Enter Values

$
Par value of the bond
%
Annual coupon as % of face value (0 for zero-coupon)
%
Enter as percentage (e.g., 4 for 4%)
years
Time until bond matures
Settlement between coupon dates
days
Days elapsed since last coupon payment
days
Total days in the current coupon period
Bond Pricing Formula
P = C/m × 1 − (1+y/m)−ny/m + F × (1+y/m)−n
P = Price | C = Annual coupon | F = Face value | y = YTM | m = Frequency | n = Total periods
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Bond Pricing Result

Clean Price --
Dirty Price --
Accrued Interest --
Premium / Discount --
Premium / Discount % --
Per-Period Coupon --
Number of Periods --
Per-Period Yield --
Undiscounted Total Cash Flows --

Formula Breakdown

P = C/m × [(1 − (1+y/m)−n) / (y/m)] + F / (1+y/m)n
Present value of coupon annuity + Present value of face value

Bond Status Interpretation

Status Condition Meaning
Premium Price > Face Value Coupon rate exceeds market yield
Par Price ≈ Face Value Coupon rate equals market yield
Discount Price < Face Value Market yield exceeds coupon rate
Model Assumptions
  • Fixed-rate coupon bond (not floating-rate or inflation-linked)
  • Periodic compounding matching payment frequency (not continuous)
  • Flat yield curve — single YTM rate discounts all cash flows
  • Accrued interest uses actual/actual day count convention (simplified)
  • Between-coupon pricing uses the simplified additive approach (Clean + AI) — educational approximation per BKM
  • No embedded options (not callable, putable, or convertible)
  • Non-negative yields assumed

For educational purposes. Not financial advice. Market conventions simplified.

Understanding Bond Pricing

Video Explanation

Video: Bond Pricing Explained

What is Bond Pricing?

Bond pricing determines the fair value of a fixed-income security by calculating the present value of its future cash flows. These cash flows consist of periodic coupon payments and the face value (par) returned at maturity, all discounted at the bond's yield to maturity (YTM).

Bond Pricing Equation
P = C/m × [(1 − (1+y/m)−n) / (y/m)] + F / (1+y/m)n
PV of Coupon Annuity + PV of Face Value

Clean Price vs. Dirty Price

Clean Price

Quoted market price
Excludes accrued interest. Used for price comparison and avoiding jumps on coupon dates.

Dirty Price

Settlement price
Clean price + accrued interest. The actual amount the buyer pays at settlement.

Price-Yield Relationship

Bond prices and yields move in opposite directions. When market interest rates rise, existing bonds with lower fixed coupons become less attractive, so their prices fall. When rates fall, existing higher-coupon bonds become more valuable.

  • Premium bond (Price > Par): Coupon rate > market yield — investors pay extra for above-market income.
  • Par bond (Price = Par): Coupon rate = market yield — fairly priced at face value.
  • Discount bond (Price < Par): Coupon rate < market yield — price compensates for below-market income.
BKM Key Insight: This convex price-yield relationship means that rate decreases produce larger price gains than equivalent rate increases produce losses — a property exploited in bond convexity analysis.

When to Use This Calculator vs. YTM Calculator

Use the Bond Pricing Calculator when you know the YTM and want to find the bond's price. Use the Yield to Maturity Calculator when you know the market price and want to find the yield. They are inverse operations — together they form a complete fixed income toolkit.

Related Topics

Frequently Asked Questions

A bond's price equals the present value of all its future cash flows — the stream of coupon payments plus the face value returned at maturity. Each cash flow is discounted at the yield to maturity (YTM). For a semi-annual coupon bond: P = Σ[C/2 / (1 + y/2)t] + F / (1 + y/2)2n, where C is the annual coupon, y is the YTM, and n is years to maturity.

The clean price is the bond's quoted market price, excluding accrued interest. The dirty price (also called the invoice or settlement price) is what the buyer actually pays — it equals the clean price plus accrued interest since the last coupon date. Bond markets quote clean prices to avoid jumps on coupon dates, but settlement occurs at the dirty price. This calculator uses the simplified additive approach (Dirty = Clean + AI), consistent with BKM's educational treatment.

Accrued interest is the portion of the next coupon payment that has been earned but not yet paid since the last coupon date. It is calculated as: AI = (Coupon per period) × (Days since last coupon / Days in coupon period). The buyer compensates the seller for this earned interest at settlement.

When market interest rates rise, the discount rate applied to a bond's fixed cash flows increases, reducing their present value — so the bond's price falls. Conversely, when rates fall, the present value of those same fixed cash flows increases, pushing the bond's price up. This inverse relationship is fundamental to fixed income investing.

A premium bond trades above its face value because its coupon rate exceeds the current market yield — investors pay extra for the higher coupon income. A discount bond trades below face value because its coupon rate is below the market yield. At maturity, both converge to face value (par), so premium bonds experience price depreciation and discount bonds experience price appreciation over time.

Coupon frequency affects bond pricing through the compounding convention. A 10% annual YTM applied semi-annually uses 5% per period, giving an effective annual rate of 10.25%. When comparing bonds with different frequencies, the yield basis must be consistent. Most U.S. bonds pay semi-annually, so yields are quoted on a semi-annual bond-equivalent basis.
Disclaimer

This calculator is for educational purposes only and uses simplified conventions (flat yield curve, actual/actual day count, additive accrued interest). Actual bond pricing may differ due to day count conventions (30/360, ACT/365), settlement rules, and market-specific practices. This tool should not be used for trading decisions.

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Course by Ryan O'Connell, CFA, FRM

Fixed Income Investing Course

Master fixed income investing from fundamentals to advanced strategies. Covers bond pricing, duration, convexity, yield curves, and interest rate risk management.

  • Bond pricing, duration & convexity deep dives
  • Yield curve analysis and term structure models
  • Interest rate risk management techniques
  • Hands-on exercises with real bond market data
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