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 accrued interest, the full price you pay, and Macaulay and modified duration. Prices and yields follow the US Treasury's own formula (31 CFR 356 Appendix B): yields compounded at the coupon frequency, accrued interest Actual/Actual.
How to Use the Bond Yield Calculator
Pull bond details from the quote sheet
Face value, coupon rate (the stated annual rate on the bond), maturity date, and the current CLEAN price — the quoted price, which excludes accrued interest. 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. Singapore Government Securities are quoted per S$100 of face (MAS).
Set the coupon frequency and the time to maturity
US Treasury notes and bonds pay every six months (TreasuryDirect), and so do Singapore Government Securities bonds (MAS); check any other bond's own terms. The yield is compounded at the same frequency, so the frequency changes the YTM. Give the time to maturity in years — a whole number of coupon periods means you are settling on a coupon date — or switch to dates: the tool then finds the previous and next coupon dates by counting back from maturity and charges accrued interest on the actual days, as the Treasury does.
Add call provisions if callable
Many corporate and municipal bonds are "callable" — the issuer can redeem early, at the call price written into the bond's terms, from a specific call date. If yields fall, callable bonds get called and you lose the higher-yield bond. Enter the first call price and date; the tool computes YTC and the yield to worst, the lower of YTM and YTC. A call is always on a coupon date, so the tool refuses a call date off the coupon cycle.
Read the three yields + duration
Use YTM for held-to-maturity analysis. Use Current Yield as a quick income-vs-price comparison. Use the yield to worst if the bond might be called. Use Modified Duration to estimate price sensitivity: a duration of 7 means a one-point rise in yield drops the price by about 7%. The summary line also reprices the bond exactly at one point higher, so you can see how much duration alone over-states the fall.
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. Between coupon dates the Treasury's formula (31 CFR 356 Appendix B) discounts the stub to the next coupon at simple interest and adds the accrued interest the buyer owes the seller; this tool uses that formula, and reproduces the Appendix's own worked examples to the six decimals it prints.
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 at a call price set in the bond's terms. If the bond is called, you receive the call price plus the coupons up to that date, but lose the higher-yield exposure beyond. YTC computes the yield assuming the call happens at the first call date. The "yield to worst" — the lower of YTM and YTC — is the conservative number to compare callable bonds on.
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. Repriced one percentage point higher it loses 7.54% of its value: duration alone says 7.90%, and the difference is convexity. 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. Treasury yields are the usual stand-in for the "risk-free rate" in financial models. Treasury interest is exempt from state and local taxation under 31 U.S.C. §3124, though federal income tax applies. Buy at auction through TreasuryDirect.gov (USD 100 minimum, in USD 100 steps) or through a bank or broker; to sell before maturity you must go through a bank, broker or dealer (TreasuryDirect).
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 Treasury's price formula, and the accrued interest a buyer owes
YTM formula: solve (P + A)·[1 + w·y/f] = c + c·aₙ + F·vⁿ for y — the Treasury's form of PV = Σ coupon/(1+y/f)^t + F/(1+y/f)^N. No closed form; this tool bisects to 10−12.
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.
Accrued interest: between coupons the buyer pays the seller the coupon earned so far, A = c × days since the last coupon ÷ days in the period. The quoted (clean) price excludes it; the full price includes it.
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 at auction in USD 100 increments — the Treasury's own retail platform. Selling before maturity goes through a bank, broker or dealer.
Day count: Treasuries accrue Actual/Actual (31 CFR 356 App. B), and so does this tool. Many US corporate and municipal bonds accrue 30/360 instead; for those the accrued interest here can differ by a day or two of coupon.
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 on a bracket that always contains the answer, to 10−12 — slower than Newton's method in principle, instant in practice, and it cannot fail to converge.
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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, at the call price in the bond's terms. Many corporate and municipal bonds are callable; check the call schedule in the bond's own terms. 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: USD 100 minimum per security, in USD 100 steps, with Treasury bills, notes, bonds, TIPS and I bonds available. Electronic I bonds are limited to USD 10,000 per Social Security number per calendar year; a non-competitive bid for a marketable note is capped at USD 10 million. Most US brokerages also offer Treasuries at auction and in the secondary market, which is more convenient if you may sell before maturity — a TreasuryDirect holding has to be transferred to a bank, broker or dealer to be sold.
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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 bonds pay a fixed coupon every six months and repay S$100 of face at maturity (MAS), so they go into this tool exactly like a Treasury. Japan's curve is a reminder that policy moves yields: the Bank of Japan ended its yield-curve-control framework on 19 March 2024. Look each curve up on the issuer's own 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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Not usefully. A Singapore Savings Bond is not traded, so it has no market price to solve a yield from: MAS describes it as a bond you can redeem in any month without penalty, getting your investment back in full, with interest that steps up the longer you hold it, for up to 10 years. MAS sets each issue's coupons so that the average annual compounded return over a holding period is linked to the yield of the SGS of that tenor — that average return, published with each issue, is the number to compare. Singapore Government Securities BONDS are different — tradable, fixed semi-annual coupon, S$100 face — and this tool prices them like any other bond.
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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), part of the money in SGS bonds offers currency-matched income; MAS lists the routes on its SGS page, including the secondary market at DBS, OCBC or UOB branches or on SGX through a securities broker. Most ASEAN expats settling long-term in the US consolidate to US Treasury + corporate bonds, with smaller home-country positions only for currency hedging.
Method & sources
How it computes
YTM by bisection (to 1e-12) on the 31 CFR 356 Appendix B price formula generalised to f coupons a year: (P + A)·[1 + w·y/f] = c + c·aₙ + F·vⁿ, w the fraction of the current period still to run, A = (1 − w)·c accrued Actual/Actual. Current yield = annual coupon ÷ clean price; YTC re-solves to the first call at the call price; duration is the exact derivative of the same price (BondKernel.analyseYield).
What this tool implements
- Semi-annual coupons and compounding by default, the US Treasury convention of 31 CFR 356 Appendix B (and the frequency of Singapore Government Securities bonds, per MAS); annual, quarterly and monthly selectable. The quoted yield is nominal annual, compounded at the coupon frequency (2 × the semi-annual periodic yield).
- Accrued interest Actual/Actual: in dates mode, r = days from settlement to the next coupon and s = days in the coupon period, with coupon dates counted back from maturity in steps of 12 ÷ f months (a month-end maturity keeps month-end coupons); in years mode w = r/s is the fractional part of years × f. The price entered is the clean (quoted) price; the full price adds A. 30/360 bonds are not modelled, so their accrued interest can differ by a day or two of coupon.
- Between coupons the stub to the next coupon is discounted at simple interest, [1 + w·y/f], as the Appendix does; a compounded stub, (1 + y/f)^w, agrees exactly on a coupon date and differs in the fourth or fifth significant figure between them.
- Reproduces the Appendix's worked examples to the six decimals it prints: §II.A 8¾% 30-year bond at 8.84% → 99.057893; §II.D 9½% note settling 29 Nov 1985, due 15 Nov 1995, at 9.54% → clean 99.730918, accrued .367403.
- Yield to call re-solves to the first call date at the call price; a call must fall on a coupon date before maturity. Yield to worst is the lower of YTM and YTC (first call only). Coupons are counted in whole cents and the total is count × coupon.
- Modified duration −(1/P)·dP/dy and convexity (1/P)·d²P/dy² are exact derivatives of the same price function; Macaulay = modified × (1 + y/f). On a coupon date these equal the PV-weighted average time and Σ CF·t(t+1)/(1+y/f)^(t+2)/(P·f²).
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. https://www.law.cornell.edu/uscode/text/31/3124
- 26 U.S.C. §103 — Interest on State and local bonds: gross income does not include interest on any State or local bond. https://www.law.cornell.edu/uscode/text/26/103
- TreasuryDirect. Treasury Notes — interest every six months; minimum purchase USD 100 in USD 100 increments; USD 10 million non-competitive maximum. https://www.treasurydirect.gov/marketable-securities/treasury-notes/
- TreasuryDirect. Selling a Treasury marketable security — through a bank, broker or dealer; a TreasuryDirect holding is transferred first. https://www.treasurydirect.gov/marketable-securities/selling-mark…
- TreasuryDirect. I bonds — up to USD 10,000 in electronic I bonds per Social Security number per calendar year. https://www.treasurydirect.gov/savings-bonds/i-bonds/
- Monetary Authority of Singapore. SGS Bonds: information for individuals — fixed semi-annual coupon, S$100 face at maturity, traded at DBS, OCBC or UOB branches or on SGX. https://www.mas.gov.sg/bonds-and-bills/singapore-government-bonds…
- Monetary Authority of Singapore. Singapore Savings Bonds — redeemable in any month without penalty; coupons set so the average annual compounded return is linked to the SGS yield of the same tenor. https://www.mas.gov.sg/bonds-and-bills/singapore-savings-bonds
What can make this go out of date
- None at runtime — every price, coupon and date is user-entered; the default settlement date in dates mode is today's Singapore date.
Abridged — the full review record for this tool runs longer than the list above.
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