Bond Price & Yield Calculator

Bond Pricing & YTM — Educational Guide

Summary (voice-friendly): A bond’s price is the present value of all future coupons plus the face value, discounted by the yield per period. YTM is the annualized rate that makes those discounted cash flows equal today’s price.

What is a bond?

A bond is a loan to a borrower (issuer). The investor receives periodic interest payments (coupons) and the face value at maturity. Prices move inversely with yields: when yields rise, present values fall, so prices drop (and vice versa).

Clean price vs dirty price: formula and example

Clean price excludes accrued interest; dirty price adds accrued interest between coupon dates. Formula: dirty price = clean price + accrued interest. Example: if a bond is quoted at a clean price of $980.00 and accrued interest is $12.50, the dirty price is $992.50.

How to calculate accrued interest on a bond

Accrued interest estimates the coupon earned between the last coupon date and settlement date. A simplified formula is accrued interest = coupon per period x accrual fraction. The accrual fraction depends on the day-count convention, such as 30/360, Actual/Actual, Actual/360, or Actual/365.

Current yield vs yield to maturity

Current yield is annual coupon income divided by current clean price. Yield to maturity is the discount rate that makes all coupon and principal cash flows equal the bond price. Current yield is simpler; YTM is more complete because it includes redemption at maturity and premium or discount amortization.

Yield to maturity vs yield to call

YTM assumes the bond remains outstanding until maturity. Yield to call assumes the issuer redeems the bond on a call date at the call price. Callable bonds are often compared using yield to worst, the lowest yield across maturity and callable redemption dates.

Coupon frequency & yield conventions

• Frequency: annual, semi-annual, quarterly, or monthly. The discount rate per period is \( r_p = y / f \), where \( y \) is annualized YTM and \( f \) is payments per year.
• Quoted vs. effective yield: Many markets quote a nominal annual yield (APR) with a compounding frequency. Effective annual yield is \( (1 + y/f)^f - 1 \).

Bond price formula (clean price)

Worked examples

Premium bond vs discount bond examples

A bond is usually priced at a premium when its coupon rate is above the market yield. For example, a 6% coupon bond priced with a 4% YTM will generally trade above par. A bond is usually priced at a discount when its coupon rate is below the market yield; a 4% coupon bond priced with a 6% YTM will generally trade below par.

Zero-coupon bond pricing example

A zero-coupon bond has no periodic coupon payments. Its clean price is the present value of the face value: P = F / (1 + y/f)^n. For example, a $1,000 zero-coupon bond due in 5 years at a 5% annual yield is priced below $1,000 because the return comes from discount accretion.

Bond price sensitivity: duration and convexity example

Modified duration estimates the percentage price change for a 1 percentage point yield move. If modified duration is 7, a 1% yield rise implies roughly a 7% price fall before convexity adjustment. Convexity improves that estimate because the price/yield relationship is curved rather than linear.

Which day-count convention should I use?

Use the convention specified by the bond market, issuer documentation, or broker quote. Corporate bonds often use 30/360 conventions, while many government bond calculations use actual-day conventions. This calculator offers common conventions for educational estimates, but exact settlement pricing can depend on market-specific rules.

Worked example

Face \( F = \$1{,}000 \), coupon rate \( 5\% \) (so \( C = \$50 \) per year), semi-annual coupons (\( f=2 \Rightarrow C/f = \$25 \) per period), maturity \( T = 10 \) years (\( n = 20 \) periods), YTM \( y = 6\% \Rightarrow r_p = 0.06/2 = 0.03 \).

Coupon PV \( = 25 \times \frac{1 - (1+0.03)^{-20}}{0.03} \approx \$372.45 \).
Face PV \( = 1000 \times (1+0.03)^{-20} \approx \$553.68 \).
Price \( P \approx \$926.13 \) (discount bond since YTM > coupon rate).

Duration & convexity (intuition)

• Macaulay duration (years): cash-flow weighted average time; a measure of timing.
• Modified duration: approximate % price change for a 1% change in yield.
• Convexity: curvature; improves the accuracy of duration-based price change estimates for larger yield moves.

Common mistakes

• Confusing coupon rate (%) with coupon amount ($). Use the toggle to select your input style.
• Using annual yield but forgetting to divide by frequency for the per-period discount rate.
• Comparing clean prices to dirty prices without adjusting for accrued interest.

Methodology, assumptions, and limitations

The YTM and yield-to-call calculations use a numerical bisection solver because yield generally has no simple closed-form solution. Cash flows are simplified to regular coupon periods. Professional pricing may require exact settlement calendars, holidays, ex-coupon rules, callable schedules, odd first or last coupon periods, embedded options, credit spread models, and market quotation conventions.

Disclaimer

This calculator is for education and estimation only and is not financial advice. Verify pricing, yield, accrued interest, suitability, and tax treatment with a qualified professional or official market source before making investment decisions.

Sources and further reading

• FINRA: Understanding Bond Yield and Return
• Investor.gov: Current Yield
• TreasuryDirect: Buying a Treasury Marketable Security

FAQ

Why does bond price fall when yield rises?

Higher yields increase the discount rate, which lowers the present value of future cash flows—so price falls.

Is YTM the same as total return?

YTM equals the internal rate of return if you hold to maturity and reinvest coupons at the same yield. Realized return may differ if you sell early or reinvest at different rates.

What affects duration?

Longer maturities and lower coupons generally increase duration (more rate sensitivity). Higher coupons and shorter maturities reduce it.

Glossary

• Face (Par): Principal repaid at maturity.
• Coupon: Interest paid to investors (rate % × face, or $ amount per year).
• YTM: Annualized discount rate equating price to PV of cash flows.
• Duration / Convexity: First/second-order measures of price sensitivity to yield changes.

Note: This page simplifies calendars and accrual. Professional workflows may require day-count conventions, holiday calendars, settlement lags, and callable/putable features.