The Formula for Interest Paid at Maturity

For a bond that pays all of its interest at maturity, accrued interest is calculated from the bond’s dated date, usually its issue date, up to but not including the settlement date. The formula is face value multiplied by the annual interest rate, multiplied by the number of accrued days divided by the days in the year under the bond’s day-count convention.

A $10,000 municipal note paying 5 percent at maturity, dated January 1 and sold for settlement on March 16, has accrued 75 days of interest on a 30/360 basis. That gives $10,000 × 0.05 × 75 ÷ 360, or $104.17, which the buyer pays to the seller on top of the price.

The only difference from an ordinary coupon bond is the starting point. A coupon bond accrues from its last interest payment date, while a bond that pays at maturity has made no payments, so interest accrues from the dated date for as long as the seller has owned it. For the full route from the exam to a career in advice, our complete guide to how to become an investment adviser representative covers every step.

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Why Accrued Interest Exists

Bond interest is earned every day but paid only on set dates. When a bond changes hands between payment dates, the seller has earned interest that the buyer will eventually collect, so the buyer compensates the seller at settlement.

Accrued interest is that compensation. The buyer pays it to the seller as part of the trade, and then receives the full interest payment from the issuer on the next payment date, or at maturity for a single-payment bond.

The result is fair to both sides. The seller is paid for every day of ownership, and the buyer, after recovering the accrued interest from the issuer’s payment, keeps only the interest earned while holding the bond. The Series 65 Exam Preparation course at FRC works through these calculations with the conventions and settlement rules the exam expects.

Which Bonds Pay Interest at Maturity

Most bonds pay interest every six months, but some pay everything at the end. Short-term municipal notes, such as tax anticipation notes and revenue anticipation notes, often pay interest at maturity, as do some certificates of deposit and short-term corporate notes.

These securities pay simple interest. A one-year note paying 5 percent on $10,000 pays $500 of interest plus the $10,000 principal at maturity, with no interest on interest along the way.

They are different from zero-coupon bonds. A zero-coupon bond has no stated interest rate at all, is bought at a deep discount and matures at face value, so it carries no accrued interest in the trading sense. Its return comes entirely from the difference between purchase price and face value.

Day-Count Conventions and Settlement at a Glance

Under 30/360, every month is treated as having 30 days and the year as having 360. Under actual/actual, the calculation uses the real number of days elapsed and the real number of days in the interest period. These conventions are set out in the industry’s settlement rules, and our FINRA rules quick reference on the Uniform Practice Code covers the rules that govern settlement and the computation of interest between firms.

Worked Example One: A Municipal Note Paying at Maturity

A client sells a $10,000 municipal note with a 5 percent interest rate payable at maturity. The note is dated January 1, 2027 and matures on January 1, 2028. The trade settles on March 16, 2027, and municipal securities use the 30/360 convention.

Step one: find the starting point. The note has paid no interest, so accrual begins on the dated date, January 1. Step two: count the days up to but not including settlement. Under 30/360, January counts as 30 days, February as 30 days and March 1 to March 15 as 15 days, for a total of 75 days.

Step three: apply the formula. $10,000 × 0.05 × 75 ÷ 360 = $104.17. Step four: add it to the trade. The buyer pays the agreed price for the note plus $104.17 of accrued interest, and at maturity the buyer receives the full $500 of interest, keeping $395.83 earned during ownership.

Worked Example Two: The Same Note on an Actual-Day Basis

Suppose an otherwise identical note used an actual-day count with a 365-day year. The actual days from January 1 to March 15 inclusive are 31 in January, 28 in February and 15 in March, a total of 74 days.

The calculation becomes $10,000 × 0.05 × 74 ÷ 365, which equals about $101.37. The difference of $2.80 comes entirely from the convention.

On a single $10,000 note the gap is small, but on a $5 million institutional trade the same difference becomes about $1,400. That is why the convention is set by the type of security, not left to the parties to choose, and why exam questions always specify the security type.

Worked Example Three: A Semiannual Coupon Bond for Comparison

Compare a standard corporate bond with a $1,000 face value and a 6 percent coupon rate, paying interest on January 1 and July 1. A trade settles on March 21.

Step one: the last payment date was January 1, so accrual starts there. Step two: under 30/360, January counts as 30 days, February as 30 days and March 1 to March 20 as 20 days, for 80 days in total. Step three: $1,000 × 0.06 × 80 ÷ 360 = $13.33.

The method is identical to the maturity-paying note. The only change is the starting point: the last coupon date instead of the dated date. Once a candidate sees that, both types of question become the same question.

Clean Price and Dirty Price

Bond prices are quoted without accrued interest. That quoted figure is called the clean price, and it allows investors to compare bonds without the price jumping up and down as interest builds and is paid.

The amount the buyer actually pays is the dirty price, also called the full or invoice price. It equals the clean price plus accrued interest. If the municipal note in Example One is quoted at 100.50, or $10,050, the buyer pays $10,050 plus $104.17, a total of $10,154.17.

For a bond paying interest at maturity, the gap between clean and dirty price grows steadily over the bond’s whole life, because no interest is paid along the way to reset it. Near maturity, accrued interest on such a note can approach the full year’s interest.

Accrued Interest Does Not Change the Yield

Paying accrued interest does not make a bond more expensive in any real sense. The buyer hands over the accrued amount at settlement and receives it back from the issuer at the next payment, so the money is returned in full.

For that reason, yield measures are calculated on the clean price, not the dirty price. The current yield of a bond, for example, divides the annual interest by the quoted clean price. Including accrued interest would distort the comparison between bonds bought at different points in their payment cycles.

What does matter is the cost of money in the meantime. On a bond that pays at maturity, the buyer may wait many months to recover a large accrued amount, which is one reason these notes are mostly held by investors who plan to keep them until they mature. It also explains why fixed income desks track accrued interest carefully on every position they hold.

Study Bond Math With FRC

Accrued interest, yield calculations and settlement rules reward practice more than any other fixed income topic. Our Series 65 course works through each calculation step by step, with day-count conventions, settlement dates and the clean and dirty price relationship set out the way the exam presents them.

Consider studying with FRC for every exam on your route. Explore our USA exam courses, from the SIE through the Series 7, Series 63 and Series 65.

To take advantage of the membership, explore FRC Professional Membership, which gives you a verified Digital Profile that shows employers your real-time course progress, together with the Video Resume. Current offers are on our membership deals page.

Tax Treatment of Accrued Interest

Accrued interest affects both parties’ taxes. The seller reports the accrued interest received from the buyer as interest income, because it represents interest earned while the seller held the bond.

The buyer receives the full interest payment from the issuer at maturity but is taxed only on the portion earned during ownership. The accrued interest paid to the seller is subtracted from the interest the buyer reports.

For tax-exempt municipal bonds, the interest is generally exempt from federal tax for both parties, but the split still matters for state tax and record keeping. Zero-coupon bonds follow a different rule: the discount accretes each year as taxable income on a taxable zero, even though no cash is received, which is often called phantom income.

Bonds That Trade Flat

Some bonds trade without accrued interest, a practice known as trading flat. A bond in default trades flat, because no one expects the missed interest to be paid on schedule, so the buyer pays only the quoted price.

Income bonds, which pay interest only if the issuer earns enough, also trade flat. So do zero-coupon bonds, which have no periodic interest to accrue.

A bond that trades flat is quoted on a price that already reflects whatever interest the market expects to recover. Exam questions sometimes describe a defaulted bond and ask about accrued interest, and the answer is that none is added.

The Memory Aid

Remember this line: start from the last payment, stop the day before settlement. For a bond that pays interest at maturity, the last payment is the dated date, because nothing has been paid yet.

For the conventions, remember that Treasuries count actual days, while corporates, municipals and agencies count every month as 30 days in a 360-day year.

For the trade, remember that the buyer pays the seller. The buyer gets it back from the issuer on the next payment, or at maturity for a single-payment bond.

Exam Traps to Avoid

The first trap is counting through the settlement date. Accrued interest runs up to but not including settlement, so the settlement day itself is never counted. The second trap is counting from the trade date rather than the settlement date, which understates the accrual by the settlement period.

The third trap is starting a maturity-paying bond from the wrong date. With no interest paid, accrual starts on the dated date, not on some assumed coupon date six months earlier.

The fourth trap is using the wrong convention. Treasuries use actual/actual, while corporate, municipal and agency bonds use 30/360. The fifth trap is adding accrued interest to a defaulted bond, which trades flat. Check each of these before choosing an answer.

A Client Scenario

A client holds $50,000 of one-year municipal notes paying 4 percent at maturity and needs cash after five months. She is worried that selling before maturity means losing the interest she has earned.

The adviser explains how accrued interest protects her. Under 30/360, five complete months from the dated date equal 150 days, so the buyer will pay her $50,000 × 0.04 × 150 ÷ 360, or about $833.33, in accrued interest on top of the price. She keeps the interest earned during her ownership, even though the issuer will not pay it until maturity.

The adviser also notes that the price she receives depends on market rates. If rates have risen since she bought, the clean price may fall below par, and that price change is separate from the accrued interest. Explaining the two components clearly helps the client understand exactly what she will receive, the kind of clear disclosure every investment advisor representative owes a client.

The Dictionary as a Video Library

The FRC dictionary is a study tool, not just a glossary. Every entry pairs a written explanation with deep-dive video, on-page quizzes and interactive flash cards, so you can read a concept, watch it explained and test yourself in one place.

Rules are covered with the same depth, from the settlement provisions of the Uniform Practice Code to the conduct rules behind every recommendation. Use the FRC dictionary to open each term in this article, from coupon rate to yield to maturity, as its own explanation, video and quiz.

Practice Questions to Test Yourself

Question one: A $20,000 corporate note paying 6 percent at maturity is dated February 1 and settles on April 11. What is the accrued interest? Using 30/360, February and March count as 60 days and April 1 to April 10 as 10 days, for 70 days. $20,000 × 0.06 × 70 ÷ 360 = $233.33.

Question two: Who pays accrued interest in a bond trade, and who receives it? The buyer pays it to the seller at settlement. The buyer then recovers it from the issuer’s next interest payment, or at maturity for a single-payment bond.

Question three: Which day-count convention applies to Treasury notes, and which to municipal bonds? Treasury notes use actual/actual. Municipal bonds use 30/360, as do corporate and agency bonds.

Question four: Accrued interest is calculated up to which date? Up to but not including the settlement date. The trade date is not used, and the settlement day itself is not counted.

Question five: A bond in default is sold. How much accrued interest does the buyer pay? None, because a defaulted bond trades flat. The buyer pays only the quoted price, which already reflects the market’s view of any interest that may be recovered.

Turn Bond Math Into Career Evidence

Accurate bond math matters in operations, trading, wealth management and municipal finance roles alike. FRC’s Digital Profile shows employers the courses you are actively studying and the progress you have earned through assessed learning, verified by FRC, and a QR code on your resume takes them straight to it.

The FRC Video Resume lets a hiring manager hear you before the interview. Walking an employer through an accrued interest calculation in plain language demonstrates precision and communication at the same time.

Candidates returning to the exam should note that the wait after a third failure drops from 180 days to 60 days for exam windows opened on or after January 4, 2027, as explained in our article on the Series 65 retake rule change.

Related Questions

Continue with Agency Bonds vs Treasury Bonds for the issuers behind each day-count convention, and Callable vs Non-Callable Bonds for yield to call and yield to worst calculations.

For credit quality, read Investment Grade vs High Yield Bonds, and for floating-rate debt, read Senior Loans vs High Yield Bonds.

Key Points to Retain

For a bond that pays interest at maturity, accrued interest runs from the dated date up to but not including the settlement date. Multiply face value by the interest rate, then by the accrued days divided by the days in the year under the bond’s convention.

Corporate, municipal and agency bonds use 30/360, while Treasuries use actual/actual. The buyer pays accrued interest to the seller, the dirty price equals the clean price plus accrued interest, and defaulted bonds, income bonds and zero-coupon bonds trade flat.

For the exam’s structure and requirements, see the Series 65 dictionary entry, and to plan your budget, read how much a Series 65 course costs.