1From the quoted price to the cash paid
A bond is quoted at 92.09831. You buy 1,000 face value, yet the settlement amount is 930.98, rather than 920.98. The difference is accrued interest: the coupon interest allocated to the seller for the part of the current coupon period that has already elapsed.
By the end of this guide, you will be able to read a bond quote, count accrued days, calculate the settlement amount, and reproduce the calculation in Excel.
Dirty price = Clean price + Accrued interest
All three quantities must use the same units: either price per 100 face value or a cash amount.
The examples use regular fixed-rate coupon bonds and stated day-count conventions. Amounts are before transaction fees and taxes. Historical dates are teaching inputs, not current market quotes.
2Three terms, three different jobs
| Term | Meaning | Why it matters |
|---|---|---|
| Clean price | The bond price excluding accrued coupon interest. | Often the quoted price used for comparison. |
| Accrued interest (AI) | The portion of the current coupon allocated to the elapsed part of the coupon period. | Compensates the seller when the buyer will receive the next full coupon. |
| Dirty price / full price / invoice price | Clean price plus accrued interest. | The bond consideration used at settlement, before separate charges. |
A quote of 92 means 92% of face value: 920 for 1,000 face. “Clean” does not mean fair value, and “dirty” does not mean an extra penalty. They are two ways of expressing the same bond’s value.
Clean price can still change every day as yields, credit conditions, and liquidity change. Removing accrued interest removes the coupon-accrual component; it does not remove market risk.
3Why the buyer compensates the seller
Suppose a bond pays 30 every six months. It changes hands one-third of the way through the coupon period. Under ordinary coupon-entitlement rules, the buyer receives the full 30 at the next payment date. At settlement, the buyer therefore pays 10 of accrued interest to the seller.
The buyer’s remaining coupon allocation is 20. This split explains the settlement adjustment, but it is not the buyer’s total investment return: price changes, purchase cost, timing, and reinvestment also matter.
Use the settlement date, when cash and securities exchange, rather than automatically using the trade date. Follow the instrument’s coupon-entitlement and day-count rules.
4Calculate accrued interest in four steps
Let F be face value, c the annual coupon rate as a decimal, m the number of payments a year, A the accrued days and E the days in the coupon period.
- Calculate the coupon per period: C = F × c ÷ m.
- Identify the previous and next coupon dates surrounding settlement.
- Count A and E using the contractual day-count convention.
- For the regular 30/360 and coupon-period Actual/Actual examples here, calculate AI = C × A ÷ E.
Alternatively, calculate AI per 100 first, add it to the clean quote, then multiply the combined dirty quote by F/100. Keep full precision until the final settlement amount is rounded.
Accrued coupon interest uses the coupon rate. Yield is used to value future cash flows and derive the bond price. Do not substitute yield for coupon rate in the accrual formula.
5Day-count conventions change the answer
| Convention | Accrual approach | Practical point |
|---|---|---|
| US 30/360 | Standardised months and a 360-day year; AI = F × c × A/360. | A regular half-year period has 180 convention days. Month-end adjustments matter. |
| Actual/Actual — regular coupon-period method | Actual elapsed days divided by actual days in that coupon period, multiplied by the period coupon. | A semiannual denominator can be 181, 182, 183 or 184 days. |
| Actual/360 | AI = F × c × actual days/360. | Do not replace 360 with the actual year length. |
| Actual/365 Fixed | AI = F × c × actual days/365. | The denominator stays 365 even in a leap year. |
| European 30/360 | A different set of month-end adjustments. | It can differ from US 30/360. |
“Actual/Actual” has several market definitions. This article’s regular-coupon examples use the coupon-period fraction, consistent with the supplied exercises. Do not assume one formula covers irregular first coupons, long or short final periods, and every market convention.
For actual-day examples, ordinary date subtraction gives the elapsed days; do not add an extra day. Use the agreed accrual boundaries consistently.
6Worked example: a 30/360 bond quote
| Input | Value |
|---|---|
| Settlement / maturity | 15 August 2025 / 15 June 2030 |
| Previous / next coupon | 15 June 2025 / 15 December 2025 |
| Annual coupon / nominal annual YTM | 6% / 8%, both with semiannual frequency |
| Redemption / quotation unit | 100 / per 100 face |
| Day count | US 30/360 |
The coupon is 100 × 6%/2 = 3. Accrued days are 60 out of a 180-day period, leaving 120 days to the next coupon.
| Component | Per 100 face | On 1,000 face |
|---|---|---|
| Clean price | 92.09831005 | 920.98310050 |
| Accrued interest | 1.00000000 | 10.00000000 |
| Dirty price / cash consideration | 93.09831005 | 930.98310050 |
Final cash settlement: 930.98. The clean price comes from discounting the remaining payments at the stated yield, as shown later. The quoted price is below par because the coupon is lower than the required yield.
Teaching source: 01., Accrued Int Clean Price Dirty Price.xlsx, “ACCRINT & Dirty Price”, D6:D27.
7Worked examples: Actual/Actual
A. A quoted price of 83.625 per 100
A 5.8% semiannual bond settles on 15 March 2015, between 15 January and 15 July 2015. Its period coupon is 2.90 per 100. There are 59 elapsed days in a 181-day coupon period.
Dirty quote = 83.625 + 0.94530387 = 84.57030387
For 1,000 face, multiply by ten: cash consideration is 845.70 after rounding.
B. A cash price of 920 on 1,000 face
An 8% semiannual bond has a coupon of 40. Settlement is 3 September 2020, with coupon dates of 1 July 2020 and 1 January 2021. The period has 184 days and 64 have elapsed.
Cash consideration = 920 + 13.91304348 = 933.91304348
Final cash settlement: 933.91. Here 920 is already a cash clean price on 1,000 face, equivalent to a quote of 92 per 100. Adding 13.913 to a quote of 92 would mix units.
C. Leap-year cross-check
For 1,000 face at a 4.5% semiannual coupon, from 15 January to settlement on 20 April 2024, A = 96 and E = 182 to 15 July. Accrued interest is 22.50 × 96/182 = 11.86813187.
Teaching source: 04. Accrued Interest(Clean Price, Dirty Price).xlsx, “Accrued Int Clean Price” D7:D22; “02. Clean Price & Accrued Int” G6:G42; “03. Accrued Int (2)” C28:H35.
8Interactive settlement calculator
Choose a workbook example, then change the quoted price, coupon, face value or settlement date. This calculator takes the clean quote as an input; it does not infer it from yield.
Regular periods only; previous and next coupon dates must match the payment frequency. Settlement may equal the previous coupon date but must precede the next. At a payment date, advance both coupon dates. No ex-coupon adjustment, default, fees or irregular coupon periods are modelled. The April 2024 preset uses an illustrative clean quote of 100 because that exercise supplies no market price.
9What happens as the next coupon approaches?
Between coupon payments, accrued interest builds up. When the coupon is paid and a new accrual period begins, accrued interest resets to zero. Holding other valuation conditions fixed, the dirty price drops by the coupon paid; receiving that coupon offsets the price drop in total wealth.
For an ordinary positive-coupon bond with positive accrual, yes. On a coupon date after reset, the two can be equal. Ex-coupon rules and securities trading flat require different treatment, so “always higher” is too broad.
10Connect the settlement price to present value
Discounting all remaining promised payments to settlement gives the full or dirty value. Subtract accrued interest to obtain the clean price.
For a regular coupon bond with more than one remaining coupon, let w be the fraction of a coupon period from settlement to the next coupon, N the number of remaining payments, y the nominal annual yield and R the redemption amount:
+ R/(1+y/m)N−1+w
Clean = Dirty − AI
In the August 2025 example, w = 120/180 = 2/3, N = 10, C = 3, R = 100 and y/m = 4%. Discounting gives 93.09831005. Subtract AI of 1 to recover the clean price of 92.09831005.
Do not discount the remaining coupons to get a full price and then add accrued interest again. That counts the settlement adjustment twice. Market pricing conventions may use a special calculation in the final coupon period.
11Reproduce the calculations in Excel
Enter dates with DATE(year,month,day) to avoid ambiguity. The following independent formulas reproduce the August 2025 example.
| Task | Formula / result |
|---|---|
| Clean quote | =PRICE(DATE(2025,8,15),DATE(2030,6,15),6%,8%,100,2,0)92.09831005 |
| Accrued days | =COUPDAYBS(DATE(2025,8,15),DATE(2030,6,15),2,0)60 |
| Days in period | =COUPDAYS(DATE(2025,8,15),DATE(2030,6,15),2,0)180 |
| Days to next coupon | =COUPDAYSNC(DATE(2025,8,15),DATE(2030,6,15),2,0)120 |
| Accrued interest per 100 | =100*6%/2*60/1801.00000000 |
| Equivalent current-period ACCRINT example | =ACCRINT(DATE(2025,6,15),DATE(2025,12,15),DATE(2025,8,15),6%,100,2,0)1.00000000 |
| Cash on 1,000 face | =(92.09831004975877+1)*1000/100930.98310050 |
For the September 2020 Actual/Actual example, the transparent manual formula is:
=1000*8%/2*(DATE(2020,9,3)-DATE(2020,7,1))/(DATE(2021,1,1)-DATE(2020,7,1))ACCRINT returns interest on the par amount you supply; it is not inherently per 100. Its default calculation method can accumulate from issue. The example above treats the previous coupon date as the start of a synthetic current-period calculation. Do not blindly replace it with the original issue date of an older bond.
For regular-period settlement accrual, the coupon-times-day-fraction cross-check makes the intended period explicit. Basis codes: 0 = US 30/360, 1 = Actual/Actual, 2 = Actual/360, 3 = Actual/365, 4 = European 30/360.
12Special cases and common mistakes
| Situation | Correct interpretation |
|---|---|
| Zero-coupon bond | No periodic coupon accrual is normally added to its quoted price. Discount accretion is already part of its value; it is different from a clean-to-dirty coupon adjustment. |
| Interest payable at maturity | ACCRINTM calculates contractual interest for this structure. It is not a universal valuation formula for discount bills or zero-coupon bonds. |
| Ex-coupon period | The buyer may not receive the imminent coupon. Accrued-interest treatment can change, including negative accrual under some conventions. |
| Bond trading flat | Some distressed or defaulted bonds trade without a separate accrued-interest addition. Check the trading convention. |
| Irregular first or last coupon | Use the instrument’s schedule and appropriate odd-period methods. A standard six-month fraction may not apply. |
| Settlement fees | Commissions and other charges can make the account debit differ from the bond’s dirty consideration. |
Frequent calculation errors include using yield instead of coupon rate, mixing quotes with cash amounts, using the trade date, adding one to date differences, assuming every half-year has 182 days, and rounding intermediate results too early.
The supplied notes also discuss zero-coupon accretion. Keep that topic separate from coupon settlement accrual. Accounting or tax accretion depends on the applicable rules and should not be inferred from the clean/dirty identity.
13Check your understanding
Try each question before opening the solution.
1. Clean quote 98.40, AI 1.20 per 100, face value 50,000. What cash amount settles?
Dirty quote = 99.60. Cash = 99.60 × 50,000/100 = 49,800, before separate charges.
2. A 1,000-face bond pays 8% semiannually. Sixty of 180 days have elapsed. What is AI?
Coupon = 40. AI = 40 × 60/180 = 13.33333333, or 13.33 after rounding. The 8% is an annual rate.
3. Market yield rises. Does accrued coupon interest rise because of that?
No. For the same coupon schedule, settlement date and day-count basis, accrued interest is unchanged. The bond’s clean and dirty market values can fall because future payments are discounted at a higher yield.
4. Why does a dirty-price drop on the coupon date not necessarily mean an investment loss?
The holder receives the coupon in cash. Total return combines cash income and the change in value; looking only at the price drop misses that cash receipt.
5. Can you add 13.913 of cash accrued interest to a clean quote of 92?
No. On 1,000 face, the clean cash amount is 920. Add 13.913 to that, or convert the accrued interest to 1.3913 per 100 and add it to 92.
6. Why can dirty and clean prices be equal?
For an ordinary coupon bond, accrued interest resets to zero after a coupon payment. Securities with no separate coupon accrual can also have no clean-to-dirty adjustment.
14References and further learning
The worked examples are adapted from the two supplied teaching workbooks: 01., Accrued Int Clean Price Dirty Price.xlsx and 04. Accrued Interest(Clean Price, Dirty Price).xlsx. Dates, day fractions and settlement arithmetic have been independently checked. The article clarifies the distinction between coupon accrual and discount accretion.
- FINRA — Bonds: coupon payments and accrued interest
- Microsoft — ACCRINT function
- Microsoft — PRICE function
- Microsoft — ACCRINTM function
Continue with Bond Prices and Yields, Duration and Convexity, or Spot Rates vs Forward Rates.