Please enter any four values into the fields below to calculate the remaining value of a bond. This calculator is for bonds issued or traded on the coupon date.
Use this calculator to value the price of bonds not traded at the coupon date. It provides the dirty price, clean price, accrued interest, and the days since the last coupon payment.
A bond calculator works out what a bond is worth and what it will earn. The first calculator on this page solves the core relationship between a bond's five defining variables - price, face value, yield, time to maturity, and coupon. Enter any four and it returns the fifth. The second calculator handles the more realistic case of a bond bought partway through a coupon period, giving the dirty price, clean price, accrued interest, and days since the last payment.
The reason both are needed is that bond quotes and bond payments are not the same thing. A bond quoted at 97.70 does not cost $97.70 - if you buy it three months into a coupon period, you also owe the seller three months of interest they earned but have not been paid. The second calculator is what turns a quoted price into the amount that actually leaves your account.
A bond is a loan made by an investor to a borrower, typically a corporation or a government. The borrower agrees to pay periodic interest - the coupon - and to return the face value (also called par value or principal) on the maturity date.
The essential terms are:
A bond's price is the present value of everything it will pay you: each future coupon, plus the face value at maturity, each discounted back to today at the market yield.
Price = Σ [ C / (1 + r)t ] + F / (1 + r)n
where C is the coupon payment per period, r is the yield per period, F is the face value, t runs from 1 to n, and n is the total number of periods remaining.
Take the calculator's default: a $100 face value bond with a 5% annual coupon, three years to maturity, and a 6% yield. Each year pays $5, and $100 comes back at the end. Discounting all of that at 6% gives a price of $97.3270.
Notice that the price is below face value. That is the central mechanic of bond pricing, and it follows directly from the arithmetic.
This is the single most important idea in bond investing, and it confuses almost everyone at first. When yields rise, bond prices fall. When yields fall, bond prices rise.
The reason is that a bond's coupon payments are fixed at issue. If you own a bond paying 5% and new bonds start paying 6%, nobody will buy yours at face value - they can get a better deal elsewhere. The only way to make your bond competitive is to sell it at a discount, so the buyer's return over the remaining life works out to 6%. That discount is exactly what the pricing formula computes.
The relationship gives three standard cases:
You can confirm this in the calculator by setting the coupon and yield equal - the price comes out at exactly face value regardless of the maturity.
Yield to maturity (YTM) is the total annualised return you earn if you buy a bond today and hold it until it matures, collecting every coupon along the way. It is the single discount rate that makes the present value of all future payments equal the current price.
YTM cannot be solved algebraically - there is no closed-form rearrangement of the pricing equation for r. Financial calculators and software find it iteratively, trying rates until the computed price matches the actual price. This calculator does the same, which is why entering a price and leaving yield blank returns a figure like 5.9868% rather than a round number.
YTM assumes you hold to maturity and that coupons are reinvested at the same rate. Neither assumption is guaranteed in practice, which is why YTM is best understood as a standardised comparison measure rather than a promise.
Two related measures are worth knowing. Current yield is simply the annual coupon divided by the price - easy to compute but it ignores any gain or loss from buying at a discount or premium. Yield to call applies to callable bonds and computes the return if the issuer redeems the bond at the earliest permitted date rather than at maturity.
Most US corporate and Treasury bonds pay semiannually, but annual, quarterly, and monthly schedules all exist. Frequency matters because money received sooner is worth more.
Using the calculator's defaults and changing only the frequency shows the effect clearly: annual gives $97.3270, semiannual $97.2914, quarterly $97.2731, and monthly $97.2607. The differences are small but real, and they run in the direction you might not expect - more frequent coupons produce a slightly lower price here, because the yield is being compounded more often as well.
Bonds are quoted at the clean price, which excludes interest earned since the last coupon. But the amount you actually pay is the dirty price - also called the invoice price - which adds the accrued interest owed to the seller.
Dirty price = Clean price + Accrued interest
The logic is straightforward. If a bond pays $50 a year and you buy it nine months into the year, the seller held it for those nine months and earned $37.50 of that coupon. But the full $50 will be paid to whoever owns the bond on the payment date - you. So you compensate the seller upfront for their share.
Accrued interest is calculated as:
Accrued interest = Coupon payment × (days since last coupon ÷ days in the coupon period)
Quoting clean prices exists to stop published bond prices from sawtoothing. If bonds were quoted dirty, the price would drift upward through each coupon period and then drop sharply on the payment date - making it look as though the bond had lost value when nothing had actually changed. Clean prices strip that artefact out.
To compute accrued interest you need to count days, and there is more than one way to do it. The convention used is specified in the bond's terms and varies by market and instrument type. This calculator supports the four most common:
The differences are small on any single trade but meaningful at institutional scale. Using the calculator's defaults with a mid-period settlement, 30/360 gives about $2.47 of accrued interest per $100 face while Actual/360 gives about $2.53 - roughly a 2% difference on that component.
Interest rate risk. If market yields rise, the price of an existing bond falls. This matters only if you sell before maturity - hold to maturity and you receive face value regardless. Longer-maturity bonds are far more sensitive, which is what duration measures.
Credit risk. The issuer may fail to pay. Government bonds from stable countries are treated as nearly risk-free; corporate bonds carry real default risk, which is why they yield more. Rating agencies grade this from AAA down to junk status.
Inflation risk. Fixed coupons lose purchasing power as prices rise. A 3% coupon during 5% inflation is a real loss. Inflation-linked bonds such as TIPS address this directly.
Reinvestment risk. YTM assumes coupons are reinvested at the same yield. If rates fall, you reinvest at less, and your realised return falls short of the quoted YTM. Zero-coupon bonds avoid this entirely by making no interim payments.
Liquidity risk. Many bonds trade thinly. Selling before maturity may mean accepting a worse price than the theoretical value.
Call risk. Callable bonds can be redeemed early by the issuer, typically when rates have fallen - exactly when you would least like to give up the bond.
Treasury securities are issued by national governments and are the benchmark for low-risk debt. In the US these run from short-dated bills through notes to 30-year bonds.
Municipal bonds are issued by states and local authorities, often with tax advantages that make their lower headline yields more attractive than they first appear.
Corporate bonds range from investment grade to high yield. They pay more than government debt to compensate for credit risk.
Zero-coupon bonds pay no periodic interest. They are issued at a deep discount and redeem at face value, with the entire return coming from that difference. Set the coupon to zero in the calculator to price one.
Agency and mortgage-backed securities are issued by government-sponsored entities and are backed by pools of loans.
First calculator. Fill in any four of the five fields and leave the one you want blank. Leave price blank to find what a bond is worth at a given yield. Leave yield blank to find the return implied by a market price. You can also solve for face value, time to maturity, or the coupon. The coupon can be entered as a percentage of face value or as a dollar amount using the dropdown.
Second calculator. Enter the bond's terms plus the maturity and settlement dates, then choose the day-count convention specified in the bond's documentation. The settlement date is when the trade actually settles - usually one or two business days after the trade itself, not the trade date.
The second calculator infers the coupon schedule by stepping backwards from the maturity date at the chosen frequency, which is how real bond schedules work: a bond maturing on 17 July with annual coupons pays every 17 July.
Because its coupon rate is lower than the current market yield. Investors will only buy a below-market coupon at a discount deep enough to bring their total return up to the market rate. If the coupon were above the market yield, the bond would trade at a premium instead.
The coupon rate is fixed at issue and never changes - it determines the cash paid. The yield reflects the return based on what you actually pay for the bond, and it moves constantly with the market price. They are equal only when the bond trades exactly at face value.
Because the quoted price is the clean price, and you also owe the seller the interest accrued since the last coupon. The total - the dirty or invoice price - is what settles. The second calculator on this page computes all three figures.
Use the one specified in the bond's terms. As a rough guide: 30/360 for US corporate and municipal bonds, Actual/Actual for US Treasury notes and bonds, and Actual/360 for many money-market instruments. Choosing the wrong one changes only the accrued interest, and usually by a small amount.
Yes - enter 0 for the annual coupon. The price becomes simply the face value discounted back at the yield over the full term, which is why zero-coupon bonds trade at deep discounts and why their prices are especially sensitive to interest rate changes.
You receive the face value regardless of how the price moved in between, plus every coupon along the way. Interim price swings become irrelevant. This is why bonds held to maturity are far less risky than the volatility of their market prices suggests - though credit risk remains, since the issuer must still be able to pay.
Yield to maturity has no closed-form solution, so it is found numerically. This calculator iterates until the computed price matches the entered price to within a fraction of a cent, which is well beyond the precision needed for any practical decision.
Because they answer different questions. The first assumes you are buying on a coupon date, with a whole number of periods remaining. The second handles settlement partway through a period, discounting each cash flow over a fractional number of periods and adding accrued interest. The second is the realistic case for a bond bought on the secondary market.
This Bond Calculator is provided for educational and general informational purposes only and does not constitute investment advice. Results are theoretical values based on the inputs supplied and standard pricing conventions. Actual bond prices are affected by credit quality, liquidity, embedded options such as call provisions, taxes, transaction costs, and market conditions not modelled here. Consult a qualified financial professional before making investment decisions.