Bond Yield Calculator

Solve a bond's promised-cash-flow yield or price at a target yield, then inspect settlement, coupon payments and rate sensitivity. Presets are hypothetical; no live quotes.

Regular coupon schedules only: enter a whole number of coupon periods from the last coupon date. With accrued interest enabled, the remaining horizon subtracts the elapsed fraction of that period. YTM is a nominal annual rate equal to periodic yield × coupon frequency.

Bond Parameters

Face Value (Par)

Annual Coupon Rate

Coupon Frequency

Current Market Price

Enter USD per bond, not per 100 par. Choose clean or dirty basis below; the result always reconciles both.

Target YTM

Nominal annual target yield. The solved price uses the selected clean or dirty basis.

Years from Last Coupon to Maturity

Settlement and price convention

Entered price basis Schedule convention

Settlement dateMaturity date

Dates anchor regular coupons backwards from maturity, preserving month-end. Accrued interest uses actual elapsed days divided by actual days in that coupon interval. This is an explicit illustration, not every bond market's day-count convention. Irregular stubs, business-day and ex-coupon adjustments are unsupported.

Include accrued interest (clean vs dirty price)

Tax, inflation and reinvestment ▾

Tax & inflation

Tax treatment Choose municipal only when calculating a tax-equivalent yield.

Tax Bracket

Muni → tax-equivalent yield. Taxable → after-tax yield.

Inflation Rate

Used to compute real (inflation-adjusted) yield.

Portfolio & reinvestment

Reinvestment Rate

Rate at which coupons are reinvested. Leave blank to assume YTM (textbook assumption).

# of Bonds Scales annual coupon, redemption difference, terminal wealth and DV01. Prices remain per bond.

Inflation-linked (TIPS) — show real & nominal yield Treats the displayed yield as the real yield and derives the nominal equivalent from the inflation rate above. This illustration also permits zero or negative assumed inflation; it does not model actual TIPS index ratios or the maturity floor.

Optional call outcome

This bond is callable

Call date (dated schedule)

Enter one regular coupon date. Modeled yield to worst compares only this call with maturity; other calls, sinking funds and puts are omitted.

Yield to Maturity (BEY)

—

Enter bond parameters to compute.

Annual Coupon

—

Current Yield

—

YTM (BEY)

—

Effective annual yield

—

Results shown per bond. Portfolio totals appear when you enter more than one bond.

Risk, return & tax details

Nominal Equiv.

—

Yield to Call

—

Yield to Worst

—

Macaulay Duration

—

Modified Duration

—

DV01 (per bp)

—

Convexity

—

Breakeven Rate Rise

—

Redemption minus clean price, position (USD)

—

Total at Maturity

—

Holding-Period CAGR

—

After-Tax Yield

—

Real Yield

—

Dirty Price

—

Modeled call and maturity outcomes
Outcome	Date or coupon-period years	Redemption USD	Nominal annual yield

How the solver converged (bracketed bisection)

The solver brackets the root in log(1 + periodic yield), then bisects until the relative price residual is at most 1e-11. Each row shows a trial yield and price residual. An unconverged estimate is not reported as a yield.

Iteration	Trial Yield (BEY)	Price Residual

Price vs Yield Sensitivity

How this bond's price changes as market yields move ±300 bps from the current YTM (—). Face value $1,000, coupon 5.00%, 10 years.

Include convexity approximation on the chart

Exact dirty price and local sensitivity approximations, USD per bond
Nominal yield	Exact dirty price	Duration approximation	Convexity approximation	Exact change

The row highlighted in cyan represents the current YTM. This demonstrates the inverse relationship between bond price and yield.

Rate Shock — exact vs duration/convexity approximation

How well the textbook estimate ΔP/P ≈ −ModDur·Δy + ½·Convexity·Δy² tracks the exact re-priced bond across rate shocks. The approximation is near-perfect for small moves and drifts at the extremes.

Rate Shock	Exact Price	Approx Price	Exact Δ%	Approx Δ%	Tracking Error

Exact price re-discounts every cash flow at the shocked yield. Approx price uses only modified duration and convexity from the current YTM.

Coupon Reinvestment Sensitivity

Reinvestment changes terminal wealth and holding-period CAGR; it does not change the promised-cash-flow YTM. The separate assumed rate is not a forecast.

Reinvestment rate

—

Illustrative coupon reinvestment
Nominal reinvestment rate	Terminal wealth USD per bond	Holding CAGR

Cash flow schedule See coupons, present value, and cumulative income

Cash Flow Schedule

Period-by-period coupons, present value, and cumulative income — discounted at the current YTM.

Complete promised cash flows per bond
Period	Coupon-period years	Payment date	Coupon USD	Redemption USD	Cash flow USD	Discount factor	Present value USD	Cumulative coupons USD

—

Compare 3 Bonds Side-by-Side

Stack three bonds to compare YTM, duration, and total return. Bond A inherits from the main calculator on first load.

Parallel nominal-yield shock (basis points)

0 bps rate move

Bond A

Face Coupon % Price Years Frequency

Maturity date

YTM—

Current Yield—

Macaulay—

Mod. Duration—

Total CAGR—

Immediate dirty-price change—

Bond B

Face Coupon % Price Years Frequency

Maturity date

YTM—

Current Yield—

Macaulay—

Mod. Duration—

Total CAGR—

Immediate dirty-price change—

Bond C

Face Coupon % Price Years Frequency

Maturity date

YTM—

Current Yield—

Macaulay—

Mod. Duration—

Total CAGR—

Immediate dirty-price change—

Bond ladder builder Advanced portfolio planning

Bond Ladder Builder

Enter 1–10 rungs. All use the main settlement and price convention; maturity and coupon frequency remain rung-specific. Weighted nominal yield is not portfolio IRR. The chart and table show actual modeled payments, including partial years.

Rung	Face	Coupon %	Price	Years	Freq	Qty	Maturity date	YTM	Mod Dur	DV01

Weighted YTM, duration, convexity, and DV01 are weighted by each rung's market value (price × quantity). Annual cash flow aggregates coupon income across all rungs each year, with face value added in the year each rung matures.

Actual portfolio cash receipts by year
Year	Cash flow USD

Bond types reference Typical yield, risk, and tax treatment

Bond Types Reference

Bond categories differ in issuer, cash flows, call terms and tax rules. Presets are hypothetical examples, not live quotes or suitability ratings. Verify the actual security's documents.

Illustrative bond categories and model limits
Category	Cash-flow or model considerations
US Treasury bills, notes and bonds	Verify quoted yield convention, coupon dates and accrued interest. This model uses regular nominal coupon yields.
TIPS and I Bonds	Inflation indexation and savings-bond rules differ from this constant real-dollar illustration.
Municipal bonds	Exemptions and gain taxes depend on the security and jurisdiction; the tax model here is simplified.
Agency, corporate and emerging-market bonds	Credit, currency, prepayment and call terms can alter realized cash flows; no credit rating or default probability is inferred.

Key Concepts

Yield Curve

A yield curve compares yields across maturities on a stated basis. Its shape is an observed input, not a forecast in this calculator.

Credit Spread

A spread compares yields on a stated benchmark and convention. Credit, liquidity, options and other differences can affect it; this model does not isolate those causes.

Callable Bonds

Some bonds allow the issuer to redeem them early. Yield to Call (YTC) may be more relevant than YTM for these bonds, especially when trading at a premium.

Convexity

Duration linearly approximates price change; convexity captures the curvature. Positive convexity means bonds gain more when rates fall than they lose when rates rise by the same amount.

Report scope Remember inputs on this device (optional)

Inputs stay off public URLs until you explicitly review sharing. Local saving is off by default. A full shared link reveals its included assumptions to anyone who receives it.

4 min read 4 steps 13 terms 3 examples 9 FAQs P_dirty = Σ[j=1..n] C/(1+r)^(j−a) + F/(1+r)^(n−a); P_clean = …

Bond yields summarize promised cash flows, price and payment timing.

YMYL Reviewed by Calculover Editorial Review · Updated 2026-10-18 · 4 sources

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Walk-through

How to Use This Calculator

4 steps

Enter Bond Parameters

Enter face, coupon, frequency and price or target yield. Prices are USD per bond, not per 100 par. Select clean/dirty price and regular periods or optional dates.

Tune the Realism

Open settlement, call and tax/reinvestment panels separately. Dates use actual coupon-interval days. Tax, reinvestment and real-dollar inflation conversions are illustrations.

Read the Full Yield Stack

Read nominal YTM, effective annual yield and the clean-plus-accrued dirty-price bridge. Coupon income, duration, position DV01 and optional tax/call outcomes state their units.

Stress-Test the Price

Select yield and payment rows in Analysis. Compare bonds on the common basis. Choose the report scope for Copy, CSV, PDF or Print. Review blank or full sharing explicitly.

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Reference

Formula & Methodology

6 formulas

Bond Price (PV of Cash Flows)

P_dirty = Σ[j=1..n] C/(1+r)^(j−a) + F/(1+r)^(n−a); P_clean = P_dirty − aC

Use regular coupon periods or optional settlement/maturity dates. Dates anchor coupons backwards from maturity and preserve month-end; elapsed accrual is actual days divided by actual coupon-interval days. No irregular stubs, business-day or ex-coupon adjustments are modeled.

Current Yield

Current Yield = Annual Coupon / P_clean

Annual coupon income divided by the clean price per bond. This simple income yield excludes redemption gain/loss, coupon timing and reinvestment; it is not YTM.

Yield to Maturity (Bond-Equivalent Yield)

PV(C,F,r,n,a)=P_dirty; BEY=r×frequency; Effective annual yield=(1+r)^frequency−1

The solver bisects log(1+r) in a verified bracket for r>−1. A yield is reported only when the relative price residual is at most 1e-11; failed convergence leaves the result unavailable.

Macaulay & Modified Duration

Mac = Σ[((j−a)/frequency) × PV(CF_j)] / P_dirty; Mod = Mac/(1+r)

Macaulay duration weights actual remaining payment times by their present values. Modified duration divides it by 1+periodic yield; the dirty-price change is locally approximated using BEY changes.

Convexity

Convexity = Σ[(j−a)(j−a+1)×PV(CF_j)] / [P_dirty×(1+r)^2×frequency^2]

Captures the curvature of the price-yield relationship that linear duration misses. Together: ΔP/P ≈ −Mod × Δy + ½ × Conv × Δy².

Simplified Tax Cash Flows

C_net=C×(1−b); F_net=F−max(F−P_dirty,0)×b; PV(C_net,F_net,r_net)=P_dirty

Tax coupons and positive redemption gains at the entered rate, with gains taxed at maturity. No loss credit, OID accrual or premium amortization. Tax-equivalent YTM grosses up those cash flows; it is not always YTM/(1−b).

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YMYL

Trust, Methodology & Sources

Reviewed by Calculover Editorial Review · Updated 2026-10-18 · 4 sources

Editorial accountability

Author: Quinn Sumner - Editor

Owner: Quinn Sumner - Editorial owner

Reviewer: Calculover Editorial Review - Source and limitation review

Last reviewed: 2026-10-18

Last verified: 2026-10-18

Data effective: 2026-10-18

Methodology

YTM discounts promised coupons and redemption to dirty price. BEY is periodic yield × frequency; effective annual yield is (1+r)^frequency−1. Neither guarantees a realized return. The solver bisects log(1+r) in a verified bracket for r>−1. A yield is reported only when the relative price residual is at most 1e-11; failed convergence leaves the result unavailable. Use regular coupon periods or optional settlement/maturity dates. Dates anchor coupons backwards from maturity and preserve month-end; elapsed accrual is actual days divided by actual coupon-interval days. No irregular stubs, business-day or ex-coupon adjustments are modeled. Tax coupons and positive redemption gains at the entered rate, with gains taxed at maturity. No loss credit, OID accrual or premium amortization. Tax-equivalent YTM grosses up those cash flows; it is not always YTM/(1−b).

Assumption: Bond Yield Calculator relies on the values the user enters and does not independently verify issuer credit, settlement details, accrued interest conventions (30/360 vs ACT/ACT), legal status, or live market quotes.

Assumption: The maturity-value projection reinvests each coupon at the entered periodic rate (default: solved YTM/frequency). The resulting annual holding-period CAGR is distinct from nominal BEY.

Assumption: Use regular coupon periods or optional settlement/maturity dates. Dates anchor coupons backwards from maturity and preserve month-end; elapsed accrual is actual days divided by actual coupon-interval days. No irregular stubs, business-day or ex-coupon adjustments are modeled.

Limitations & guidance

Bond Yield Calculator does not recommend securities, predict default risk, model credit-spread changes, or assess whether a bond is suitable for a given investor.

Realized returns depend on market conditions at each coupon date, the issuer's ability to make payments, call decisions, and applicable taxes and fees.

The residual-checked log(1+r) solver and explicit cash-flow ledger are tested numerically; this is not a claim of certification by CFA Institute, FINRA, the IRS or the U.S. Treasury. The dated FINRA source discusses promised yields and call/reinvestment risks. Actual issuer terms, market conventions and tax rules require separate verification.

This tool is for educational and informational purposes only. It does not constitute investment advice. Bond prices, yields, and tax treatment vary by issuer, settlement date, and jurisdiction. Consult a registered investment advisor or CPA before making investment decisions.

Professional guidance: Bond Yield Calculator is for investment-math education only and is not investment, tax, legal, or financial advice. Consider credit risk, fees, taxes, and suitability before acting.

Primary sources

Bond yield and risk education (2005) - FINRA / NASD

Treasury Inflation-Protected Securities (TIPS) - TreasuryDirect

Publication 550 (2025), Investment Income and Expenses - Internal Revenue Service

Accrued Interest Calculator and convention inputs

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Glossary

Key Terms Explained

13 terms

Face Value (Par) The principal amount of the bond, repaid to the investor at maturity — typically $1,000 per bond for US corporates and Treasuries.

Coupon Rate The fixed annual interest rate paid on the face value, set at issuance and unchanged for the life of the bond.

Yield to Maturity (YTM) YTM discounts promised coupons and redemption to dirty price. BEY is periodic yield × frequency; effective annual yield is (1+r)^frequency−1. Neither guarantees a realized return.

Current Yield Annual coupon income divided by the clean price per bond. This simple income yield excludes redemption gain/loss, coupon timing and reinvestment; it is not YTM.

Macaulay Duration The weighted average time to receive all bond cash flows, expressed in years. For a zero-coupon bond it equals maturity exactly.

Modified Duration Macaulay duration divided by 1+periodic yield. It approximates immediate dirty-price sensitivity to a nominal annual yield change, in years; it is not credit or total-return risk.

Convexity Second-order dirty-price sensitivity to nominal annual yield, in years squared. It improves the local duration approximation but is not an option-adjusted measure or a guaranteed benefit.

Yield to Call (YTC) Yield for the single entered call price and regular coupon date, compared with maturity. It is not a prediction, an exhaustive call schedule or a guaranteed minimum return.

Yield to Worst (YTW) Here YTW is the lower of maturity yield and the single entered call outcome. Other call dates, sinking funds, default and the embedded call option are not modeled.

Bond-Equivalent Yield (BEY) Nominal annual yield is periodic yield × frequency. Semiannual BEY is 2r; effective annual yield is (1+r)^frequency−1. Other instruments can use different quote conventions.

Clean vs Dirty Price Clean price excludes accrued interest; dirty price (a.k.a. invoice price) is the actual amount paid at settlement = clean price + accrued interest.

Premium Bond A bond with clean price above face value. This label alone does not establish credit quality, suitability or the yield/coupon relationship under every settlement convention.

Discount Bond A bond with clean price below face value. This label alone does not establish credit quality, suitability or the yield/coupon relationship under every settlement convention.

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Scenarios

Real-World Examples

3 worked examples

Sarah

Treasury Bond at Discount

Face value $10,000 Coupon rate 4.0% Market price $9,400 Years to maturity 10 Frequency Semi-annual

Current yield is 4.26% and promised-cash-flow YTM (BEY) is about 4.76%. The schedule includes $600 of redemption gain plus coupons. These figures do not guarantee payments or reinvestment returns.

Marcus

Corporate Bond at Premium (Callable)

Face value $10,000 Coupon rate 6.5% Market price $10,800 Years to maturity 7 Call price / Years to call $10,200 / 3 Frequency Semi-annual

Current yield is 6.02%, YTM is about 5.13%, and the entered call scenario yields about 4.26%. Modeled YTW is 4.26% across these two outcomes; it does not predict a call or provide a guaranteed floor.

Priya

Muni Bond — Tax-Equivalent Comparison

Face value $5,000 Coupon rate 3.5% Market price $5,000 Years to maturity 15 Tax bracket 35%

At par, YTM is 3.50%. With a 35% tax rate, this simplified cash-flow gross-up gives tax-equivalent YTM about 5.38%. Actual exemptions, gain treatment and issuer credit risk still matter.

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Reference

Cite This Calculator

APA & MLA

Use either format to cite this calculator in a paper, report, or resource list.

APA

MLA

📄

Deep Dive

Understanding Bond Yield

4 chapters · 4 min read

Bond yields summarize promised cash flows, price and payment timing. Current yield, nominal BEY, effective annual yield and a reinvestment-based holding-period return measure different things; compare matching conventions and risks.

Why Bond Prices Move Opposite to Yields

With positive promised coupons and redemption, present value decreases as the discount yield rises within its valid periodic domain. Reprice the complete cash-flow ledger; dividing coupon income by price gives current yield, not YTM.

Clean price plus accrued interest equals dirty settlement price. Timing and the chosen day-count convention affect accrual and yields. The date option uses actual coupon-interval days, not a universal market convention.

Current Yield vs. Yield to Maturity

YTM discounts promised coupons and redemption to dirty price. BEY is periodic yield × frequency; effective annual yield is (1+r)^frequency−1. Neither guarantees a realized return. Coupon frequency defines the periodic yield. Nominal BEY multiplies that yield by frequency; effective annual yield compounds it. For 5% semiannual BEY, the effective annual yield is 5.0625%.

The maturity-value projection reinvests each coupon at the entered periodic rate (default: solved YTM/frequency). The resulting annual holding-period CAGR is distinct from nominal BEY.

Duration, Modified Duration, and Convexity

Macaulay duration weights remaining payment times by their dirty-price present values. Modified duration is Macaulay/(1+r), where r is periodic yield. Convexity adds the second-order term. These approximate immediate dirty-price changes for parallel nominal-yield moves; compare with exact repricing. They are not total-return, credit-risk or option-adjusted measures. DV01 covers the entered quantity in USD per basis point.

Callable Bonds and Yield to Worst

A call is a possible early-redemption scenario, not a predicted issuer decision. This calculator compares the entered call outcome with maturity only. Duration and convexity use maturity cash flows and are not option-adjusted. Reinvestment rates and actual payments can differ from the assumptions. Here YTW is the lower of maturity yield and the single entered call outcome. Other call dates, sinking funds, default and the embedded call option are not modeled.

The maturity-value projection reinvests each coupon at the entered periodic rate (default: solved YTM/frequency). The resulting annual holding-period CAGR is distinct from nominal BEY. Tax coupons and positive redemption gains at the entered rate, with gains taxed at maturity. No loss credit, OID accrual or premium amortization. Tax-equivalent YTM grosses up those cash flows; it is not always YTM/(1−b).

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Questions

Frequently Asked Questions

9 questions

What is Yield to Maturity (YTM)?+

YTM discounts promised coupons and redemption to dirty price. BEY is periodic yield × frequency; effective annual yield is (1+r)^frequency−1. Neither guarantees a realized return.

How is YTM calculated?+

The solver bisects log(1+r) in a verified bracket for r>−1. A yield is reported only when the relative price residual is at most 1e-11; failed convergence leaves the result unavailable.

Why use semi-annual vs annual coupons?+

Coupon frequency defines the periodic yield. Nominal BEY multiplies that yield by frequency; effective annual yield compounds it. For 5% semiannual BEY, the effective annual yield is 5.0625%.

What is modified duration and how do I use it?+

Modified duration approximates the immediate percentage dirty-price change from a parallel nominal annual yield move: ΔP/P≈−Mod×Δy. It is in years and uses maturity cash flows. Compare it with exact repricing; it does not measure default risk or a one-year total return.

What is convexity?+

Convexity adds the local second-order term: ΔP/P≈−Mod×Δy+½×Conv×Δy². Its units are years squared for nominal annual yield changes. Compare with exact repricing for large shocks. The maturity-based result is not option-adjusted and does not guarantee a realized gain.

How does a callable bond change my yield?+

What does it mean when a bond trades at a premium or discount?+

Premium means clean price above face; discount means below. Neither rates credit quality. Yield/coupon identities depend on settlement timing. At par on a coupon date, a regular fixed-coupon bond has nominal YTM equal to its coupon rate.

Are municipal bond yields better after tax?+

Tax-exempt status alone does not make one bond better. This simplified model grosses up coupons and positive redemption gains; actual exemptions, credit risk, gain taxes and premium/OID rules can change the comparison.

What is the difference between coupon rate and yield?+

Coupon rate is fixed at issuance and determines the dollar coupon payment. Yield (current yield or YTM) changes as the bond's market price fluctuates. A 5% coupon bond priced at $950 has current yield 5.26% and a higher YTM because you also gain $50 at maturity.

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Bond Yield Calculator

Bond Parameters

Tax & inflation

Portfolio & reinvestment

Price vs Yield Sensitivity

Rate Shock — exact vs duration/convexity approximation

Coupon Reinvestment Sensitivity

Cash Flow Schedule

Compare 3 Bonds Side-by-Side

Bond A

Bond B

Bond C

Bond Ladder Builder

Bond Types Reference

Key Concepts

How to Use This Calculator

Enter Bond Parameters

Tune the Realism

Read the Full Yield Stack

Stress-Test the Price

Formula & Methodology

Trust, Methodology & Sources

Key Terms Explained

Real-World Examples

Cite This Calculator

Understanding Bond Yield

Why Bond Prices Move Opposite to Yields

Current Yield vs. Yield to Maturity

Duration, Modified Duration, and Convexity

Callable Bonds and Yield to Worst

Frequently Asked Questions

Get a branded PDF of your results

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