CFA Level IFixed IncomeEasy
A bond has an 8% annual coupon rate paid semiannually and a face value of $1,000. The bond's clean (flat) price is quoted at 970.00. It has been 45 days since the last coupon payment, and the coupon period has 180 days (30/360 convention). The bond's full (invoice) price is closest to:
- A$970.00
- B$980.00
- C$975.00
- D$990.00
Show answer & explanationAnswer & explanation
Correct answer: B. $980.00
Semiannual coupon = 8%/2 × $1,000 = $40. Accrued interest = $40 × (45/180) = $10.00. Full price = clean price + accrued interest = $970 + $10 = $980.00.
Why the other options are wrong
- A. This is only the clean price, ignoring accrued interest.
- C. Understates accrued interest; correct AI is $10, not $5.
- D. Overstates accrued interest beyond the $10 actually accrued.
Full (Dirty) Price vs Clean Price
The full price is the amount a buyer actually pays, equal to the clean (quoted) price plus accrued interest since the last coupon date.
- Full price = Clean price + Accrued Interest
- Accrued Interest = Coupon × (days since last coupon/days in period)
- Bond quotes in the market are typically clean prices
Memory trick: Clean is quoted, dirty is what you pay.