What is Bond Price?
Bond price is the present value of all future cash flows from a bond, which includes periodic coupon payments and the return of face value at maturity. The price is calculated by discounting these future cash flows at the current market yield rate (YTM). When market rates rise above the bond's coupon rate, the bond trades at a discount. When rates fall below the coupon rate, the bond trades at a premium.
This calculator helps you determine what you should pay for a bond given your required yield. Understanding bond pricing is essential for fixed-income investors to ensure they don't overpay when yields are rising or miss opportunities when yields fall. The inverse relationship between bond prices and yields is fundamental to fixed-income investing.
Examples
Example 1 - Discount Bond: Face: $1,000, Coupon: 4%, YTM: 6%, Years: 10. Price: ~$852. Trading at discount because coupon < market yield. Investor pays less to achieve higher effective yield.
Example 2 - Premium Bond: Face: $1,000, Coupon: 7%, YTM: 5%, Years: 8. Price: ~$1,130. Trading at premium because coupon > market yield. Investor pays more for higher income stream.
Example 3 - Par Bond: Face: $1,000, Coupon: 5%, YTM: 5%, Years: 5. Price: $1,000. Trading at face value because coupon rate equals market yield exactly.
Frequently Asked Questions
What is the bond pricing formula?
Bond Price = Σ [Coupon / (1 + YTM)^t] + [Face Value / (1 + YTM)^n]. This calculates the present value of all future cash flows. The sum of present values of all coupon payments plus the present value of face value redemption equals the bond's fair price. Each coupon is discounted by the yield rate for its time period.
Why do bond prices fall when interest rates rise?
Existing bonds with fixed coupons become less attractive when new bonds offer higher rates. To compete, existing bonds must drop in price so their yield matches the market. Mathematically, higher discount rates (YTM) reduce present value of future cash flows. This inverse relationship is fundamental: when yields rise, prices fall, and vice versa.
What are premium and discount bonds?
Premium bonds trade above face value (coupon > market yield), offering higher current income but capital loss at maturity. Discount bonds trade below face value (coupon < market yield), offering price appreciation potential plus coupons. Par bonds trade at face value (coupon = market yield). Neither premium nor discount is inherently better - they reflect different income/capital gain trade-offs.
How does time to maturity affect bond price?
Longer maturities mean greater price sensitivity to rate changes. A 30-year bond's price changes more dramatically than a 2-year bond for the same yield shift. This is because: 1) More coupon payments are affected by discounting, 2) Face value is discounted over longer periods, 3) Rate changes compound over more periods. Long-term bonds offer higher yields but with greater volatility.
What is accrued interest?
Accrued interest is the interest earned since the last coupon payment but not yet paid. When buying a bond between coupon dates, you pay the seller accrued interest. At the next coupon date, you receive the full coupon payment. Clean price excludes accrued interest; dirty price includes it. The actual transaction uses dirty price.
What is a zero-coupon bond?
Zero-coupon bonds pay no periodic interest. They're purchased at deep discounts to face value and redeemed at full face value at maturity. The difference represents implied interest. Price = Face Value / (1 + YTM)^n. Zeros have no reinvestment risk (no coupons to reinvest) but higher duration and tax on phantom income annually in many jurisdictions.
How do I know if a bond is priced fairly?
Compare the calculated theoretical price (from this calculator) with the market price. If market price < calculated price, the bond may be undervalued. Also compare yields to similar bonds with same credit rating and maturity. Check recent trade prices using TRACE or Bloomberg data. Consider bid-ask spreads - wide spreads may indicate illiquidity rather than mispricing.