2026-09-22 7 min read

YTM Calculator

The yield to maturity implied by the market price for a bond. Live calculator with worked steps, charts and formulas.

Calculator

Market Price Help

What the bond costs today (clean price).

Face (Par) Value Help

Principal repaid at maturity, usually $1,000.

Annual Coupon Rate(%) Help

Interest paid on face value each year.

Years to Maturity(years)

years

Coupon Frequency

This bond calculators calculator runs on standard bond mathematics: coupons and face value discounted at the market yield with 2 payment(s) per year. Money is calculated at full precision and rounded only for display.

Results

Optimal

Yield to Maturity

5.66%

Total return if held to maturity with coupons reinvested at this rate.

Current Yield

5.26%

Discount / Premium

$50

Discount bond

Annual Coupon Income

$50

Periods to Maturity

Live results update as you type — currently showing yield to maturity of 5.66%. Replace the defaults with your own quote for an exact comparison.

Visualizations

Income vs Principal

Annual coupons5%

Face at maturity95%

Yield vs Typical Investment-Grade Range

5.7%

012

Formula

The YTM is the internal rate of return of the bond cash flows: the discount rate equating price to present value.

Solve P = Σ C/(1+r)ⁱ + Face/(1+r)ⁿ for r

Alternative Form

APY = (1+r)^m − 1

Variables

Symbol	Name	Unit	Description
P	Bond price (clean)	currency	Present value of coupons plus face at the market yield
C	Coupon per period	currency	Face × coupon ÷ frequency
r	Periodic yield	decimal	Annual YTM ÷ payments per year
n	Periods to maturity	count	Years × payments per year

Explanation

The market discount rate implied by the price — the comparable return across bonds.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Write the pricing equation with the yield as the unknown.

Price = Σ Coupon/(1+r)ⁱ + Face/(1+r)ⁿ

Price:$950

Face:$1,000

Result: One unknown: periodic rate r

Step 2

Solve iteratively (bisection) until the model price matches the market price.

Iterate r until model price = market price

Intermediate: Converged at r = 2.8308% per period

Result: YTM = 5.662%

Step 3

Cross-check with current yield (coupon ÷ price).

Current yield = Annual coupon ÷ Price

Annual coupon:$50

Result: 5.26%

Final Answer

5.66%

Worked Examples

See how the calculator works with different scenarios.

Scenario

The ytm calculator run on the values above, showing the full calculation path rather than only the answer.

Inputs

Market Price:950

Face (Par) Value:1000

Annual Coupon Rate:5

Years to Maturity:10

Calculation

1. Write the pricing equation with the yield as the unknown. → One unknown: periodic rate r 2. Solve iteratively (bisection) until the model price matches the market price. → YTM = 5.662% 3. Cross-check with current yield (coupon ÷ price). → 5.26%

Result

Yield to Maturity: 5.66%

Interpretation

YTM 5.662% (2.8308% per period); current yield 5.26%.

Understanding Your Result

Your Result: Yield to Maturity: 5.66%

What This Means

The market discount rate implied by the price — the comparable return across bonds.

Why It Matters

YTM 5.662% (2.8308% per period); current yield 5.26%.

Professional Interpretation

YTM 5.662% (2.8308% per period); current yield 5.26%.

How this is calculated

The YTM is the internal rate of return of the bond cash flows: the discount rate equating price to present value.

What drives the result

Price and yield move in opposite directions. When market yields rise, the fixed coupons are worth less in present value and the price falls; when yields fall, the price rises. The coupon sets income, the yield sets value, and the difference between price and par (premium or discount) converges to zero at maturity.

Recommendations

•YTM assumes coupons reinvest at the YTM — treat it as a comparison rate, not a guarantee.
•Higher YTM usually means higher credit or rate risk; check the rating.

Educational Content

Introduction

A bond is a contract: fixed coupons plus a face value at maturity. Its market price is the present value of those promised cash flows discounted at the market yield. Every figure on this page — price, yield, premium, accrued interest — comes from that single discounting relationship.

Concept Explanation

Applications

▸Pricing a bond before buying or selling in the secondary market

▸Comparing two bonds with different coupons on yield, not coupon alone

▸Splitting clean (quoted) and dirty (settlement) prices between coupon dates

▸Measuring total return including coupons plus price change

Benefits

•Locks valuation to one consistent present-value model
•Separates income (coupons) from price gain or loss
•Makes premium and discount bonds directly comparable
•Produces worked steps you can check against a dealer quote

Limitations

•Assumes a flat yield for every period rather than a full yield curve
•Ignores credit risk, taxes and liquidity premiums unless entered
•Reinvestment at the YTM is assumed, which markets rarely guarantee
•Callable and convertible features need their own modes

Best Practices

•Compare yield to maturity, never coupon rates, across bonds
•Add accrued interest for any settlement between coupon dates
•Confirm frequency: semiannual means half the annual rate each half-year
•Reinvest coupons to approach the quoted yield

Common Misconceptions

Myth: A higher coupon means a cheaper bond

Truth: Higher coupons usually trade at a premium above par. Price is set by the yield relative to the coupon, not by the coupon alone.

Myth: The quoted price is what you pay

Truth: Between coupon dates you pay the dirty price — clean plus accrued interest owed to the seller.

Practical Tips

•Annualize the periodic rate by frequency for the quoted YTM.
•Check after-tax YTM for taxable accounts.

Common Mistakes

Ignoring pull-to-par

Deep discounts add capital gain that current yield misses entirely.

Assumptions

This calculator makes the following assumptions to provide estimates:

Held to maturity: Selling early realizes the market price, not the YTM.

Limitations

Be aware of these limitations when using this calculator:

Limitation: Assumes a flat yield for every period rather than a full yield curve

Limitation: Ignores credit risk, taxes and liquidity premiums unless entered

Limitation: Reinvestment at the YTM is assumed, which markets rarely guarantee

Limitation: Callable and convertible features need their own modes

Frequently Asked Questions

Answers to common questions about this calculator.

Current yield vs YTM — which matters?

Current yield measures income; YTM measures total return including pull-to-par. Use YTM to choose between bonds.

Who uses the ytm calculator?

It is used by investors comparing bond options, by advisers checking a quote before a client commits, and by planners sizing contributions for a goal. It sits in the Bond Calculators group of the Bonds & Fixed Income section of Atlascalcs.

How accurate is the ytm calculator?

Every figure follows directly from the inputs using standard bond mathematics, so it is accurate to the quality of the values you enter. Dealer quotes round to cents and apply day-count conventions, so expect pennies of difference on accrued interest and settlement figures.

How current are the yields used here?

The calculator uses the figures you enter, so update the yield to your dealer quote or auction result. Market yields move intraday; ratio and tax thresholds follow the conventions in the references.

Does rounding change the results?

All math runs at full precision and rounds only for display. Dealers round to cents and apply day-count conventions, so expect pennies of difference on accrued interest.

Should I compare coupons or yields?

Always yields (YTM for total return, current yield for income). Two bonds with different coupons price identically at the same YTM.

What should I have ready before buying?

Face, coupon, maturity, frequency, price or yield, settlement date, tax bracket and any call or conversion terms. With those, every figure here ties to a quote.

Related Calculators

Explore more calculators related to this topic.

Related Guides

Deepen your understanding with these educational resources.

Understanding bond pricing and yield to maturity

Coupons, discounting, and why price moves opposite the yield.

Building a bond ladder

Stagger maturities to collect income and reduce rate risk.

Tax implications of bond income

How Treasury, municipal, and corporate bond interest are taxed.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Yield to Maturity: Total return holding to maturity with coupons reinvested at that rate.
Current Yield: Annual coupon divided by market price; ignores maturity gain or loss.
Premium / Discount: Amount price sits above (premium) or below (discount) par.
Par (Face) Value: Principal repaid at maturity, usually $1,000 per bond.

Authoritative References

Trusted sources and standards referenced by this calculator.

SEC — Investor.gov: Bonds TreasuryDirect — U.S. Government Bonds TreasuryDirect — TIPS FINRA — Learn About Bonds SIFMA — U.S. Fixed Income Research Federal Reserve — Treasury yields (H.15)

Applicable Standards

Present-value pricing with periodic compounding at the quoted yieldYTM solved numerically (bisection) to full precision; display rounded onlyT-Bill bank discount on 360 days; investment yield on 365 daysMoney rounded for display only; all calculations run at full precision

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Page Information

Last Updated:

2026-09-22

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.