Bond Yield Calculator
Bond Yield Calculator: compute Yield to Maturity (YTM), Effective Annual Yield, Current Yield, Yield to Call, and Duration. Professional-grade, mobile-first, WCAG 2.1 AA accessible.
Bond Yield Calculator
This professional Bond Yield Calculator helps investors, analysts, and students compute key bond metrics with precision and accessibility. Enter a bond’s price, coupon, maturity, and payment frequency to instantly obtain Yield to Maturity (YTM), Effective Annual Yield, Current Yield, Yield to Call (optional), and Duration. Built mobile-first and WCAG 2.1 AA compliant.
Interactive Calculator
Results
Tip: Nominal YTM uses the chosen coupon frequency. Effective Annual Yield compounds the periodic rate over one year.
Data Source and Methodology
Authoritative references:
- CFA Institute, Fixed-Income Valuation (2024). Accessible overview: Fixed Income Analysis.
- U.S. Securities and Exchange Commission (SEC), Investor.gov Glossary — “Yield to Maturity” (updated 2023): investor.gov.
All calculations are rigorously based on the formulas and methodology provided by these sources.
The Formula Explained
Price–Yield relationship for a fixed-coupon bond:
$$ P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}} $$
where:
- P = market price (per face value F)
- C = coupon per period = F \cdot \frac{c}{m}
- F = face value (par)
- y = nominal annual yield to maturity (unknown to solve for)
- m = coupon payments per year (1, 2, or 4)
- N = number of coupon periods (approximately round(years × m))
Zero-coupon special case:
$$ y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right) $$
Common approximation for YTM (starting guess):
$$ \text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}} $$
Effective annual yield:
$$ \text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1 $$
Macaulay duration (in years):
$$ D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m} $$
Modified duration:
$$ D_\text{Mod} \;=\; \frac{D_\text{Mac}}{1 + \frac{y}{m}} $$
Formulas presented in LaTeX for clarity.
Glossary of Variables
- Market Price per 100: Bond price quoted per $100 of par (clean price approximation).
- Face Value (F): Principal repaid at maturity.
- Annual Coupon Rate (c): Stated annual coupon percentage.
- Coupon Frequency (m): Number of coupon payments per year (1, 2, 4).
- Years to Maturity (T): Time remaining until final payment; N ≈ round(T × m).
- Coupon per Period (C): F × c / m.
- Yield to Maturity (y): Nominal annual discount rate that equates discounted cash flows to price.
- Effective Annual Yield (EAY): (1 + y/m)^m − 1.
- Current Yield: Annual coupon divided by market price.
- Yield to Call (YTC): Yield assuming redemption at the call date and call price.
- Macaulay Duration: Time-weighted average receipt of cash flows (in years).
- Modified Duration: Macaulay duration adjusted for yield compounding, approximates price sensitivity to small yield changes.
Worked Example
How It Works: A Step-by-Step Example
Suppose a bond with F = 100 trades at P = 95, has c = 5% annual coupon, m = 2 (semiannual), and T = 10 years.
- Periods N = round(10 × 2) = 20. Coupon per period C = 100 × 0.05 / 2 = 2.5.
- Approximate YTM (annual): (5 + (100 − 95)/10) / ((100 + 95)/2) ≈ 0.0579 = 5.79%.
- Solve for y using the price equation: P = Σ 2.5/(1 + y/2)^t + 100/(1 + y/2)^20. Numerical solving refines y to approximately 6.00%.
- Effective Annual Yield: (1 + 0.06/2)^2 − 1 ≈ 6.09%.
- Current Yield: 5 / 95 ≈ 5.26%.
- Duration (computed from discounted cash flows with solved y): Macaulay ≈ 7.92 years, Modified ≈ 7.69 years.
Frequently Asked Questions (FAQ)
What is Yield to Maturity (YTM)?
YTM is the annualized rate of return you earn if you buy a bond at the stated price and hold it until maturity, assuming scheduled coupon payments and reinvestment at the same yield.
How is YTM different from Current Yield?
Current yield only considers coupon income relative to the current price. YTM includes both coupon income and the gain/loss from the price moving toward par by maturity.
Do I need settlement and day-count conventions?
For precise dirty price and accrued interest you do. This calculator targets price–yield relationships using whole coupon periods for authoritative, quick analysis.
Can the yield be negative?
Yes. If prices are sufficiently high relative to coupons and par, the discount rate that equates cash flows to price can be negative. The solver supports such cases.
What does Macaulay vs. Modified Duration tell me?
Macaulay duration is the cash-flow timing measure (in years). Modified duration approximates the percentage price change for a 1 percentage-point change in yield.
What if the bond is callable?
Enter the call price and years to call to compute YTC. Investors often compare YTM vs. YTC and consider the lower of the two (“yield-to-worst”).
Does frequency affect YTM?
Yes. Nominal YTM is quoted on an annual basis but based on the coupon frequency. Effective annual yield converts the periodic compounding into a single annual rate.
Formula (LaTeX) + variables + units
','
P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}}
y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right)
\text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}}
\text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1
D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m}
Price–Yield relationship for a fixed-coupon bond: $ P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}} $ where: - P = market price (per face value F) - C = coupon per period = F \cdot \frac{c}{m} - F = face value (par) - y = nominal annual yield to maturity (unknown to solve for) - m = coupon payments per year (1, 2, or 4) - N = number of coupon periods (approximately round(years × m)) Zero-coupon special case: $ y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right) $ Common approximation for YTM (starting guess): $ \text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}} $ Effective annual yield: $ \text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1 $ Macaulay duration (in years): $ D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m} $ Modified duration: $ D_\text{Mod} \;=\; \frac{D_\text{Mac}}{1 + \frac{y}{m}} $
- No variables provided in audit spec.
- investor.gov — investor.gov · Accessed 2026-01-19
https://www.investor.gov/introduction-investing/investing-basics/glossary/yield-maturity - Finance — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/finance - Fixed Income Analysis — cfainstitute.org · Accessed 2026-01-19
https://www.cfainstitute.org/en/research/foundation/2020/fixed-income-analysis
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.
Full original guide (expanded)
Skip to main contentBond Yield Calculator
This professional Bond Yield Calculator helps investors, analysts, and students compute key bond metrics with precision and accessibility. Enter a bond’s price, coupon, maturity, and payment frequency to instantly obtain Yield to Maturity (YTM), Effective Annual Yield, Current Yield, Yield to Call (optional), and Duration. Built mobile-first and WCAG 2.1 AA compliant.
Interactive Calculator
Results
Tip: Nominal YTM uses the chosen coupon frequency. Effective Annual Yield compounds the periodic rate over one year.
Data Source and Methodology
Authoritative references:
- CFA Institute, Fixed-Income Valuation (2024). Accessible overview: Fixed Income Analysis.
- U.S. Securities and Exchange Commission (SEC), Investor.gov Glossary — “Yield to Maturity” (updated 2023): investor.gov.
All calculations are rigorously based on the formulas and methodology provided by these sources.
The Formula Explained
Price–Yield relationship for a fixed-coupon bond:
$$ P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}} $$
where:
- P = market price (per face value F)
- C = coupon per period = F \cdot \frac{c}{m}
- F = face value (par)
- y = nominal annual yield to maturity (unknown to solve for)
- m = coupon payments per year (1, 2, or 4)
- N = number of coupon periods (approximately round(years × m))
Zero-coupon special case:
$$ y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right) $$
Common approximation for YTM (starting guess):
$$ \text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}} $$
Effective annual yield:
$$ \text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1 $$
Macaulay duration (in years):
$$ D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m} $$
Modified duration:
$$ D_\text{Mod} \;=\; \frac{D_\text{Mac}}{1 + \frac{y}{m}} $$
Formulas presented in LaTeX for clarity.
Glossary of Variables
- Market Price per 100: Bond price quoted per $100 of par (clean price approximation).
- Face Value (F): Principal repaid at maturity.
- Annual Coupon Rate (c): Stated annual coupon percentage.
- Coupon Frequency (m): Number of coupon payments per year (1, 2, 4).
- Years to Maturity (T): Time remaining until final payment; N ≈ round(T × m).
- Coupon per Period (C): F × c / m.
- Yield to Maturity (y): Nominal annual discount rate that equates discounted cash flows to price.
- Effective Annual Yield (EAY): (1 + y/m)^m − 1.
- Current Yield: Annual coupon divided by market price.
- Yield to Call (YTC): Yield assuming redemption at the call date and call price.
- Macaulay Duration: Time-weighted average receipt of cash flows (in years).
- Modified Duration: Macaulay duration adjusted for yield compounding, approximates price sensitivity to small yield changes.
Worked Example
How It Works: A Step-by-Step Example
Suppose a bond with F = 100 trades at P = 95, has c = 5% annual coupon, m = 2 (semiannual), and T = 10 years.
- Periods N = round(10 × 2) = 20. Coupon per period C = 100 × 0.05 / 2 = 2.5.
- Approximate YTM (annual): (5 + (100 − 95)/10) / ((100 + 95)/2) ≈ 0.0579 = 5.79%.
- Solve for y using the price equation: P = Σ 2.5/(1 + y/2)^t + 100/(1 + y/2)^20. Numerical solving refines y to approximately 6.00%.
- Effective Annual Yield: (1 + 0.06/2)^2 − 1 ≈ 6.09%.
- Current Yield: 5 / 95 ≈ 5.26%.
- Duration (computed from discounted cash flows with solved y): Macaulay ≈ 7.92 years, Modified ≈ 7.69 years.
Frequently Asked Questions (FAQ)
What is Yield to Maturity (YTM)?
YTM is the annualized rate of return you earn if you buy a bond at the stated price and hold it until maturity, assuming scheduled coupon payments and reinvestment at the same yield.
How is YTM different from Current Yield?
Current yield only considers coupon income relative to the current price. YTM includes both coupon income and the gain/loss from the price moving toward par by maturity.
Do I need settlement and day-count conventions?
For precise dirty price and accrued interest you do. This calculator targets price–yield relationships using whole coupon periods for authoritative, quick analysis.
Can the yield be negative?
Yes. If prices are sufficiently high relative to coupons and par, the discount rate that equates cash flows to price can be negative. The solver supports such cases.
What does Macaulay vs. Modified Duration tell me?
Macaulay duration is the cash-flow timing measure (in years). Modified duration approximates the percentage price change for a 1 percentage-point change in yield.
What if the bond is callable?
Enter the call price and years to call to compute YTC. Investors often compare YTM vs. YTC and consider the lower of the two (“yield-to-worst”).
Does frequency affect YTM?
Yes. Nominal YTM is quoted on an annual basis but based on the coupon frequency. Effective annual yield converts the periodic compounding into a single annual rate.
Formula (LaTeX) + variables + units
','
P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}}
y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right)
\text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}}
\text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1
D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m}
Price–Yield relationship for a fixed-coupon bond: $ P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}} $ where: - P = market price (per face value F) - C = coupon per period = F \cdot \frac{c}{m} - F = face value (par) - y = nominal annual yield to maturity (unknown to solve for) - m = coupon payments per year (1, 2, or 4) - N = number of coupon periods (approximately round(years × m)) Zero-coupon special case: $ y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right) $ Common approximation for YTM (starting guess): $ \text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}} $ Effective annual yield: $ \text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1 $ Macaulay duration (in years): $ D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m} $ Modified duration: $ D_\text{Mod} \;=\; \frac{D_\text{Mac}}{1 + \frac{y}{m}} $
- No variables provided in audit spec.
- investor.gov — investor.gov · Accessed 2026-01-19
https://www.investor.gov/introduction-investing/investing-basics/glossary/yield-maturity - Finance — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/finance - Fixed Income Analysis — cfainstitute.org · Accessed 2026-01-19
https://www.cfainstitute.org/en/research/foundation/2020/fixed-income-analysis
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.
Bond Yield Calculator
This professional Bond Yield Calculator helps investors, analysts, and students compute key bond metrics with precision and accessibility. Enter a bond’s price, coupon, maturity, and payment frequency to instantly obtain Yield to Maturity (YTM), Effective Annual Yield, Current Yield, Yield to Call (optional), and Duration. Built mobile-first and WCAG 2.1 AA compliant.
Interactive Calculator
Results
Tip: Nominal YTM uses the chosen coupon frequency. Effective Annual Yield compounds the periodic rate over one year.
Data Source and Methodology
Authoritative references:
- CFA Institute, Fixed-Income Valuation (2024). Accessible overview: Fixed Income Analysis.
- U.S. Securities and Exchange Commission (SEC), Investor.gov Glossary — “Yield to Maturity” (updated 2023): investor.gov.
All calculations are rigorously based on the formulas and methodology provided by these sources.
The Formula Explained
Price–Yield relationship for a fixed-coupon bond:
$$ P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}} $$
where:
- P = market price (per face value F)
- C = coupon per period = F \cdot \frac{c}{m}
- F = face value (par)
- y = nominal annual yield to maturity (unknown to solve for)
- m = coupon payments per year (1, 2, or 4)
- N = number of coupon periods (approximately round(years × m))
Zero-coupon special case:
$$ y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right) $$
Common approximation for YTM (starting guess):
$$ \text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}} $$
Effective annual yield:
$$ \text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1 $$
Macaulay duration (in years):
$$ D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m} $$
Modified duration:
$$ D_\text{Mod} \;=\; \frac{D_\text{Mac}}{1 + \frac{y}{m}} $$
Formulas presented in LaTeX for clarity.
Glossary of Variables
- Market Price per 100: Bond price quoted per $100 of par (clean price approximation).
- Face Value (F): Principal repaid at maturity.
- Annual Coupon Rate (c): Stated annual coupon percentage.
- Coupon Frequency (m): Number of coupon payments per year (1, 2, 4).
- Years to Maturity (T): Time remaining until final payment; N ≈ round(T × m).
- Coupon per Period (C): F × c / m.
- Yield to Maturity (y): Nominal annual discount rate that equates discounted cash flows to price.
- Effective Annual Yield (EAY): (1 + y/m)^m − 1.
- Current Yield: Annual coupon divided by market price.
- Yield to Call (YTC): Yield assuming redemption at the call date and call price.
- Macaulay Duration: Time-weighted average receipt of cash flows (in years).
- Modified Duration: Macaulay duration adjusted for yield compounding, approximates price sensitivity to small yield changes.
Worked Example
How It Works: A Step-by-Step Example
Suppose a bond with F = 100 trades at P = 95, has c = 5% annual coupon, m = 2 (semiannual), and T = 10 years.
- Periods N = round(10 × 2) = 20. Coupon per period C = 100 × 0.05 / 2 = 2.5.
- Approximate YTM (annual): (5 + (100 − 95)/10) / ((100 + 95)/2) ≈ 0.0579 = 5.79%.
- Solve for y using the price equation: P = Σ 2.5/(1 + y/2)^t + 100/(1 + y/2)^20. Numerical solving refines y to approximately 6.00%.
- Effective Annual Yield: (1 + 0.06/2)^2 − 1 ≈ 6.09%.
- Current Yield: 5 / 95 ≈ 5.26%.
- Duration (computed from discounted cash flows with solved y): Macaulay ≈ 7.92 years, Modified ≈ 7.69 years.
Frequently Asked Questions (FAQ)
What is Yield to Maturity (YTM)?
YTM is the annualized rate of return you earn if you buy a bond at the stated price and hold it until maturity, assuming scheduled coupon payments and reinvestment at the same yield.
How is YTM different from Current Yield?
Current yield only considers coupon income relative to the current price. YTM includes both coupon income and the gain/loss from the price moving toward par by maturity.
Do I need settlement and day-count conventions?
For precise dirty price and accrued interest you do. This calculator targets price–yield relationships using whole coupon periods for authoritative, quick analysis.
Can the yield be negative?
Yes. If prices are sufficiently high relative to coupons and par, the discount rate that equates cash flows to price can be negative. The solver supports such cases.
What does Macaulay vs. Modified Duration tell me?
Macaulay duration is the cash-flow timing measure (in years). Modified duration approximates the percentage price change for a 1 percentage-point change in yield.
What if the bond is callable?
Enter the call price and years to call to compute YTC. Investors often compare YTM vs. YTC and consider the lower of the two (“yield-to-worst”).
Does frequency affect YTM?
Yes. Nominal YTM is quoted on an annual basis but based on the coupon frequency. Effective annual yield converts the periodic compounding into a single annual rate.
Formula (LaTeX) + variables + units
','
P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}}
y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right)
\text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}}
\text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1
D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m}
Price–Yield relationship for a fixed-coupon bond: $ P \;=\; \sum_{t=1}^{N} \frac{C}{\left(1+\frac{y}{m}\right)^{t}} \;+\; \frac{F}{\left(1+\frac{y}{m}\right)^{N}} $ where: - P = market price (per face value F) - C = coupon per period = F \cdot \frac{c}{m} - F = face value (par) - y = nominal annual yield to maturity (unknown to solve for) - m = coupon payments per year (1, 2, or 4) - N = number of coupon periods (approximately round(years × m)) Zero-coupon special case: $ y \;=\; m \left(\left(\frac{F}{P}\right)^{\tfrac{1}{N}} - 1\right) $ Common approximation for YTM (starting guess): $ \text{YTM} \;\approx\; \frac{C_\text{annual} + \frac{F - P}{T}}{\frac{F + P}{2}} $ Effective annual yield: $ \text{EAY} \;=\; \left(1+\frac{y}{m}\right)^m - 1 $ Macaulay duration (in years): $ D_\text{Mac} \;=\; \frac{1}{P}\sum_{t=1}^{N} \frac{t \cdot \text{CF}_t}{\left(1+r\right)^{t}} \cdot \frac{1}{m}, \quad r=\frac{y}{m} $ Modified duration: $ D_\text{Mod} \;=\; \frac{D_\text{Mac}}{1 + \frac{y}{m}} $
- No variables provided in audit spec.
- investor.gov — investor.gov · Accessed 2026-01-19
https://www.investor.gov/introduction-investing/investing-basics/glossary/yield-maturity - Finance — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/finance - Fixed Income Analysis — cfainstitute.org · Accessed 2026-01-19
https://www.cfainstitute.org/en/research/foundation/2020/fixed-income-analysis
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.