Full Price Calculator

The Full Price Calculator works out final selling price from cost, margin, VAT, discounts, fees, and delivery.

Full Price Calculator Explained

Full price is the bond’s “dirty” price. It equals the quoted clean price plus accrued interest from the last coupon date up to settlement. Markets often quote clean prices to keep comparisons tidy. But you pay full price when the trade settles.

Why the difference matters: coupons accrue between payment dates. The seller is owed their share for the time they held the bond in the current period. The buyer compensates that by paying accrued interest on top of the clean price. This matters in yield calculations, cash planning, and regulatory reporting.

Our calculator models these details using standard market conventions. It handles different coupon frequencies, day count choices, and settlement calendars. You can input prices or yields, then test ranges and scenarios to see how changes ripple through the full price.

How the Full Price Method Works

At a high level, the method adds accrued interest to the clean price. Clean price reflects the present value of future cash flows at the trade’s yield, excluding current-period accrual. Accrued interest compensates the seller for time since the last coupon date.

• Identify the last and next coupon dates around the settlement date.
• Compute the accrual fraction using the chosen day count convention.
• Calculate period coupon = coupon rate × face value ÷ frequency.
• Accrued interest = period coupon × accrual fraction (adjust for ex-coupon rules when required).
• Clean price from yield: discount remaining cash flows to settlement under the compounding basis.
• Full price (dirty) = clean price + accrued interest.

This framework mirrors common market practice. With it, you can move between quoted prices and settlement amounts under different assumptions. You can also check sensitivity to yield shifts, settlement dates, and day count choices.

Full Price Formulas & Derivations

Start with the present value of cash flows discounted to settlement. For a coupon bond with face value F, coupon rate c, frequency m, and yield y (with compounding aligned to frequency), clean price equals the sum of discounted coupon and principal cash flows, excluding current-period accrual.

• Period coupon: C = (c × F) ÷ m.
• Let k be the number of whole coupon periods remaining after the next coupon date; let s be the fraction of a period from settlement to next coupon. Clean price = sum over i from 1 to k+1 of [cash flow at i × (1 + y/m)^(−(i − 1 + s))], where cash flows are C for coupons and C + F at maturity.
• Accrued interest: AI = C × α, where α = (accrued days) ÷ (days in coupon period) under the selected day count convention.
• Full price (dirty): P_dirty = P_clean + AI.
• If using continuous compounding: discount factor for time t years is exp(−y × t). Replace (1 + y/m)^(−n) with exp(−y × t).

These expressions reflect bond valuation at settlement rather than coupon dates. They align with standard textbooks and trading systems. The key is applying the correct timing s and accrual α, both of which depend on calendar rules.

Inputs and Assumptions for Full Price

Gather the bond’s terms and the market conventions before you run the numbers. Each input carries assumptions that affect valuation. Keep them consistent across scenarios to avoid mismatches.

• Settlement date, last coupon date, and next coupon date (calendar matters).
• Face value (common default: 100 or 1,000).
• Coupon rate and coupon frequency (annual, semiannual, quarterly, monthly).
• Yield or clean price (provide one to solve for the other).
• Day count convention (30/360, Actual/Actual, Actual/365, Actual/360).
• Compounding basis and ex-coupon rule, if relevant to the market.

Expect variation across markets and issuers. Edge cases include negative yields, long or short first coupons, irregular schedules, and leap-year effects. Corporate and government bonds can differ in ex-coupon timing. Use ranges for dates and yields to see how sensitive full price is to these choices.

Using the Full Price Calculator: A Walkthrough

Here’s a concise overview before we dive into the key points:

1. Select the bond type and input face value, coupon rate, and frequency.
2. Enter settlement date, last coupon date, and next coupon date or provide schedule.
3. Choose the day count convention and compounding basis used in your market.
4. Provide yield to maturity or clean price, then select which variable to solve.
5. Review assumptions about ex-coupon rules and confirm the calendar settings.
6. Run the calculation, then compare results across scenarios by adjusting inputs.

These points provide quick orientation—use them alongside the full explanations in this page.

Case Studies

A semiannual U.S. Treasury note has F = 100, coupon rate 4%, and yield 3.20% (street convention). Settlement is 47 days after the last coupon in a 182-day period. Period coupon is 2.00, accrual fraction is 47/182 ≈ 0.2582, accrued interest is about 0.52 per 100. The clean price from the 3.20% yield is approximately 102.57, producing a full price near 103.09. What this means: the buyer pays about 103.09 per 100 at settlement, with 0.52 of that compensating the seller’s earned coupon.

A corporate bond pays 6% semiannually on F = 1,000. It is quoted clean at 101.20 per 100. Settlement occurs 20 days into a 180-day period, so the accrual fraction is 20/180 = 0.1111. Period coupon is 30.00 per 1,000, accrued interest is 3.33 per 1,000. Full price equals 1,012.00 + 3.33 = 1,015.33 per bond. What this means: you remit 1,015.33 per bond at settlement, even though the quote shows 101.20.

Limits of the Full Price Approach

The full price framework assumes fixed coupons, standard day count, and known schedules. Real markets include features and frictions that complicate pricing beyond clean plus accrued. Note where this approach may fall short.

• Callable, putable, or convertible bonds need option pricing; full price alone may mislead.
• Floating-rate notes and inflation-linked bonds change cash flows; you must project indices or resets.
• Tax, transaction fees, and settlement fails are excluded from the calculation.
• Day count or ex-coupon misalignment with market practice can cause basis errors.
• Irregular schedules and stubs require accurate date generation, not simple rules of thumb.

Use the method as a baseline for cash settlement and yield comparisons. For path-dependent features or embedded options, add appropriate models. Always document the conventions you apply so stakeholders can reproduce your results.

Units & Conversions

Bond pricing mixes percentages, per-100 quotes, and time fractions. Converting units consistently prevents errors. It also makes it easier to compare across instruments and to run scenarios. When in doubt, translate everything to present value per 100 face value and then scale.

Read left to right: identify the unit, convert to the working form, and scale by face value when needed. Keep yields in decimal during math and convert to percent only for display. Align the accrual fraction with the day count your market uses.

Tips If Results Look Off

Most discrepancies come from date rules and unit slips. Start by confirming the schedule and conventions. Then check how yields and prices were entered.

• Verify settlement, last coupon, and next coupon dates against the issuer’s schedule.
• Confirm day count (30/360 vs Actual/Actual) and compounding basis match the quote source.
• Enter yields as percents or decimals consistently; avoid mixing formats.
• Check face value units: per 100 vs per 1,000 affects scaling.
• Note ex-coupon periods; accrued interest may be reduced or zero near payment dates.

If a quote seems far from your clean price, try a small yield bump and watch the price change. That sanity check shows if duration and direction line up. Use ranges to test robustness under alternative assumptions.

FAQ about Full Price Calculator

What is the difference between clean price and full price?

Clean price excludes accrued interest and is used for quoting; full price includes accrued interest and is the actual settlement amount.

Which day count convention should I choose?

Use the convention standard for the bond’s market, such as Actual/Actual for many government bonds or 30/360 for some corporates; match your quote source.

Can this handle zero-coupon bonds?

Yes. Zero-coupon bonds have no accrual between payments, so full price equals clean price; discount the single maturity cash flow to settlement.

Why does full price change around coupon dates?

Accrued interest resets to zero on the coupon date, so full price drops by the coupon amount while clean price stays continuous absent yield changes.

Glossary for Full Price

Accrued Interest

The portion of the current coupon earned by the seller from the last coupon date up to settlement, based on the day count rule.

Clean Price

The quoted bond price excluding accrued interest; used for comparisons across dates without accrual effects.

Dirty Price (Full Price)

The settlement price that includes accrued interest: full price equals clean price plus accrued interest.

Day Count Convention

The rule for measuring days and periods, such as Actual/Actual, 30/360, Actual/365, or Actual/360; it affects accrual and discounting.

Ex-Coupon Date

A date before the coupon payment when the bond trades without the next coupon; the buyer may not receive the upcoming interest.

Yield to Maturity

The single discount rate that equates the present value of future cash flows to the clean price, assuming on-time payments and holding to maturity.

Basis Point

One hundredth of a percent, equal to 0.01%; 25 basis points equals 0.25% or 0.0025 in decimal yield.

Compounding Basis

The frequency at which interest is compounded for discounting cash flows, commonly aligned with coupon frequency.

Disclaimer: This tool is for educational estimates. Consider professional advice for decisions.

References

Here’s a concise overview before we dive into the key points:

• FINRA: Bond Prices, Rates, and Yields
• Investopedia: Dirty Price (Full Price) Definition
• Investopedia: Accrued Interest Explained
• Wikipedia: Day Count Convention
• Wikipedia: Bond Valuation Overview

These points provide quick orientation—use them alongside the full explanations in this page.