What is the difference between clean price and dirty price?

The clean price is the quoted market price of the bond excluding interest accrued since the last coupon. The dirty price (invoice price) is what the buyer actually pays: clean price plus accrued interest, compensating the seller for holding the bond part-way through the coupon period. Dirty = clean + accrued, always.

Is the yield here yield to maturity or current yield?

The solver's yield is the yield to maturity — the discount rate that makes the present value of all remaining coupons plus face value equal the price. The results also show the current yield (annual coupon ÷ price) for comparison; the two are equal only when the bond trades exactly at par.

Why does day-count convention matter?

Accrued interest depends on how days are counted. 30/360 pretends every month has 30 days (U.S. corporate and municipal bonds); Actual/360 and Actual/365 count real days over a fixed year; Actual/Actual (U.S. Treasuries) counts real days over the real period. The differences are small — at most a few days of interest — but they decide real money on large trades.

Why is the price below face value when yield exceeds the coupon rate?

Because the bond's fixed coupons are worth less than what new money can earn. The market discounts the price until the bond's total return — coupons plus the pull back to face value at maturity — matches the required yield. Coupon above yield produces the mirror image: a premium price above par.

Bond Calculator

Enter any four values and solve for the fifth — for a bond issued or traded on a coupon date. The yield is the yield to maturity. (Trades between coupon dates? Use the second calculator below.)

Solve for

Price

Face Value

Yield (to maturity)

Time to Maturity

years

Annual Coupon

Coupon Frequency

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Bond Pricing Calculator — Between Coupon Dates

Most bonds trade between coupon dates, so the buyer owes the seller interest accrued since the last coupon. This calculator gives the dirty price (what changes hands), the clean price (the quoted price), the accrued interest, and the accrued days under your chosen day-count convention.

Face Value

Yield (to maturity)

Annual Coupon

Coupon Frequency

Maturity Date

Settlement Date

Day-count convention:

30/360 (bond basis) Actual/360 Actual/365 Actual/Actual

Bonds, From the Ground Up

A bond is a loan dressed as a security: an investor lends money to a borrower — usually a government or a company — which promises fixed interest payments and the principal back at the end. Issuers raise funds without selling ownership; investors get a contract instead of a hope. Types track the borrower: government bonds, municipal bonds, corporate bonds, and high-yield ("junk") bonds for shakier borrowers. Against stocks, bonds are the lower-risk shelf — but "bond" spans U.S. Treasuries (about as safe as lending gets) to junk paper whose yield is high precisely because repayment isn't certain. Both calculators on this page handle fixed-rate coupon bonds, the majority of the market; neither models credit quality, supply and demand, call features or other real-world price movers.

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The anatomy of a bond

Face value (par): what the issuer repays at maturity — and the base every coupon is computed on.

Maturity date: when the principal comes due. Terms run from under a year to 30+ years; "time to maturity" is whatever is left.

Coupon rate: the fixed annual interest rate on face value, typically paid annually or semiannually (floating and zero-coupon variants exist; these tools assume fixed).

Coupon frequency: how often interest is paid — annual, semiannual, quarterly, monthly.

Yield: the return if held to maturity — in these calculators, the yield to maturity: the single discount rate that equates the price to all remaining cash flows. (The related current yield, annual coupon ÷ price, ignores the pull to par; both appear in the results.)

Price: what the bond trades for — the present value of its coupons plus face, bent by credit risk, duration and the current rate environment.

Around that core sit the issuer's identity, call and put options, credit ratings, covenants and liquidity — all live influences on real prices that no closed-form calculator captures.

Pricing a bond

Price = C × [1 − (1+r)^−N] / r + F × (1+r)^−N

where C is the coupon per period, N the number of periods to maturity, r the yield per period, and F the face value. Every future payment is discounted back at the required yield and summed. Worked example: face $1,000, coupon 5% paid semiannually, 10 years to maturity, required yield 6%. Then C = $25, N = 20, r = 3% per period — and the price comes to $925.61. Below par, exactly as expected: the market demands 6%, the bond pays 5%, so the price falls until the discount itself supplies the missing return. Flip the numbers (coupon above yield) and the price rises above par by the same logic.

Clean price, dirty price, accrued interest

The first calculator assumes trades happen on coupon dates. Real trades don't. Between coupons, interest accrues daily to whoever holds the bond — so a mid-period buyer compensates the seller for the days the seller held it. That slice is the accrued interest: coupon per period × (days since last coupon ÷ days in the period, under the bond's day-count rule). Markets quote the clean price — the bond's value excluding accrued interest — because it compares cleanly across bonds and dates. But the check the buyer writes is the dirty price (invoice price):

Dirty price = Clean price + Accrued interest

At the defaults of the second calculator — settling three days after an annual coupon — accrued interest is just $0.0417 on a $100 bond, moving the dirty price to $97.3743 against a clean $97.3326. Small numbers, real money at institutional size.

Day-count conventions

30/360 (bond basis): every month counts 30 days, the year 360. Standardizes the calendar so accrued interest is hand-computable; the U.S. convention for corporate, agency and municipal bonds.

Actual/360: real days in the numerator, a 360-day year below. Common in money markets — commercial paper, short-term CDs.

Actual/365: real days over a fixed 365 (leap years usually ignored). Seen in some non-U.S. government bonds and swaps.

Actual/Actual: real days over the real coupon period — the most precise, and the U.S. Treasury convention.

Convention choice moves accrued interest by a little — up to roughly six days' worth in extreme cases — which is why the second calculator lets you switch and compare.

FAQ

Why do bond prices move opposite to interest rates?

The coupons are fixed. When new bonds pay more, an old bond's lower coupons must be compensated by a lower price — and vice versa. The discounting formula above is that mechanism, exactly.

Can this price a zero-coupon bond?

Yes — set the coupon to 0. The price becomes face value discounted over the full term, which is the whole economics of a zero.

What about floating-rate or callable bonds?

Out of scope — their cash flows aren't fixed in advance, so they need spread and option models rather than a closed-form price.

Disclaimer: This calculator provides estimates for educational purposes only and does not constitute financial advice. Bond prices also depend on credit quality, liquidity, tax status and market conditions not modeled here.