Accrued Interest Formula for Bonds: Calculate It

The accrued interest formula for a bond is accrued interest = annual coupon payment × days since the last coupon date ÷ days in the coupon period, using the day-count convention specified for the bond. This calculator estimates the amount due to the seller when a bond is traded between coupon dates; enter its annual coupon rate, face value, and the relevant day counts.

Formula

For a simple coupon bond between payment dates, the standard proportional calculation is:

AI = C × d / D

• AI is accrued interest, in dollars.
• C is the coupon amount for one coupon period, in dollars. For a bond paying coupons twice a year, C is generally face value × annual coupon rate ÷ 2.
• d is the number of days from the previous coupon date to the settlement date, counted under the bond’s day-count convention.
• D is the number of days in the relevant coupon period under that convention.

The calculator expresses the same proportional calculation using the annual coupon: AI = face value × annual coupon rate ÷ 100 × elapsed days ÷ coupon-period days. The coupon rate is entered as a percentage, so 5 means 5%, not 0.05. The second output is the approximate coupon amount for the period, based on the period’s share of a 365-day year; it is a reference value, not an input to the accrued-interest calculation.

This is a simplified calculator, not a substitute for a bond’s pricing rules. Its inputs let you enter the day counts used by a particular transaction, but the calculator does not identify holidays, coupon schedules, or the correct market convention for you.

Worked Example

Using the calculator’s defaults: face value is $1,000, annual coupon rate is 5%, elapsed time is 45 days, and the coupon period is 180 days.

1. Annual coupon amount: $1,000 × 5 ÷ 100 = $50 per year.
2. Coupon for the relevant period, using the entered period’s fraction of a 365-day year: $50 × (180 ÷ 365) = $24.6575, or $24.66 rounded to cents.
3. Accrued interest: $1,000 × 5 ÷ 100 × 45 ÷ 180 = $12.50.

The calculator’s headline result is $12.50 in accrued interest. This example follows the supplied 180-day period and 45 elapsed days exactly; an actual bond may use a different convention or schedule.

Assumptions

• The bond pays a fixed coupon calculated from the face value and stated annual coupon rate.
• Elapsed days and coupon-period days use the same day-count basis, and settlement is between coupon dates.
• The calculation allocates the coupon proportionally by days; it does not model reinvestment or compound interest.
• It excludes transaction charges, accrued-interest adjustments for special settlement circumstances, taxes, and any other amount that may appear in a trade confirmation.
• The period coupon reference output uses a 365-day year only to show a rough period amount. It is not a substitute for the bond’s actual coupon schedule.

How Accrued Interest Works in a Bond Trade

Most coupon bonds pay interest on set dates rather than every day. If a bond is sold after one coupon date but before the next, the seller has held it for part of the period. In many standard transactions, the buyer pays the seller accrued interest at settlement along with the quoted bond price. The buyer then receives the full next coupon payment, subject to the bond’s terms and settlement mechanics.

This amount is separate from the bond’s quoted price. A price stated without accrued interest is commonly called the clean price; the amount including accrued interest is the dirty price or invoice price. In a straightforward case, dirty price equals clean price plus accrued interest. A trade confirmation can specify the actual amounts and conventions applied, so do not infer the final cash settlement solely from this estimate.

Accrued interest is not an additional coupon created by the sale. It is an allocation of the upcoming coupon between the holder who sold and the holder who bought during the coupon period. The full coupon remains determined by the bond’s stated terms.

Day-Count Conventions and Coupon Frequency

The key source of differences between calculations is often the day-count convention. Actual/Actual counts actual calendar days and uses the actual length of the relevant year or period, according to the specific version of the convention. 30/360 treats months and years according to a defined 30-day/360-day framework. Actual/360 and Actual/365 count actual days but use a 360- or 365-day denominator for interest calculations. The convention and its details depend on the bond documentation and market practice.

For a semiannual coupon, the coupon payment is generally half the annual coupon amount. The accrued fraction should then be calculated against the applicable semiannual period using the stated convention. Do not automatically divide days elapsed by 365 if the bond’s convention instead uses another denominator or a schedule-based method. This calculator uses the entered elapsed-days-to-period-days fraction and therefore works only when those two counts represent the same convention consistently.

• Find the bond’s coupon dates and settlement date.
• Identify the applicable day-count convention from the bond terms or trade details.
• Count elapsed days and total period days under that same convention.
• Apply the coupon amount for the period to the elapsed fraction.

Common Calculation Mistakes and Limits

• Mixing day-count bases: Dividing actual elapsed days by 180 while using a period defined under a different convention can produce a misleading estimate.
• Using the wrong coupon amount: For a bond paying twice yearly, do not treat the full annual coupon as one semiannual payment.
• Confusing price with interest: Accrued interest is generally added to the clean price to arrive at a settlement amount; it is not the same as the bond’s market-price change.
• Ignoring settlement timing: A date that falls on a non-business day or is subject to special settlement terms may affect the applicable dates or calculations.
• Rounding too early: Keep full precision in intermediate steps and round the final currency amount as required by the transaction.

The calculator is intended for a simple fixed-coupon bond with a regular period. It does not handle floating-rate coupons, amortizing principal, irregular first or final coupon periods, inflation-linked adjustments, payment-in-kind interest, or special market rules. For those cases, use the bond’s terms and transaction calculation rather than forcing the inputs into a regular-period formula.

Frequently Asked Questions

Who pays accrued interest when a bond is sold?
In many ordinary coupon-bond trades, the buyer pays the seller accrued interest at settlement, in addition to the clean price. The trade’s settlement statement and bond terms determine the actual amount.

Is accrued interest included in a bond’s quoted price?
It depends on whether the quote is clean or dirty. A clean quote excludes accrued interest; a dirty or invoice amount generally includes it. Check how the quoted price is presented.

Does accrued interest reset after a coupon payment?
For a regular coupon bond, the next accrual period begins after a coupon date. The precise date-count treatment follows the bond’s schedule and convention.

Can accrued interest be more than one coupon payment?
For a regular period between adjacent coupon dates, the simple proportional amount ordinarily grows from zero toward that period’s coupon. Unusual schedules or special terms can require a different calculation.

What day-count convention should I use?
Use the convention specified in the bond’s documentation or trade details. The calculator cannot determine the correct convention from the coupon rate and face value alone.

Is accrued interest the same as yield?
No. Accrued interest allocates a coupon amount over time. Yield is a return measure based on the bond’s price, cash flows, and timing, and requires more information than this calculator uses.

This result is an estimate for educational purposes; the lender’s disclosure gives the exact figures.

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in cr | Annual coupon rate | % | 5 | 0.01 | 100
in fv | Face value | $ | 1000 | 0.01 | 100000000
in el | Days elapsed in coupon period | days | 45 | 0 | 366
in cp | Days in coupon period | days | 180 | 1 | 366
out ai | Accrued interest | $ | fv * cr / 100 * el / cp | 2
out cpmt | Coupon payment per period | $ | fv * cr / 100 * (cp / 365) | 2