Clean vs dirty price: quoted 97.60, you pay 99.60
A bond is quoted at 97.60 and you buy 100 of par. The cash that leaves your account on settlement is 99.60, not 97.60, because the quote is the flat price and the invoice is the full price. The 2.00 gap is accrued interest, and a question that asks for one while you computed the other will happily list both in the answer choices.
What the quoted price leaves out
Between coupon dates a bond has two prices, and the CFA curriculum names them deliberately. The full price, also called the dirty or invoice price, is everything the buyer pays. The flat price, also called the clean or quoted price, is the full price with accrued interest stripped out.
Full price = Flat price + Accrued interest
Accrued interest = (t ÷ T) × PMT
Here t is the number of days from the last coupon payment to settlement, T is the number of days in the whole coupon period, and PMT is the coupon payment for that period. Accrued interest is the seller’s share of the coupon that has not been paid yet. The buyer will collect the entire next coupon from the issuer, so at settlement the buyer hands the seller the slice the seller earned by holding the bond.
Dealers quote the flat price for a practical reason. Accrued interest resets to zero on every coupon date and climbs steadily until the next one, so the full price carries a sawtooth that has nothing to do with the bond getting cheaper or richer. Strip that out and the quoted series is comparable day to day. The sawtooth is a calendar artifact, not a price move.
Working a number end to end
Take a bond paying a 6% annual coupon on 100 of par, three coupons left as of the last coupon date, priced to a market discount rate of 7%. Settlement falls 120 days into a 360-day coupon period under the 30/360 convention.
First, value the remaining cash flows at the last coupon date:
PV = 6 ÷ 1.07 + 6 ÷ 1.07² + 106 ÷ 1.07³ = 5.6075 + 5.2406 + 86.5276 = 97.3757
Then carry that value forward to settlement, 120/360 of a period later:
Full price = 97.3757 × 1.07^(120/360) = 99.5967
That is the invoice. The accrued interest, and then the quote:
Accrued interest = (120 ÷ 360) × 6 = 2.00
Flat price = 99.5967 − 2.00 = 97.5967
Notice which one the discounting produced. Present-value arithmetic lands on the full price, always, because the cash flows are being discounted to the settlement date. The flat price is a subtraction you do afterwards. Candidates who report 99.60 when the question asked for the quoted price did the valuation correctly and stopped one step early.
The fraction and the coupon must describe the same period
The second way this calculation breaks is a mismatch inside the formula. PMT is the coupon for that period, not the annual coupon. Take the same 6% bond paying semiannually, 60 days into a 180-day period. The period coupon is 3.00, so accrued interest is (60 ÷ 180) × 3 = 1.00. Pair the semiannual fraction with the annual coupon instead and you get (60 ÷ 180) × 6 = 2.00, exactly double. The ratio and the payment have to be measured on the same clock.
The day-count convention is what fixes t and T, and the exam states it on purpose. The 30/360 convention treats every month as 30 days and every year as 360, and it is the one typically used for corporate bonds. Actual/actual counts real calendar days, weekends and leap days included, and it is typically used for government bonds. Changing the convention changes accrued interest, which changes the invoice while the quote stays put.
Quick reference
| Question wording | What it establishes | Risk if missed |
|---|---|---|
| Quoted price, clean price, flat price | Price excluding accrued interest | Reporting the invoice amount instead |
| Invoice price, dirty price, full price | Total cash paid at settlement | Reporting the quote and understating the payment |
| Corporate bond, 30/360 | Months count as 30 days, years as 360 | Counting actual calendar days for t and T |
| Government bond, actual/actual | Real days elapsed over real days in the period | Applying the 30/360 shortcut |
| Semiannual coupon | PMT is the period coupon, not the annual one | Doubling accrued interest |
One habit removes most of the damage. After any between-coupon valuation, write down which of the two prices you are holding before you look at the answer choices. The distractor set for this question type is usually the correct full price, the correct flat price, and one number built from an accrued-interest slip, so all three look defensible until you check what was asked.
The same reading problem drives the current yield versus yield to maturity trap: several correct measures of one bond, and the question quietly names a particular one.
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