90 ÷ 180 = $15

On these assumptions, accrued interest is $15. If the quoted clean price is $980, the buyer’s price before any other transaction costs would be $995: $980 plus $15 accrued interest. The actual figure could differ if the bond uses another day-count convention, has different coupon dates, or settlement occurs on a different date.

The example assumes a regular coupon period and a straightforward allocation of the coupon. Real bonds can have irregular first or final periods, adjusted payment dates, or other terms that make the calculation less simple.

Clean price, dirty price, and settlement

Bond prices are commonly described as either clean or dirty. The clean price excludes accrued interest and is the price often quoted for comparison. The dirty price, also called the invoice or full price in some contexts, includes accrued interest and is closer to the amount paid for the bond at settlement.

Dirty price = clean price + accrued interest

For example, a clean price of $980 and accrued interest of $15 produce a dirty price of $995 per $1,000 face value, before other charges. Price quotations may be expressed as a percentage of face value rather than in dollars, so confirm whether a quoted number is per bond, per $100 of face value, or for another stated amount.

The settlement date matters because accrued interest is generally calculated through the date specified by the market’s trading and settlement conventions. A trade date is when the transaction is agreed; settlement is when the bond and payment are exchanged. The exact treatment of dates, weekends, holidays, and coupon dates depends on the instrument and applicable market conventions.

What accrued interest means for buyers and sellers

For a buyer, accrued interest increases the amount due at settlement, but the buyer will generally receive the next full scheduled coupon. That coupon includes interest attributable to the time before the buyer owned the bond; paying accrued interest to the seller offsets that portion.

For a seller, the accrued amount compensates for the coupon interest accumulated during the seller’s holding period, even though the seller will not receive the next coupon after selling the bond. This does not mean the bond has earned an extra payment overall: the coupon is divided economically between the former and new owner through the settlement adjustment.

Accrued interest is separate from a bond’s market-price movement. Changes in interest rates, credit concerns, supply and demand, and other factors can affect the clean price. Accrued interest usually follows the coupon schedule and day-count rules, although the quoted total price can also reflect market movements.

Common mistakes and points to check

• Confusing the coupon rate with investment yield: The coupon rate determines scheduled interest relative to face value. Yield also reflects the price paid and, depending on the measure, timing of payments and repayment.
• Adding accrued interest to a price that already includes it: Check whether a displayed or quoted price is clean or dirty to avoid counting accrued interest twice.
• Using the wrong number of days: The relevant day-count convention may not equal actual elapsed days divided by 365 or by the apparent length of the coupon period.
• Assuming every bond pays twice a year: Coupon frequency and dates vary. Use the bond’s stated schedule rather than assuming a standard frequency.
• Overlooking settlement timing: Accrual can depend on the settlement date, which may differ from the date the trade was agreed.

Before relying on a quoted amount, check the bond’s coupon rate, face value, payment frequency, coupon dates, day-count convention, settlement date, and whether the displayed price is clean or dirty. A broker’s trade confirmation or the bond’s offering documents can clarify these details.

Frequently Asked Questions

Do I pay accrued interest when I buy a bond?
Usually, when buying a coupon-paying bond between coupon dates, the buyer pays accrued interest to the seller as part of settlement. The precise treatment depends on the bond and transaction terms.

Do I receive the full coupon after buying a bond?
The buyer generally receives the next full scheduled coupon. The accrued-interest payment made at purchase accounts for the portion of that coupon period before the buyer owned the bond.

Is accrued interest included in a bond’s quoted price?
It depends on how the quote is presented. A clean price excludes accrued interest; a dirty price includes it. Verify the convention before comparing prices or calculating the settlement amount.

Does accrued interest increase a bond’s yield?
Accrued interest is a settlement adjustment, not a separate coupon or a yield measure. Yield calculations depend on the purchase price and expected cash flows, among other details.

Do zero-coupon bonds have accrued interest?
They do not pay periodic coupons, so the usual coupon-accrual calculation does not apply. Their value can reflect the build-up toward the amount payable at maturity, under the bond’s terms.

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