Bond Yield Calculator
Compute Yield to Maturity (YTM), Yield to Call (YTC), current yield, and duration for any US Treasury, corporate, or municipal bond.
Bond Yield Calculator
Compute the three canonical bond yields — Yield to Maturity (YTM), Current Yield, and Yield to Call (YTC) — plus Macaulay + Modified Duration. Standard US Treasury and corporate bond convention (semi-annual coupons, semi-annual compounding).
How to Use the Bond Yield Calculator
Pull bond details from the quote sheet
Face value (USD 1,000 standard), coupon rate (the stated annual rate on the bond), maturity date, and current market price. US Treasury prices are on TreasuryDirect.gov and in the daily Treasury yield-curve table; corporate bond trades are published on FINRA TRACE and municipal trades on the MSRB's EMMA system.
Set the coupon frequency
US Treasury and most US corporate bonds pay semi-annually. Some municipal and foreign bonds pay annually. Quarterly is rare but used in some preferred stocks. This affects the YTM calculation — the default is semi-annual.
Add call provisions if callable
Many corporate and municipal bonds are "callable" — the issuer can redeem early, typically at face + 1-3% premium, after a specific call date. If yields fall, callable bonds get called and you lose the higher-yield bond. YTC tells you the worst-case yield assuming early call.
Read the three yields + duration
Use YTM for held-to-maturity analysis. Use Current Yield as a quick income-vs-price comparison. Use YTC as the "yield to worst" if the bond might be called. Use Modified Duration to estimate price sensitivity to rate changes: a duration of 7 means a 1% rate rise drops price by ~7%.
Bond Yields — The Three Numbers Every Fixed-Income Investor Needs
YTM, Current Yield, and YTC — What Each Tells You
Yield to Maturity (YTM) is the total return you earn if you buy the bond at current price and hold it until maturity, receiving all coupon payments and the face value at the end. It's the single best comparison metric across bonds with different prices, coupons, and maturities. YTM is computed by solving the bond pricing equation backward: at what discount rate does the present value of all future cash flows equal today's price? The answer requires iterative solution (bisection or Newton-Raphson) — this tool does it for you. US Treasury convention assumes semi-annual coupons and semi-annual compounding, so the "annual" YTM shown is 2 × the periodic yield.
Current Yield is the simple ratio of annual coupon to current price (coupon ÷ price). It's useful for quick income comparison but ignores capital gain/loss at maturity. A bond bought at USD 950 (discount to USD 1,000 par) with 4.5% coupon has current yield of 4.74% (45 ÷ 950), but YTM is higher because you also gain USD 50 at maturity. Conversely, a premium bond (price above par) has current yield higher than YTM because of the eventual capital loss back to par.
Yield to Call (YTC) applies to callable bonds — those where the issuer can redeem early, typically at par + 1-3% premium. If the bond is called, you receive the call price plus accumulated coupons up to that date, but lose the higher-yield exposure beyond. YTC computes the yield assuming the call happens at the earliest call date. The "yield to worst" (lower of YTM and YTC) is the conservative number used by most institutional bond analysts.
Duration — The Bond Price Sensitivity Number
Macaulay Duration is the weighted-average time to receive a bond's cash flows, where each cash flow's weight is its present value. A 10-year bond with high coupons might have Macaulay duration of 7-8 years; a zero-coupon 10-year bond has duration exactly equal to maturity (10 years), since all cash flow happens at the end. Macaulay duration intuitively captures "when do I get my money back?"
Modified Duration is the more practically useful number: it estimates the percentage price change for a 1 percentage point change in yield. A modified duration of 7 means a 1% rise in yields drops the bond price by ~7%; a 1% drop in yields raises the price by ~7%. This is the interest-rate-risk measure. Longer-maturity bonds have higher duration; lower-coupon bonds have higher duration (because more of the cash flow is concentrated at maturity). How high duration gets depends on coupon as much as maturity: run a 30-year bond with a 4.5% coupon priced at par and this tool returns a modified duration of about 16.4; the same maturity with a 1.25% coupon at a 4.5% yield returns about 21.6. Reprice the par bond at 6.5% and it falls 26% — the exact figure, which duration alone over-states because it ignores convexity.
The tool's default bond — USD 1,000 face, 4.5% coupon, 10 years, bought at USD 950 — solves to a YTM of 5.15% and a modified duration of 7.90. If yields rise one percentage point the bond loses roughly 7.9% of value, meaningful even on a security with no credit risk.
US Treasury, Corporate, Municipal — The Three Pools
US Treasury bonds are issued by the federal government — the gold standard for credit-free risk. The 10-year Treasury yield is the canonical reference for "risk-free rate" in nearly every financial model. Treasury interest is exempt from state and local income tax under 31 U.S.C. §3124, though federal income tax applies. Buy directly via TreasuryDirect.gov (USD 100 minimum, no commission) or through a brokerage.
Corporate bonds are issued by companies, with credit risk priced into the yield spread over Treasuries. Investment-grade issuers (AAA to BBB) trade at a narrower spread over Treasuries, high-yield issuers (BB and below) at a wider one, and both spreads widen sharply in a recession — look the current spread up on FINRA TRACE rather than carrying a rule of thumb. Corporate bond interest is taxed as ordinary income — important consideration vs Treasury (federal-only) or muni (federal + state-exempt).
Municipal bonds are issued by state and local governments. The headline feature: interest is generally exempt from federal income tax (Internal Revenue Code §103), and usually from state income tax for residents of the issuing state. For an investor in the top federal brackets the tax-equivalent yield — muni yield ÷ (1 − marginal rate) — is what makes the comparison. The trade-off: lower headline yield, a thinner market, and credit quality that varies from state general-obligation debt to single-project revenue bonds.
Semi-annual compounding, the bisection solve, and the day count that separates Treasuries from corporates
YTM formula: solve PV = Σ (coupon/(1+y)^t) + FV/(1+y)^N for y. Requires iterative solution; this tool uses bisection.
US Treasury convention (31 CFR 356 App. B): semi-annual coupons, semi-annual compounding. The quoted 10-year yield is twice the semi-annual periodic yield — the convention this tool uses.
Discount bonds (price below par) have YTM > coupon rate. Premium bonds (price above par) have YTM < coupon rate.
The 10-year US Treasury yield is the canonical "risk-free rate" reference in finance models.
Modified duration estimates price change for a 1% yield move. A duration of 7 means 1pp rate rise drops price ~7%.
Coupon drives duration as much as maturity: a 30-year 4.5% bond at par has modified duration ≈ 16.4 in this tool; a 30-year 1.25% coupon at a 4.5% yield, ≈ 21.6.
US Treasury interest is exempt from state and local tax (31 U.S.C. §3124) but not federal tax. Municipal bond interest is generally exempt from federal tax (IRC §103).
FINRA TRACE publishes corporate bond trades; municipal trades are on the MSRB's EMMA. Both are free to read.
TreasuryDirect.gov sells notes and bonds direct in USD 100 increments with no commission — the Treasury's own retail platform.
Day count: Treasuries accrue Actual/Actual (31 CFR 356 App. B); US corporates and munis conventionally 30/360. This tool prices whole periods and ignores accrued interest.
Frequently Asked Questions
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YTM is the total annualised return you earn if you buy a bond at the current price and hold it until maturity, receiving all coupon payments and the face value at the end. It's the single best comparison metric across bonds. The math: solve for the discount rate y in PV = Σ(coupon/(1+y)^t) + FV/(1+y)^N. Requires iterative solution because the equation can't be rearranged analytically. This tool uses bisection — most financial calculators and Excel's =YIELD() function use Newton-Raphson, faster but more code.
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Current Yield = annual coupon ÷ current price. Simple, but ignores capital gain/loss at maturity. A bond bought at USD 950 (discount) with 4.5% coupon has Current Yield of 4.74% but YTM higher than that because you also gain USD 50 at maturity. A bond bought at USD 1,050 (premium) with 4.5% coupon has Current Yield 4.29% but YTM LOWER than that because you lose USD 50 at maturity. YTM is the right comparison number; Current Yield is the quick-look income comparison.
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YTC applies to callable bonds — issued securities where the issuer has the option to redeem early, typically at face value + 1-3% premium. Most corporate and municipal bonds are callable; US Treasury bonds are not. If interest rates fall after issuance, callable issuers redeem to refinance at lower rates, leaving holders to reinvest at lower yields. YTC computes the yield assuming the bond is called at the earliest call date. The "yield to worst" — lower of YTM and YTC — is the conservative analysis number for callable bonds.
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Modified Duration estimates the percentage price change for a 1 percentage point change in yields. A bond with modified duration of 7 will lose roughly 7% if rates rise 1pp, and gain 7% if rates fall 1pp. Long-maturity, low-coupon bonds have high duration (a 30-year zero has Macaulay duration of exactly 30). Short-maturity, high-coupon bonds have low duration (a 2-year 5% coupon at par: Macaulay 1.93, modified 1.88 in this tool). The higher the coupon and the yield, the further duration falls below maturity — a 30-year 4.5% bond at par sits at about 16.4, barely half its maturity.
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Because the coupon is fixed at issuance. If you buy a 10-year bond paying 4% coupon and then 10-year yields rise to 6%, your bond's 4% coupon is suddenly worth less — new bonds yielding 6% are more attractive. The market re-prices your 4% bond down so its new buyer earns 6% equivalent yield. Conversely, if yields fall to 2%, your 4% bond is more valuable and prices up. This inverse relationship is mathematical — embedded in the bond pricing equation. The size of the price move depends on duration: longer-duration bonds move more for the same rate change.
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Bond ETFs (BND, AGG, TLT, IEF, MUB) offer diversification and liquidity but with constant-duration mechanics — they're rebalanced to maintain target duration, which means you never "get back to par" the way you do with an individual bond held to maturity. Individual bonds give you predictable cash flows and a guaranteed return-to-par at maturity (assuming no default). For most retail investors, low-cost bond ETFs are the easier choice. For investors wanting to ladder maturities (specific income years), individual bonds make sense. For US Treasury exposure specifically, TreasuryDirect.gov is the lowest-friction option.
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Depends on your tax bracket. Municipal bond interest is exempt from federal income tax (and from state income tax for in-state residents in many states). For a US investor in the 32% federal bracket, a 4% muni yield is equivalent to a 5.88% taxable bond yield (4% ÷ 0.68). For someone in the 12% bracket, the same 4% muni is equivalent to 4.55% taxable — much smaller premium. Munis are most attractive for high-income US investors in high-tax states (California, NY, NJ); less attractive for low-bracket investors and not relevant for non-US tax residents.
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TreasuryDirect.gov — the US Treasury's direct retail platform. No commissions, USD 100 minimum (per security), Treasury bills, notes, bonds, TIPS, and I-Bonds all available. Limit USD 10K per person per year for I-Bonds; no limit for marketable Treasuries. Alternative: most US brokerages offer Treasury access at auction and in the secondary market, which is more convenient if you may sell before maturity — TreasuryDirect holdings must be transferred to a broker to be sold. Some brokers also offer automatic reinvestment of maturing Treasury bills.
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The arithmetic is identical — enter the bond's own coupon frequency — but the yields differ for reasons that have nothing to do with the formula: currency, expected inflation, credit rating and central-bank policy. Singapore Government Securities have at times yielded below US Treasuries despite Singapore's AAA rating, Hong Kong Government Bonds track US yields because of the currency peg, and Japanese government bond yields moved up after the Bank of Japan ended its yield-curve-control framework in March 2024. Look each curve up on the issuer's debt-management site before comparing. For investors with local-currency liabilities, a home-country sovereign can make sense as currency-matched income even at a lower yield.
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US Treasury for US-based investing — same currency as your income and expenses, no FX conversion, interest exempt from state and local tax (though not federal tax), and TreasuryDirect.gov makes direct purchase simple. Singapore Government Securities add SGD/USD currency exposure that a US-resident investor is not paid to take. If you have specific SGD-denominated future needs (planning to return to Singapore for retirement, sending children to Singapore schools), partial allocation to SGS bonds via DBS, OCBC, or Endowus offers currency-matched income. Most ASEAN expats settling long-term in the US consolidate to US Treasury + corporate bonds, with smaller home-country positions only for currency hedging.
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Method & sources
How it computes
Solves yield to maturity by bisection on the bond price identity P = Σ C/(1+y/n)^t + F/(1+y/n)^N with n coupons a year (default 2, the US Treasury convention in 31 CFR 356 Appendix B), reports current yield = annual coupon ÷ price and yield to call by re-solving with the call price and years to call, then computes Macaulay duration as the PV-weighted average time to cash flow and modified duration = Macaulay/(1+y/n).
What this tool implements
- Semi-annual coupons and semi-annual compounding by default (31 CFR 356 Appendix B); annual and quarterly selectable
- Yield to maturity solved by bisection to USD 0.001 of price; quoted annual yield = n × periodic yield (bond-equivalent, not effective annual)
- Clean price on a coupon date: whole periods only, no accrued interest, no settlement-date day count
- Yield to call re-solves the same identity to the earliest call date at the call price; 'yield to worst' is the lower of YTM and YTC
Sources
- 31 CFR Part 356, Appendix B — Formulas for Determining Prices, Yields and Accrued Interest on Treasury Notes and Bonds. https://www.govinfo.gov/content/pkg/CFR-2024-title31-vol2/pdf/CFR…
- 31 U.S.C. §3124 — Exemption from taxation: obligations of the United States are exempt from state and local taxation except estate or inheritance taxes. https://www.law.cornell.edu/uscode/text/31/3124
- Fabozzi FJ. Bond Markets, Analysis, and Strategies. 10th ed. MIT Press; 2021.
- TreasuryDirect. Treasury Notes — interest paid every six months; minimum purchase USD 100. https://www.treasurydirect.gov/marketable-securities/treasury-notes/
What can make this go out of date
- None at runtime — every price, coupon and date is user-entered
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