Understanding your bond price result
| Relationship | Result | Why |
|---|---|---|
| Yield to maturity > coupon rate | Price below face value (discount) | Fixed coupon pays less than the market currently requires, so the bond sells for less |
| Yield to maturity = coupon rate | Price equals face value (par) | The fixed coupon exactly matches the market's required return |
| Yield to maturity < coupon rate | Price above face value (premium) | Fixed coupon pays more than the market currently requires, so the bond sells for more |
- This calculator prices a bond using semiannual coupon compounding, the U.S. market-standard convention; bonds that pay annually or on another schedule would price slightly differently.
- It assumes the bond is priced exactly at a coupon date with no accrued interest; in practice, bonds trading between coupon dates also have an accrued-interest component added to the quoted 'clean' price.
- This is a mathematical pricing model, not a prediction of market price; actual bond prices can also reflect credit risk, liquidity, and call features not modeled here.
What is bond pricing?
A bond's price is the sum of the present values of every coupon payment it will make until maturity, plus the present value of the face (par) value repaid at maturity, all discounted at the bond's yield to maturity. Because most bonds pay coupons semiannually, standard bond pricing splits the annual coupon rate and years to maturity into semiannual periods for this calculation.
When the yield to maturity used for discounting is higher than the bond's own coupon rate, the bond prices below its face value — trading at a discount — because investors require a higher return than the fixed coupon alone provides, so they pay less upfront. When the yield is lower than the coupon rate, the bond prices above face value — a premium — and when the yield equals the coupon rate, the bond prices exactly at par.
Bond prices and yields move inversely: as market yields rise, the present value of a bond's fixed coupon and face value payments falls, and vice versa. This inverse relationship is one of the foundational concepts in fixed-income investing.
How to use this bond calculator
- Enter the face value (par value) — the amount the bond repays at maturity, commonly $1,000 for most corporate and government bonds.
- Enter the annual coupon rate — the fixed percentage of face value paid out each year, typically split into two semiannual payments.
- Enter the years to maturity — the time remaining until the bond repays its face value.
- Enter the yield to maturity (YTM) — the market discount rate used to price the bond, which may differ from the coupon rate.
- Read the bond price, the annual coupon payment in dollars, and whether the bond is trading at a premium, discount, or par relative to face value.
- Example: a $1,000 face-value bond with a 5% annual coupon, 10 years to maturity and a 6% yield to maturity prices at $925.61 — a discount, because the yield exceeds the coupon rate.
The formula behind bond pricing
The bond price sums the present value of each semiannual coupon payment, discounted at half the annual yield to maturity per semiannual period, plus the present value of the face value repaid at maturity. This is the standard present-value model used for fixed-coupon bonds in fixed-income analysis.
Common mistakes
- Confusing the coupon rate with the yield to maturity — the coupon rate is fixed at issuance, while the yield to maturity reflects current market conditions and can differ substantially.
- Forgetting that bond prices and yields move in opposite directions; a rising yield input will always lower the calculated price, not raise it.
- Assuming a bond trading at a discount is a 'bad' bond — a discount simply reflects that its fixed coupon is below the current market yield, not necessarily higher credit risk.
- Overlooking that this model uses semiannual coupon payments, the standard convention, which affects the exact numbers versus an annual-coupon calculation.
- Ignoring accrued interest when comparing this calculator's price to a real bond quote purchased between coupon payment dates.
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Why does a bond's price fall when interest rates rise?
A bond's coupon payments and face value are fixed at issuance, but when market yields rise, investors discount those fixed future payments at a higher rate, which lowers their present value. This inverse relationship between bond prices and yields is one of the most fundamental concepts in fixed-income investing.
What does it mean for a bond to trade at a discount?
A bond trades at a discount when its price is below its face value, which happens when the yield to maturity used to price it is higher than its fixed coupon rate. Investors pay less upfront because the fixed coupon alone provides a lower return than the market currently requires, so the price adjusts downward to compensate.
What does it mean for a bond to trade at a premium?
A bond trades at a premium when its price is above its face value, which happens when its fixed coupon rate exceeds the current market yield to maturity. Investors pay more upfront because the fixed coupon provides a higher return than the market currently requires elsewhere.
Why are bond coupons typically calculated semiannually?
Most U.S. Treasury and corporate bonds pay interest twice a year rather than once, so standard bond pricing divides the annual coupon rate in half and doubles the number of periods to maturity to match that semiannual payment schedule. This calculator follows that market-standard convention.
Does this calculator include accrued interest?
No. This calculator computes the theoretical bond price as of a coupon payment date, without accrued interest. A bond purchased between coupon dates in the real market would typically also include an accrued-interest adjustment added to this 'clean' price to produce the 'dirty' or invoice price.
Kaynaklar
- U.S. Securities and Exchange Commission (SEC), Investor.gov. Bonds — how bond prices, yields and interest rates relate. investor.gov.
- Financial Industry Regulatory Authority (FINRA). Bond basics — understanding fixed-income pricing and yield. finra.org.
- CFA Institute. CFA Program Curriculum — Fixed Income: Bond Pricing and Yield Measures.
- TreasuryDirect (U.S. Department of the Treasury). Understanding Treasury bond pricing and semiannual coupon conventions. treasurydirect.gov.