How do you calculate a bond's full price from its yield to maturity, and what's the difference between full price and clean price?

Bond pricing from YTM is the foundation of fixed income analysis at CFA Level I. The core idea is that a bond's price equals the present value of all future cash flows, discounted at the yield to maturity.

The Full Price Formula

For a bond with semiannual coupons:

Full Price = C/(1+y)^1 + C/(1+y)^2 + ... + (C+FV)/(1+y)^N

Where C = coupon payment per period, y = YTM per period, FV = face value, N = total periods remaining.

Worked Example:

Consider a bond issued by Hargrove Industries:

• Face value: $1,000
• Coupon rate: 6% (semiannual, so $30 every 6 months)
• Maturity: 3 years (6 periods)
• YTM: 8% (4% per semiannual period)
• Settlement: 75 days into the current coupon period (180-day period)

Step 1 — Calculate PV at last coupon date:

PV = $30/(1.04)^1 + $30/(1.04)^2 + $30/(1.04)^3 + $30/(1.04)^4 + $30/(1.04)^5 + $1,030/(1.04)^6

PV = $28.85 + $27.74 + $26.67 + $25.65 + $24.66 + $813.86 = $947.43

Step 2 — Compound forward to settlement date:

Fraction of period elapsed: t/T = 75/180 = 0.4167

Full Price = $947.43 x (1.04)^0.4167 = $947.43 x 1.0164 = $962.97

Step 3 — Calculate accrued interest:

AI = $30 x (75/180) = $12.50

Step 4 — Clean price:

Clean Price = Full Price - Accrued Interest = $962.97 - $12.50 = $950.47

Key Distinctions:

• Full Price (Dirty Price): What the buyer actually pays. Includes accrued interest.
• Clean Price (Flat Price): Quoted in markets. Excludes accrued interest so that price comparisons aren't distorted by timing within the coupon period.
• Accrued Interest: The seller's earned but unpaid portion of the next coupon. The buyer compensates the seller for this at settlement.

Exam Tip: If a question says "quoted price," it means clean price. If it says "settlement amount" or "invoice price," it means full price. Always check which convention the question uses.

Practice more bond pricing calculations in our CFA Level I question bank.