--- title: "Bond Yield to Maturity Calculator (YTM) | Coupon Beacon" description: "Find a bond's yield to maturity and yield to call from its price, coupon and dates, with clean and dirty price and accrued interest explained." url: https://couponbeacon.bond/ --- # Bond yield to maturity calculator Enter a bond's price, coupon and time to maturity to find its yield to maturity, and its yield to call if the issuer can redeem it early. Clean price, dirty price and accrued interest are worked out alongside. ## How the yield is found Yield to maturity is the one annual rate that makes the present value of every remaining coupon, plus the face value at maturity, equal to the price paid. There is no direct formula for it, so the calculator brackets the answer and closes in with Newton steps until the price matches. Dirty price = Σ C ÷ (1 + y/f)^t + 100 ÷ (1 + y/f)^TC = coupon per period per 100 of face, f = coupons a year, t = periods until each coupon, T = periods until maturity. ### Clean price, dirty price and accrued interest Bonds are quoted at a clean price. Between coupon dates the seller has already earned part of the next coupon, the accrued interest, so the buyer pays the dirty price: clean price plus accrued interest. Choose "By dates" to count the days: actual/actual, as U.S. Treasuries do, or 30/360, which MSRB Rule G-33 sets for municipal securities. ### Yield to call For a callable bond the same solve runs to the call date, with the call price in place of face value; the lower of the two yields is the yield to worst. Example: 10 years left, a 4.5% semiannual coupon, price 96.25. Twenty coupons of 2.25 and the final 100, discounted at 4.981% a year (2.490% per half-year), come back to 96.25. ## Sources - U.S. Treasury, [31 CFR Part 356, Appendix B](https://www.ecfr.gov/current/title-31/subtitle-B/chapter-II/subchapter-A/part-356/appendix-Appendix%20B%20to%20Part%20356), sections I and II: accrued interest on actual days in the half-year, and the formulas for converting yields to prices. The calculator's "U.S. Treasury formula" option reproduces its worked examples (for instance 99.057893 and 99.730918) to six decimals. - Municipal Securities Rulemaking Board, [Rule G-33, Calculations](https://www.msrb.org/Rules-and-Interpretations/MSRB-Rules/General/Rule-G-33): the 30/360 day count and the price and yield formulas behind the street convention. - Investor.gov (U.S. Securities and Exchange Commission), glossary: [accrued interest](https://www.investor.gov/introduction-investing/investing-basics/glossary/accrued-interest) and [callable or redeemable bonds](https://www.investor.gov/introduction-investing/investing-basics/glossary/callable-or-redeemable-bonds). - Microsoft Support, [YIELD function](https://support.microsoft.com/en-us/office/yield-function-f5f5ca43-c4bd-434f-8bd2-ed3c9727a4fe): its worked example (price 95.04287 gives 6.5%) is one of the cases this calculator is tested against. ## More bond calculators Prices, yields, bills and payment dates, each with its formula shown. 1. [Bond price calculator From a yield to the clean and dirty price, with duration, convexity and a price–yield curve.](https://couponbeacon.bond/bond-price-calculator/) 2. [Current yield calculator A year's coupons divided by the price, compared with yield to maturity.](https://couponbeacon.bond/current-yield-calculator/) 3. [T-bill yield calculator Discount yield, investment rate and money market yield of a Treasury bill.](https://couponbeacon.bond/t-bill-yield-calculator/) 4. [Coupon payment schedule Every remaining payment date and amount to maturity, ready to download as CSV.](https://couponbeacon.bond/coupon-payment-schedule/) ## Recommended Two free services for the online side of researching bonds. Disposable email · no sign-up ### CleanTempMail Rate newsletters, webinar sign-ups and research downloads usually want an email address first. CleanTempMail gives you a free temporary inbox straight away, with no sign-up, a random or custom address on hundreds of domains, and messages deleted automatically after 3 days. Read what you came for and keep your main inbox for your own accounts. [Open a temporary inbox](https://cleantempmail.com/) Disposable cloud browser · free domain lookups ### WebTraceCheck Sent a link to an investment site you have never heard of, or an unsolicited bond offer that sounds too good? WebTraceCheck's free DNS and domain lookup shows the details behind a site's domain, and its disposable cloud browser opens unfamiliar links on an isolated desktop that is deleted after each session. Nothing to install, with free time every day. [Look up a site with WebTraceCheck](https://webtracecheck.com/) ## Questions **Why is the yield higher than the coupon rate?** The bond costs less than face value, and the gain when it repays at par counts on top of the coupons. Above face value it works the other way round. **What is the difference between the street convention and the Treasury formula?** Only how the part period up to the next coupon is discounted: the street convention compounds it, the Treasury formula uses simple interest. The yields usually differ in the third decimal place. **Does yield to maturity tell me what I will earn?** Only under its assumptions: you hold to maturity, every payment arrives in full and on time, and each coupon is reinvested at the same yield. Selling early, a default or a call changes the result. It compares bonds; it does not forecast. **Which date is the settlement date?** The day the bond changes hands, shown on the trade confirmation. It can fall after the trade date, and accrued interest is counted up to it.