Bond Calculator

The first calculator handles a fixed-rate coupon bond on a coupon date: fill in every value except the one you want, and it solves for the rest. The second prices the same kind of bond on any date between coupons, which is how most trades actually settle, using the day-count convention you choose. Neither accounts for credit risk, call features, taxes or liquidity, all of which affect real market prices.

What is a bond?

A bond is a loan packaged as a security. The investor lends money to an issuer, such as the US Treasury, a city, or a corporation, and in return receives regular interest payments and the return of the loan amount on a set date. Unlike stockholders, bondholders do not own part of the issuer; they are creditors, and in a bankruptcy they are paid before shareholders.

Governments issue bonds to fund budgets and public works, and companies issue them to finance expansion or refinance debt without giving up ownership. Investors buy them for predictable income, for diversification against stocks, and for safety when the issuer is highly creditworthy. Once issued, most bonds trade in the secondary market, where their prices rise and fall with interest rates and with the market's view of the issuer's ability to pay.

Bond structure

Every plain fixed-rate bond is described by a handful of terms set when it is issued:

• Face value (par): the amount repaid at maturity and the base for coupon payments. US Treasury and corporate bonds are commonly issued in $1,000 or $100 units, and prices are quoted per $100 of face.
• Coupon rate: the annual interest rate on face value. A 5% coupon on $1,000 pays $50 a year, often as two $25 payments.
• Coupon frequency: how often interest is paid. US Treasuries and most US corporate bonds pay semiannually; many European bonds pay annually.
• Maturity date: when the face value is repaid and the bond ends. Bills mature within a year, notes in two to ten years, and bonds in up to 30 years.
• Issuer and credit rating: who owes the money, and agencies' assessment of default risk. Bonds rated BBB−/Baa3 or higher are investment grade; lower-rated bonds are called high-yield.
• Yield to maturity: the annual return an investor earns by buying at today's price and holding to maturity, assuming every payment is made. It moves with the market, while the coupon is fixed.
• Special features: some bonds can be called (repaid early) by the issuer, converted into stock, or have coupons that float with a benchmark rate. The calculators on this page assume none of these.

How to calculate the bond price?

A bond's fair price is the present value of the cash it will pay: each coupon and the final face value, discounted at the market yield. Because the yield sits in the denominator, price and yield move in opposite directions. When market rates rise above a bond's coupon, buyers will only pay less than face value; when rates fall below it, the bond sells at a premium.

Take the default example: a 3-year bond with $100 face value, a 5% annual coupon and a 6% market yield. The three cash flows are $5, $5 and $105. Discounted at 6%, they are worth $4.7170, $4.4500 and $88.1600, for a price of $97.3270. At a 4% yield the same bond would cost $102.7751, and at exactly 5% it would trade at $100.

Price = Σ (C ÷ f) ÷ (1 + y/f)ᵏ + F ÷ (1 + y/f)ᴺ

C

annual coupon in dollars

f

coupon payments per year

y

yield to maturity, annual, as a decimal

F

face value repaid at maturity

N

number of coupon payments left; the sum runs from k = 1 to N

Between coupon dates each exponent is reduced by the fraction of the current period that has already passed. That gives the dirty price; subtracting accrued interest gives the clean price.

Clean price and dirty price

Coupons are paid on fixed dates, but bonds trade every business day. When a bond changes hands between coupon dates, the seller has earned part of the next coupon by holding the bond, yet the buyer will receive the whole payment. To settle fairly, the buyer pays the seller the interest that has built up since the last coupon, called accrued interest.

The dirty price (also called the full or invoice price) is what the buyer actually pays: the present value of all remaining cash flows on the settlement date. The clean price is the dirty price minus accrued interest. Markets quote clean prices because they move only with yields and credit, while dirty prices also climb steadily between coupons and drop by the coupon amount on each payment date, producing a sawtooth pattern.

Accrued interest = coupon per period × days since the last coupon ÷ days in the coupon period. How days are counted depends on the market convention:

• 30/360: every month counts as 30 days and the year as 360. Common for US corporate, agency and municipal bonds.
• Actual/Actual: actual calendar days in the numerator and in the coupon period. Used for US Treasury notes and bonds.
• Actual/360: actual days elapsed over a 360-day year. Common in money markets and floating-rate loans.
• Actual/365: actual days over a fixed 365-day year. Used in some UK and other markets.

Frequently asked questions

Sources

• Investor.gov – Introduction to Investing
• TreasuryDirect – Treasury Notes
• FINRA – Investor Insights