What Is a Bond? Coupons, Par, and Accrued Interest

Buying a bond between coupon dates without understanding accrued interest means you pay more than the quoted price—often $125-250 extra per $10,000 invested—and wonder why your settlement statement doesn't match. The practical antidote isn't memorizing formulas. It's understanding that bond prices come in two flavors: the quoted "clean" price you see on screens, and the "dirty" settlement price you actually pay.

Why Bond Mechanics Matter (The $58 Trillion Market)

The U.S. fixed income market totals $58.2 trillion—larger than the entire stock market (SIFMA, 2024). Treasury securities alone comprise 45.4% of that figure, serving as the global reference for pricing all other debt. When you buy any bond—corporate, municipal, or government—you're participating in cash flows governed by the same core terms: coupon, par value, maturity, and accrued interest.

The point is: these aren't abstract concepts. They determine exactly how much income you receive, when you receive it, and what you pay at purchase.

Par Value (The Principal You're Lending)

Par value (also called face value) is the amount the issuer promises to repay at maturity. Most corporate and Treasury bonds use $1,000 par value as the standard denomination.

What par value determines:

• The dollar amount of each coupon payment (calculated as percentage of par)
• The principal returned to you at maturity
• The baseline for quoting bond prices (as percentage of par)

Example: A bond quoted at "98.5" trades at 98.5% of par = $985 for a $1,000 face value bond. A bond quoted at "102.3" trades at 102.3% of par = $1,023.

Why this matters: when interest rates rise, bond prices fall below par (discount). When rates fall, prices rise above par (premium). But regardless of what you pay, you receive par value at maturity—unless the issuer defaults.

Coupon Rate (Your Income Stream)

The coupon rate is the annual interest rate the bond pays, expressed as a percentage of par value. A 5% coupon on a $1,000 bond pays $50 annually.

The calculation: Annual Coupon Payment = Par Value × Coupon Rate

Semi-annual payment (standard for most bonds): Each Payment = (Par Value × Coupon Rate) / 2

Example with 5% coupon, $1,000 par:

• Annual interest: $1,000 × 5% = $50
• Semi-annual payment: $50 / 2 = $25 every six months
• Total payments over 10-year bond: 20 payments × $25 = $500

The durable lesson: coupon rate is fixed at issuance. A bond issued with a 5% coupon pays 5% forever (regardless of what happens to market rates). This is why bonds issued in 1981 at 15.84% yields became extremely valuable when rates subsequently fell—they kept paying those high coupons while new bonds offered far less.

Maturity (When You Get Your Principal Back)

Maturity is the date when the issuer returns your par value. Bond maturities range from 1 month (T-bills) to 30 years (long-term Treasuries).

Cash flow timeline for 5% coupon, 10-year, $1,000 bond:

Total cash received: $500 coupons + $1,000 principal = $1,500 on a $1,000 investment.

The practical point: maturity determines your exposure to interest rate changes. Longer maturities mean higher sensitivity—a 30-year bond loses approximately 20% of its value when rates rise 1 percentage point, while a 2-year bond loses only 2%.

Accrued Interest (The Settlement Adjustment)

Accrued interest is the portion of the next coupon payment that has accumulated since the last payment date. When you buy a bond between coupon dates, you pay this to the seller (because they held the bond during that period).

Why accrued interest exists: The seller held the bond for part of the coupon period. When the next coupon pays, you (the new owner) receive the full payment. Accrued interest compensates the seller for days they owned the bond but won't receive the coupon.

The formula: Accrued Interest = Par Value × (Annual Coupon Rate / 365) × Days Since Last Coupon

Example:

• Bond: 5% coupon, $1,000 par, semi-annual payments (January 1 and July 1)
• Purchase settlement date: April 1 (90 days after last coupon)
• Accrued interest: $1,000 × (0.05 / 365) × 90 = $12.33

You pay the seller $12.33 in addition to the quoted bond price. On July 1, you receive the full $25 coupon. Your net interest income for 3 months of ownership: $25 - $12.33 = $12.67 (exactly your 90-day share).

Clean Price vs. Dirty Price (What You Actually Pay)

This distinction trips up more investors than any other bond concept.

Clean price: The quoted price you see on trading screens, in newspapers, and on financial websites. Excludes accrued interest. Used because it reflects true value changes (rather than just time passing).

Dirty price: The settlement price you actually pay. Includes accrued interest.

Dirty Price = Clean Price + Accrued Interest

Example:

• Clean price: $985.00 (98.5% of par)
• Accrued interest: $12.33
• Dirty price (your payment): $997.33

The test: Before confirming any bond purchase, calculate the dirty price yourself. Surprises at settlement cost you trust (with your broker) and potentially money (if you're not prepared).

Common pitfall: Investors see a bond quoted at $985, expect to pay $985, then receive a settlement statement for $997.33. The "buy clean, pay dirty" rule means the quote is never the final price (except on coupon payment dates when accrued interest equals zero).

Day-Count Conventions (The Calculation Detail)

Different bonds use different methods for counting days in accrued interest calculations.

30/360 (Corporate and Municipal Bonds): Assumes 30 days per month, 360 days per year. Simplifies calculations.

• January through March = 90 days (3 × 30)
• Used for corporate bonds, municipal bonds, agency bonds

Actual/365 (Treasury Securities): Uses actual calendar days, 365-day year.

• January through March = 90 days (31 + 28 + 31)
• Used for U.S. Treasury notes and bonds

Why this matters: On a $100,000 bond position, the difference between day-count conventions can mean $50-100 in settlement disputes. Know which convention applies before trading.

Worked Example: Complete Cash Flow Analysis

Your situation: You're buying a 5% coupon, 10-year Treasury bond with $1,000 par value on April 1 (90 days after the January 1 coupon payment). The bond is quoted at 98.5 (clean price).

Step 1: Calculate clean price in dollars $1,000 × 98.5% = $985.00

Step 2: Calculate accrued interest Using Actual/365 for Treasury: $1,000 × (0.05 / 365) × 90 = $12.33

Step 3: Calculate dirty price (your payment) $985.00 + $12.33 = $997.33

Step 4: Project cash flows

Total profit: $502.67 on $997.33 invested over 10 years.

Yield implication: Because you paid less than par ($997.33 vs. $1,000), your yield to maturity exceeds the 5% coupon rate. You receive 5% annual income plus the $14.67 discount ($1,000 - $985.33 = $14.67) amortized over 10 years.

Historical Context: Why Coupon Rates Vary

Bond coupon rates reflect interest rate conditions at issuance. Understanding this history prevents confusion when comparing bonds.

1981 (Volcker Era Peak): 10-year Treasury yields hit 15.84%—the highest in U.S. history. Bonds issued that year with 15% coupons became tremendously valuable when rates subsequently fell. An investor who bought in 1981 locked in income of $150 per year per $1,000 bond—nearly 4x current yields.

2008 (Financial Crisis): Treasury bonds returned +20.10% while stocks lost -36.55%. The flight to safety drove prices up (and yields down). Coupon income provided stability when equity dividends were being cut.

2020-2024: Fed funds rate rose from 0% to 5.25%, causing bond prices to fall. A 10-year bond issued in 2020 at 1% coupon trades at substantial discount today—investors selling early took losses, while those holding to maturity still receive their 1% coupons and full par value.

The durable lesson: coupon rate is a historical artifact of when the bond was issued. Current yield (coupon / price) tells you what income you're earning based on today's purchase price.

Common Mistakes and Dollar Consequences

Mistake #1: Ignoring Accrued Interest at Purchase

Error: Seeing $10,000 bond quoted at 100 and expecting to pay exactly $10,000.

Consequence: If purchased 90 days into coupon period on 5% bond, actual settlement = $10,000 + $123.29 accrued interest = $10,123.29. Budget shortfall of $123.

Fix: Always calculate dirty price = clean price + accrued interest before committing to trade.

Mistake #2: Confusing Coupon Rate with Yield

Error: Thinking a 5% coupon bond always yields 5%.

Consequence: A 5% coupon bond purchased at 110 (premium) actually yields approximately 4.1% to maturity. You paid $1,100 for $1,000 par—the $100 premium loss offsets some coupon income.

Fix: Check yield to maturity, not coupon rate, when comparing bond investments.

Mistake #3: Assuming All Bonds Pay Semi-Annually

Error: Modeling quarterly or annual coupons as semi-annual.

Consequence: Quarterly payers provide 4 smaller payments; annual payers provide 1 larger payment. Liquidity planning and reinvestment strategy change accordingly.

Fix: Verify payment frequency in prospectus or bond details before projecting cash flows.

Implementation Checklist

Essential (prevents 80% of confusion)

• Know the par value (usually $1,000)
• Calculate coupon payment: (Par x Rate) / Payment Frequency
• Before any purchase, compute dirty price = clean price + accrued interest
• Verify payment dates to project your income timeline

High-impact (for active bond investors)

• Confirm day-count convention (30/360 for corporates, Actual/365 for Treasuries)
• Calculate yield to maturity (not just coupon rate) when comparing bonds
• Track settlement dates—bonds settle T+1 (next business day)

Optional (for portfolio builders)

• Compare current yield (coupon/price) across holdings
• Model total cash flows to maturity including final principal return
• Assess duration sensitivity for interest rate risk management

Next Step (Put This Into Practice)

Pull up any bond you own or are considering. Calculate the following:

1. Annual coupon income: Par value × coupon rate
2. Per-payment amount: Annual income / payment frequency
3. If buying today: Find quoted price, estimate days since last coupon, calculate dirty price

Interpretation:

• Dirty price > clean price: You're compensating seller for accrued interest (normal)
• Clean price > 100: Bond trades at premium (yields less than coupon rate)
• Clean price < 100: Bond trades at discount (yields more than coupon rate)

Action: Compare your calculated dirty price to your brokerage's settlement amount. If they don't match within a few cents, investigate the day-count convention or trade date assumptions.

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References:

Source: Damodaran, A. 2024. Historical Returns on Stocks, Bonds and Bills: 1928-2024. NYU Stern School of Business.

Source: SIFMA. 2024. US Fixed Income Securities Statistics. Securities Industry and Financial Markets Association.

Source: Federal Reserve History. 2024. Recession of 1981-82. Federal Reserve Bank.