Compute the fair value of a bond given its coupon rate, yield to maturity, and years to maturity. See whether a bond trades at par, discount, or premium with a full step-by-step pricing breakdown.
A $1,000 bond with a 5% coupon and 6% YTM maturing in 10 years with semi-annual payments.
Coupon Payment: $1,000 ร 5% รท 2 = $25 every 6 months
Bond Price: $925.61 (trading at a discount)
Price per $100: $92.56
Since the coupon rate (5%) is lower than the YTM (6%), the bond trades below its face value.
A $1,000 bond with an 8% coupon and 6% YTM maturing in 10 years with semi-annual payments.
Coupon Payment: $1,000 ร 8% รท 2 = $40 every 6 months
Bond Price: $1,148.77 (trading at a premium)
Price per $100: $114.88
The higher coupon attracts investors, pushing the bond's price above its face value.
A $1,000 bond with a 5% coupon and 5% YTM maturing in 10 years with annual payments.
Bond Price: $1,000.00 (trading at par)
Price per $100: $100.00
When coupon rate equals YTM, the bond's fair value equals its face value.
A $1,000 bond with a 4% coupon and 5% YTM maturing in 2 years with semi-annual payments.
Bond Price: $981.42 (trading at a discount)
Current Yield: 4.08%
Short-term bonds are less sensitive to YTM changes. The discount is smaller than for long-term bonds.
Bond pricing determines the fair value of a fixed-income security by discounting all future cash flows โ coupon payments and principal repayment โ back to the present using the yield to maturity (YTM) as the discount rate. The relationship between coupon rate and YTM determines whether a bond trades at par, a discount, or a premium.
Bond prices and yields move in opposite directions. When interest rates rise, bond prices fall, and vice versa. A 1% increase in YTM reduces a 10-year, 5% coupon bond's price by roughly 7-8%.
As a bond approaches its maturity date, its price converges toward its face value. Premium bonds gradually decline toward par, while discount bonds rise toward par.
When coupon rate > YTM โ premium bond; coupon rate < YTM โ discount bond; coupon rate = YTM โ par bond. The size of the premium or discount depends on the magnitude and timing of the difference.
Bond markets quote prices per $100 of face value (e.g., 98.25 means $982.50 for a $1,000 bond). This standardization makes it easy to compare bonds with different face values.
Bond pricing is the process of determining the fair value of a fixed-income security. A bond's price equals the present value of all its future cash flows โ the periodic coupon payments plus the repayment of face value at maturity โ discounted at the yield to maturity (YTM). The YTM reflects the total return an investor can expect if they hold the bond until maturity, assuming all payments are made on time.
As of 2026, the U.S. Treasury 10-year yield sits around 4.2-4.5% โ significantly higher than the near-zero rates seen in the early 2020s. This environment means bonds issued with lower coupons during the low-rate era are now trading at substantial discounts. Conversely, bonds issued more recently with coupons near current market rates trade closer to par.
Individual bond investors use this calculator when evaluating whether a bond is trading at a fair price in the secondary market. For example, if you see a 10-year corporate bond with a 5% coupon being offered, but current yields for similar bonds are 6%, this calculator tells you the bond's fair value is approximately $925 per $1,000 face โ meaning the bond is trading at a discount and the seller's asking price should reflect that.
Investment-grade corporate bonds typically yield 0.8-1.5% more than Treasuries of the same maturity โ this difference is called the credit spread. High-yield ("junk") corporate bonds yield 3-5% over Treasuries. Higher spreads compensate investors for greater default risk, and they directly impact a bond's price: a larger spread means a higher discount rate and a lower bond price.
Different bond types offer different yields based on their risk profiles. The table below compares typical yields and credit spreads relative to benchmark U.S. Treasuries as of 2026.
| Bond Type | Typical Coupon Range | Spread vs. Treasury | Key Feature |
|---|---|---|---|
| U.S. Treasury | 4.0โ4.5% | Benchmark (0%) | Risk-free rate; no credit default risk |
| Municipal (Tax-Exempt) | 3.5โ4.2% | 0.1โ0.3% lower than taxable equivalent | Interest exempt from federal tax; tax-equivalent yield typically higher |
| Investment-Grade Corporate | 4.8โ6.0% | 0.8โ1.5% | BBB-rated or higher; moderate default risk |
| High-Yield Corporate | 7.0โ9.5% | 3โ5% | BB-rated or lower; significant default risk premium |
Note: A municipal bond's tax-equivalent yield = Tax-Exempt Yield รท (1 โ Tax Rate). For an investor in the 32% tax bracket, a 3.8% muni yield is equivalent to a 5.59% taxable yield.
The inverse relationship between bond prices and yields is a fundamental concept in fixed-income investing. When market interest rates rise, newly issued bonds offer higher coupon rates, making existing bonds with lower coupons less attractive. As a result, the prices of existing bonds fall until their yields match the new market rates.
The magnitude of the price change depends on the bond's duration. A 1 percentage point rise in YTM for a 10-year, 5% coupon bond lowers its price by roughly 7-8%. This sensitivity increases with longer maturities and lower coupons. For example, a 30-year bond will experience a much larger price drop from the same rate increase than a 2-year bond.
Understanding this relationship is crucial for bond investors. If you expect interest rates to rise, you may prefer shorter-duration bonds (less price sensitivity) or floating-rate notes. If you expect rates to fall, longer-duration bonds capture more price appreciation. This calculator helps you quantify exactly how much a bond's price changes given the current YTM.
Treasury bonds are quoted per $100 of face value (e.g., 98.25 means $982.50 for a $1,000 bond). This standardization allows investors to quickly compare bonds with different face values. Our calculator includes this normalized output so you can cross-reference prices against market quotes.
โ ๏ธ Important Note: Bond pricing estimates are for educational purposes only. Actual trades include accrued interest, bid-ask spreads, commissions, and market liquidity factors that affect the final transaction price. This calculator does not account for accrued interest between coupon dates, call provisions, put features, or other embedded options. Results should not be considered investment advice. Always consult a qualified financial advisor before making investment decisions.