Understanding Bonds and Bond Pricing
A bond is a loan you make to a government or company. In exchange, the issuer promises to pay you a fixed interest payment (the coupon) on a set schedule, then return your original investment (the face value, also called par value) when the bond matures. Once a bond is issued, its coupon payments never change — but the bond can still trade hands on the open market before maturity, and that market price moves constantly as interest rates move, even though nothing about the bond itself has changed.
This calculator is for marketable coupon bonds — Treasury notes and bonds, corporate bonds, and municipal bonds that trade at a price set by the market. It is not for U.S. Savings Bonds (EE or I bonds): those are non-marketable, purchased directly from the Treasury at face value, and grow by a fixed formula rather than trading at a fluctuating market price. If that's what you're looking for, TreasuryDirect runs its own official Savings Bond Calculator for that purpose.
How This Calculator Works
A bond's fair price is the present value of everything it will pay you: every coupon between now and maturity, plus the face value you get back at the end. With F as face value, C as the coupon payment per period, y as the market yield per period, and n as the number of periods remaining:
The first term is the present value of every coupon payment; the second is the present value of getting your face value back at maturity. The Bond Price tab computes this directly. The Yield to Maturity tab runs the same formula in reverse: since there's no clean algebraic way to isolate y once a bond has more than one payment left, it tries a yield, checks the price that yield implies, and narrows the guess (the same bisection approach used elsewhere on this site for reverse calculations) until the implied price matches the market price you entered — accurate to a small fraction of a basis point.
What Each Input Means
Face value is the amount the bond pays back at maturity — $1,000 is the standard for most Treasury and corporate bonds, though municipal bonds often use $5,000. Coupon rate is the fixed annual interest rate printed on the bond, applied to face value — it never changes over the bond's life. Market yield (YTM), on the Bond Price tab, is the return currently available on comparable bonds — this is what actually moves day to day and is what the price reacts to. Current market price, on the Yield to Maturity tab, is what you'd actually pay to buy the bond today. Years to maturity is the time remaining until the issuer repays the face value. Payment frequency defaults to semi-annual, the convention for most U.S. Treasury and corporate bonds, though some bonds pay annually or quarterly.
Price vs. Yield: Why They Move in Opposite Directions
This is the single most important relationship in the bond market, and the chart above illustrates it directly: as yield rises, price falls — and as yield falls, price rises. The reason is straightforward once you see it from the buyer's side. A bond's coupon is locked in at issuance. If new bonds start offering a higher yield than your bond's fixed coupon, nobody will pay full face value for your lower-paying bond — its price has to drop until its effective return matches what's newly available elsewhere. The reverse happens when rates fall: your fixed coupon suddenly looks generous compared to new issues, so your bond's price rises above face value to compensate. Notice the curve isn't a straight line — it bends, a property called convexity, meaning price is more sensitive to a given rate move when yields are already low than when they're already high.
Premium, Par, and Discount Bonds
A bond trades at exactly par (price equals face value) only when its coupon rate exactly matches the current market yield — a coincidence, not the norm. When the coupon rate is higher than the market yield, the bond trades at a premium (price above face value), since its above-market coupon is worth paying extra for. When the coupon rate is lower than the market yield, it trades at a discount (price below face value), since buyers need a lower purchase price to make up for the below-market coupon. Either way, holding the bond to maturity converges the two: a premium bond's price gradually falls to face value by maturity, and a discount bond's price gradually rises to face value — which is exactly why yield to maturity, not the coupon rate alone, is the number that captures your true total return.
Current Yield vs. Yield to Maturity
Current yield is the simplest snapshot: annual coupon divided by today's price. It's easy to calculate but incomplete — it ignores the gain (for a discount bond) or loss (for a premium bond) you'll realize when the bond returns exactly its face value at maturity, regardless of what you paid for it. Yield to maturity folds all of that together into one annualized number: every coupon, the timing of each payment, and the eventual return of face value. For a discount bond, YTM is always higher than current yield, since it captures the built-in price appreciation to come. For a premium bond, YTM is always lower than current yield, since it captures the price decline to come. The two are only identical for a bond trading exactly at par.
Accrued Interest, Clean Price, and Dirty Price
Bonds don't only change hands on coupon payment dates — most real-world trades settle somewhere between two coupons. When that happens, the seller has already earned a slice of the next coupon just by holding the bond since the last payment, so the buyer owes the seller that slice on top of the bond's quoted price. That's accrued interest. The clean price is the quoted price you see everywhere (in the news, on a broker's screen) and excludes accrued interest. The dirty price (also called the full or settlement price) is what actually changes hands: clean price plus accrued interest.
Dirty Price = Clean Price + Accrued Interest
How "days since last coupon" and "days in period" are actually counted depends on the day-count convention, which the Accrued Interest tab above lets you choose: 30/360 assumes every month has 30 days and every year 360, the traditional convention for U.S. corporate and municipal bonds. Actual/360 and Actual/365 count real calendar days but divide by a fixed 360- or 365-day assumption, common in money-market-adjacent instruments. Actual/Actual counts real calendar days both since the last coupon and in the current coupon period itself, and is the standard for U.S. Treasury notes and bonds. The four conventions usually land within a few days of each other in the resulting accrued interest — rarely more than about 6 days' worth even in unusual cases — but the exact convention matters for matching a specific bond's official trade confirmation to the penny.
Municipal Bonds and Tax-Equivalent Yield
Municipal bonds ("munis") pay interest that's typically exempt from federal income tax (and often state tax too, if you live in the issuing state), which is why their stated yields usually look lower than a comparable Treasury or corporate bond. To compare them fairly against a taxable bond, use the tax-equivalent yield formula:
For example, a 3% muni yield for someone in the top federal bracket (37% plus the 3.8% Net Investment Income Tax, for a combined 40.8%) works out to a taxable-equivalent yield of roughly 3% ÷ (1 − 0.408) ≈ 5.07% — meaningfully higher than the muni's stated rate once the tax exemption is properly accounted for. This is exactly why high earners often find municipal bonds competitive with, or better than, taxable alternatives even though the sticker yield looks smaller at first glance.
What This Calculator Doesn't Cover
The Accrued Interest tab's coupon schedule is generated by counting back from the maturity date at regular intervals — it doesn't adjust for weekends, holidays, or the odd short/long "stub" first or last coupon period some real bonds have, so double-check against the bond's official schedule for a live trade. This tool also doesn't compute duration or convexity as standalone risk metrics, doesn't model callable or puttable bonds (where the issuer or holder can end the bond early), and doesn't account for credit/default risk — the yields you enter should already reflect the market's view of that specific issuer's creditworthiness. Treat this as a fair-value, yield, and accrued-interest estimate for a standard fixed-rate coupon bond, not a substitute for your broker's official trade confirmation.
Frequently Asked Questions
Why does a bond's price move opposite to interest rates?
A bond's coupon payments are fixed once issued. If market yields rise above that fixed coupon, new bonds look more attractive, so the old bond's price has to fall to offer a comparable return — and vice versa when yields fall.
What's the difference between coupon rate, current yield, and yield to maturity?
The coupon rate is fixed at issuance and based on face value. Current yield divides the annual coupon by the bond's current market price. Yield to maturity (YTM) goes further, factoring in the gain or loss you'll realize if you hold the bond to maturity and get face value back — it's the single most complete measure of a bond's return.
Is this calculator for U.S. Savings Bonds (EE or I bonds)?
No. This calculator prices marketable coupon bonds — Treasury notes/bonds, corporate bonds, and municipal bonds that trade on the market at a price that moves with interest rates. U.S. Savings Bonds (EE and I bonds) work completely differently: they're non-marketable, bought at face value, and grow by a fixed formula rather than trading at a market price. For those, use TreasuryDirect's own Savings Bond Calculator.
Why semi-annual payments by default?
Most bonds, especially U.S. Treasury and corporate bonds, pay interest twice a year — it's the market convention this calculator defaults to, though some bonds do pay annually or quarterly instead, which you can select.
What does it mean if a bond is trading at a premium or a discount?
A bond trades at a premium when its price is above face value, which happens when its coupon rate is higher than the current market yield. It trades at a discount when its price is below face value, when the coupon is lower than the market yield. A bond trades at par, right at face value, only when its coupon rate exactly equals the market yield.
How do I calculate yield to maturity from a bond's price?
There's no clean algebraic formula for YTM when a bond has more than one payment left, so it's solved iteratively: try a yield, compute the price that yield implies, and narrow the guess until the implied price matches the actual market price. The Yield to Maturity tab above does exactly this automatically.
What's the difference between clean price and dirty price?
Clean price is the quoted price you see on a broker's screen or in the news, and it excludes accrued interest. Dirty price (also called the full or settlement price) is clean price plus accrued interest — it's the actual dollar amount that changes hands when you buy a bond between coupon dates. The two are identical only on an actual coupon payment date, when accrued interest is exactly zero.
Which day-count convention should I use?
Use whichever convention actually applies to your bond: 30/360 for most U.S. corporate and municipal bonds, Actual/Actual for U.S. Treasury notes and bonds, and Actual/360 or Actual/365 mainly for money-market-adjacent instruments. If you're not sure, 30/360 is the most common default and rarely differs from the others by more than a few days' worth of accrued interest.
This calculator provides estimates for general informational purposes only and is not financial advice. It assumes a standard fixed-rate coupon bond priced on a coupon date, with no default risk — always confirm the exact price and yield on your broker's official trade confirmation before making an investment decision.