Updated for the 2026-2027 CFA® Level I curriculum.
A bond's price is the present value of its remaining promised cash flows discounted at the yield to maturity. Settlement timing determines whether the result is a coupon-date price or a between-coupon full price.
Quick Answer
To calculate bond price, convert YTM to the rate per coupon period, discount each coupon and the principal, and add the present values. Between coupon dates, use a fractional first period. The full price includes accrued interest, while the flat price equals full price minus accrued interest.
Key Takeaways
Match the discount rate to coupon frequency.
Include principal in the final cash flow.
Use fractional periods between coupon dates.
Full price includes accrued interest; flat price excludes it.
A YTM above the coupon rate produces a discount price on a coupon date.
What You Need to Know for CFA Level I
Calculate periodic coupon and yield.
Price on a coupon date.
Adjust exponents for a fractional coupon period.
Convert full price to flat price.
This page calculates price from a given YTM. Broader price-feature relationships and matrix pricing are covered separately.
What Does Yield to Maturity Do in Bond Pricing?
YTM is the single discount rate that equates the present value of promised cash flows with the bond's full price, given the stated compounding convention. It assumes the bond makes promised payments and uses one rate for all maturities.
Bond Price Formula on a Coupon Date
When settlement occurs on a coupon date, calculate the bond price by discounting each remaining coupon payment and the face value at the periodic YTM.
Where:
= current bond price
= coupon payment per period
= face value
= yield per coupon period, equal to YTM/m
= annual yield to maturity
= number of payments per year
= annual coupon rate
= number of remaining payments
= payment period
Pricing a Bond Between Coupon Dates
If w is the fraction of a coupon period from settlement to the next coupon:
where:
= full bond price, including accrued interest
= cash flow paid in period t
= yield per coupon period
= payment number
= number of remaining payments
= fraction of a coupon period from settlement to the next coupon
State the day-count convention used to determine w. Consistent timing is more important than memorizing a calendar shortcut.
Accrued Interest, Full Price, and Flat Price
Once you have the full price, subtract accrued interest to determine the bond's flat price.
Where:
= flat bond price, excluding accrued interest
= full bond price, including accrued interest
= coupon interest earned since the previous coupon date
The buyer pays the full price at settlement. Market quotations often report the flat price so that regular coupon accrual does not appear as a daily price gain.
Worked Bond Price Calculation
A two-year annual-pay bond has par USD 1,000, a 5% coupon, and 6% YTM immediately after a coupon date. The annual coupon is USD 50.
The bond trades below par because its coupon rate is below its required yield.
Working Example
Assume the same bond settles one-quarter of a coupon period after the last coupon, so 0.75 of a period remains to the next payment. Discount the first USD 50 by (1.06)(0.75) and the final USD 1,050 by (1.06)(1.75) to obtain full price. Then subtract accrued interest based on the stated day-count convention to obtain flat price. The timeline controls the exponents.
Common Exam Traps
Discounting semiannual coupons with an annual rate
Convert the quoted YTM into a periodic rate and use the matching number of periods; keep rate and cash-flow frequency consistent.
Leaving par value out of the last payment
The final cash flow of a standard coupon bond contains both the last coupon and principal repayment, unless the problem states otherwise.
Using a whole number of periods between coupon dates
A settlement date between payments calls for the appropriate fractional-period convention and accrued interest treatment.
Reporting full price when flat price is requested
Full or dirty price includes accrued interest; flat or clean price excludes it. Use the requested quote basis and subtract accrued interest when appropriate.
Rounding the periodic yield before valuation
Small rate rounding can alter several discounted cash flows. Carry precision through the calculation and round only the final answer.
Practice Question
A two-year annual-pay bond has a USD 1,000 par value, a 5% coupon, and a 6% YTM. Its price immediately after a coupon payment is closest to:
USD 981.67
USD 1,000.00
USD 1,018.33
Correct Answer: Option A
Discounting the two remaining cash flows at the 6% YTM gives:
.
Option B: The bond would price at par only if its coupon rate equaled its YTM. Here, the 5% coupon rate is below the 6% YTM.
Option C: A premium price would be expected when the coupon rate exceeds the YTM, which is not the case here.
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FAQs About Bond Price Calculation Based on Yield to Maturity (YTM)
How do you calculate a bond price from YTM?
Discount every remaining coupon and principal payment using the periodic YTM, then sum the present values.
What is the difference between full price and flat price?
Full price includes accrued interest. Flat price excludes it.
How is a bond priced between coupon dates?
Use fractional-period exponents based on the settlement date and the stated day-count convention.