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Debt & Yield Curvesbeginner

Coupon, Yield, and Accrued Interest

The coupon rate is the annual interest the bond promises to pay, expressed as a percentage of face value. The yield to maturity (YTM) is the discount rate that equates the present value of all future cash flows to the bond's market price, the effective return if held to maturity with coupons reinvested at the same rate. Accrued interest is the share of the next coupon that has accumulated since the last payment date. It is added to the clean (quoted) price to give the dirty price that actually settles.

Why it matters

Coupon is what the bond's prospectus promises. YTM is what you actually earn given today's price. The two are equal only when you buy the bond at par. Accrued interest is the seller's earned interest for the days they held the bond mid-coupon period. If you buy a 6\% semi-annual bond 45 days into a 182-day period, you owe the seller about $6/2 \times 45/182 = 0.74\%$ of face. The clean price is what hits the screen, the dirty price is what hits your account.

Formulas

Accrued interest
AI=C×days since last coupondays in coupon periodAI = C \times \frac{\text{days since last coupon}}{\text{days in coupon period}}
CC is the coupon paid for the current period (semi-annual coupon for most bonds). Day-count convention varies. AGS uses ACT/ACT, US Treasuries use ACT/ACT, US corporates use 30/360.
Dirty price
Pdirty=Pclean+AIP_{\text{dirty}} = P_{\text{clean}} + AI
Current yield
yc=annual couponPcleany_c = \frac{\text{annual coupon}}{P_{\text{clean}}}
A simple income measure that ignores capital gain or loss to maturity. YTM accounts for both.

Worked examples

Scenario

Bond with $6\%$ semi-annual coupon, face value A$100, 45 days since last coupon out of a 182-day period.

Solution

Semi-annual coupon payment C = 6/2 = \text{A\}3.00$ per A$100 face. Accrued interest AI = 3.00 \times 45/182 = \text{A\}0.742$ per A$100 face. On a A$1 million holding, accrued is approximately A$7,420.

Scenario

A 10-year bond with $4\%$ annual coupon, market price A$92.50. Compute coupon yield and current yield, and explain why YTM differs from both.

Solution

Coupon rate =4%= 4\% of face by definition. Current yield =4/92.50=4.32%= 4/92.50 = 4.32\%. YTM is higher than $4.32\%$ because the buyer will also realise a capital gain of $100 - 92.50 = \text{A\}7.50 at maturity. Solving the full DCF gives YTM of approximately $5.00\%$.

Common mistakes

  • ✗Yield and coupon rate are the same thing. They are only equal when the bond is priced at par. A discount bond has YTM greater than coupon. A premium bond has YTM less than coupon.
  • ✗Accrued interest is income for the buyer. The buyer pays accrued interest to the seller at settlement and then receives the full coupon at the next coupon date. Net economic effect for the buyer is interest earned only from settlement to coupon date.
  • ✗Current yield and YTM mean the same thing. Current yield is simply annual coupon divided by price and ignores all capital movement. YTM is the IRR that equates the price to the full present value of coupons plus principal. The two diverge sharply for bonds trading far from par.

Revision bullets

  • •Coupon rate is annual coupon as %\% of face value
  • •YTM is the IRR of holding the bond to maturity
  • •Current yield is annual coupon over market price
  • •Accrued interest prorates the next coupon by days held
  • •Dirty price == clean price ++ accrued interest
  • •Coupon == YTM only at par

Quick check

A bond trading at par has

A bond pays a $5\%$ semi-annual coupon. 60 days have elapsed in a 182-day coupon period. Accrued interest per A$100 face value is closest to

Connected topics

Bond PriceSettlement

In learning paths

Fixed Income & Rates Path

Sources

  1. Hull (2022), §4.4
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Defines coupon, YTM, accrued interest, and the dirty/clean price distinction within bond pricing.
  2. Fabozzi (2021), Ch. 3
    Fabozzi, Frank J. Bond Markets, Analysis, and Strategies. 10th ed. MIT Press, 2021. ISBN 978-0-262-04627-3.
    Comprehensive treatment of yield measures, accrual conventions, and the bond pricing framework.
  3. ICMA Day Count Appendix
    International Capital Market Association. ICMA Primary Market Handbook, Appendix A5 Day Count Fraction. ICMA, March 2022.
    Industry reference for ACT/ACT and 30/360 day-count conventions used to compute accrued interest across markets.
  4. AOFM Treasury Bonds
    Australian Office of Financial Management. Treasury Bonds. AOFM, accessed 2026.
    Australian Government Bond contract terms including coupon frequency and ACT/ACT accrual.
  5. AFMA Debt Capital Markets Conventions
    Australian Financial Markets Association. AFMA Debt Capital Markets Conventions. AFMA, accessed 2026.
    Practitioner reference for AUD bond market conventions including yield calculations and settlement mechanics.
How to cite this page
Dr. Phil's Quant Lab. (2026). Coupon, Yield, and Accrued Interest. Derivatives Atlas. https://phucnguyenvan.com/concept/coupon-yield-accrued
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