Bond Calculator - Calculate Bond Price, Yield, Duration, and Convexity
Bond Parameters
Enter bond parameters and click Calculate
Understanding Bond Valuation and Investment
What You Will Learn
- ✓ How bond pricing works and the present value formula
- ✓ The difference between coupon rate and yield to maturity
- ✓ Understanding duration and convexity for risk management
- ✓ Clean price vs dirty price and accrued interest
- ✓ Bond investment strategies and portfolio construction
- ✓ How to compare multiple bond investments
What is a Bond?
A bond is a fixed-income security that represents a loan made by an investor to a borrower, typically corporations or governments. When you purchase a bond, you are lending money to the issuer in exchange for regular interest payments (called coupons) and the return of your principal at maturity. Bonds are considered one of the fundamental building blocks of a diversified investment portfolio, offering predictable income streams and generally lower volatility compared to stocks.
The bond market is actually larger than the stock market, with over $100 trillion in outstanding bonds worldwide. Bonds play a crucial role in financing government operations, infrastructure projects, and corporate expansion. For investors, bonds provide portfolio stability, regular income, and capital preservation. Understanding how to value bonds and assess their risks is essential for making informed investment decisions, whether you are building a retirement portfolio, seeking steady income, or diversifying away from equities.
Key Bond Features:
✓ Face Value (Par Value)
Principal amount repaid at maturity, typically $1,000
✓ Coupon Rate
Fixed interest rate paid periodically to bondholders
✓ Maturity Date
Date when principal is repaid, ranging from months to 30+ years
✓ Yield to Maturity
Total return if bond is held until maturity
How Bond Pricing Works
Bond prices are determined by calculating the present value of all future cash flows (coupon payments and principal repayment) discounted at the current market yield. The fundamental pricing formula is: Price = Sum of [Coupon / (1+yield)^period] + [Face Value / (1+yield)^n]. This inverse relationship between price and yield is crucial: when market interest rates rise, bond prices fall, and vice versa.
For example, consider a $1,000 face value corporate bond with a 5% annual coupon, 10 years to maturity, paying semiannually. If the market yield (YTM) is 6%, the bond has 20 payment periods (10 years × 2) with $25 coupon payments ($1,000 × 5% / 2). Discounting each $25 payment and the final $1,000 principal at 3% per period (6% / 2) gives a bond price of approximately $925. The bond trades at a discount because the market demands a 6% return but the coupon only pays 5%.
Duration and Interest Rate Risk
Duration is one of the most important bond metrics, measuring both the weighted average time until cash flows are received and the bond's price sensitivity to interest rate changes. Modified duration tells you approximately how much a bond's price will change for a 1% change in yield. For example, a bond with 7-year modified duration will decrease in price by about 7% if interest rates rise 1%, or increase 7% if rates fall 1%.
Duration is affected by maturity (longer = higher duration), coupon rate (lower coupon = higher duration), and yield level (lower yield = higher duration). Zero-coupon bonds have duration equal to their maturity since all cash flow comes at the end. Our calculator computes both Macaulay duration (weighted average time) and modified duration (price sensitivity), helping you assess and manage interest rate risk in your portfolio.
Convexity: Refining Duration Estimates
While duration provides a linear approximation of price changes, the actual price-yield relationship is curved. Convexity measures this curvature and refines duration estimates, especially for large yield changes. Positive convexity (typical for standard bonds) means bond prices rise more when yields fall than they decline when yields rise by the same amount—an advantageous asymmetry for investors.
Bonds with higher convexity provide better upside potential and downside protection, making them more valuable. Factors that increase convexity include lower coupon rates, longer maturities, and lower yields. Professional bond investors are willing to pay a premium for bonds with higher convexity. Our calculator computes convexity and displays the curved price-yield relationship graphically, helping you visualize this important property.
Scenario Comparison Feature
Our calculator's most powerful feature lets you save multiple bond calculations and compare them side-by-side. This is invaluable when choosing between different bond investments or building a diversified fixed-income portfolio. Calculate each potential bond investment, save it with a descriptive name (e.g., "Corp 10Y 5.5%", "Treasury 5Y 4.2%"), then click compare to view:
- Side-by-side comparison of price, YTM, duration, convexity, and total returns
- Visual charts showing relative pricing and risk metrics
- Overlaid price-yield curves revealing relative interest rate sensitivity
- Cash flow timelines for each bond
This comparison view helps you identify which bonds offer the best combination of yield and risk for your specific objectives—whether you are seeking maximum income, lowest duration, highest after-tax returns, or optimal risk-adjusted performance.
Key Resources for Bond Investors:
- TreasuryDirect.gov - Buy U.S. Treasury bonds directly
- FINRA - Bond price transparency and education
- Bloomberg - Real-time bond market data
Frequently Asked Questions
How do I calculate the price of a bond?
Bond price is calculated as the present value of all future cash flows discounted at the yield to maturity. The formula sums the present value of each coupon payment plus the present value of the principal repayment. Our calculator automates this complex process and provides detailed results including duration, convexity, and risk metrics. You simply enter the face value, coupon rate, years to maturity, and yield to maturity to get comprehensive bond valuation.
What is yield to maturity and how is it different from coupon rate?
Yield to Maturity (YTM) is the total return you will receive if you hold a bond until maturity, accounting for all coupon payments and the difference between purchase price and face value. The coupon rate is simply the annual interest rate stated on the bond, which determines the periodic interest payments. If you buy a bond at a discount (below face value), your YTM will be higher than the coupon rate because you also gain from the price appreciation to par at maturity.
What is bond duration and why is it important?
Bond duration measures a bond's price sensitivity to interest rate changes and represents the weighted average time until cash flows are received. Modified duration tells you the approximate percentage price change for a 1% change in yield. For example, a bond with 7-year modified duration will decrease in price by about 7% if interest rates rise 1%. Duration is crucial for managing interest rate risk in portfolios. Our calculator computes both Macaulay and modified duration to help you assess risk.
What is convexity and how does it affect bond pricing?
Convexity measures the curvature of the price-yield relationship. While duration assumes a linear relationship, convexity captures the actual curve. Positive convexity means bond prices rise more when yields fall than they decline when yields rise by the same amount. This provides better upside potential and downside protection. Higher convexity is more valuable to investors. Bonds with lower coupons, longer maturities, and lower yields typically have higher convexity.
What is the difference between clean price and dirty price?
Clean price is the quoted market price excluding accrued interest, while dirty price includes accrued interest and represents the actual amount you pay when purchasing a bond. Bonds accrue interest daily between coupon payment dates. When you buy a bond between payment dates, you must compensate the seller for interest earned since the last payment. Clean price is used for trading quotes to avoid daily fluctuations, while dirty price reflects true economic value for settlement.
How can I use this calculator to compare different bonds?
Our calculator features a powerful scenario comparison tool. First, calculate each bond's metrics and click Save as Scenario with a descriptive name. Repeat for up to 4 different bonds. Then click on the bond cards you want to compare and click Compare Scenarios to view side-by-side metrics including price, YTM, duration, convexity, risk levels, and total returns. The comparison includes visual charts and overlaid price-yield curves to help you make data-driven investment decisions.