Bond Calculator

A bond's price and its yield move in opposite directions — when interest rates rise, existing bond prices fall. Understanding this relationship, and knowing how to calculate a bond's fair value from its yield (or vice versa), is foundational to fixed-income investing. The bond calculator computes price, YTM, duration, and modified duration for any bond — the tools professional fixed-income investors use daily.

Bond Pricing Formula

A bond's fair price is the present value of all future cash flows discounted at the required yield:

P = Σ [C / (1+r)ᵗ] + F / (1+r)ⁿ

where C = periodic coupon payment, r = periodic required yield (YTM/periods per year), F = face value, n = total periods to maturity, t = period number (1 to n).

Example: 10-year, 5% coupon bond with face value $1,000, required yield 6%:

P = Σ [25 / (1.03)ᵗ, t=1 to 20] + 1,000 / (1.03)²⁰ = $925.61

The bond trades at a discount because the coupon rate (5%) is below the market yield (6%). Use this online calculator for your specific bond. The compound interest calculator and APR calculator provide complementary fixed-income tools.

Bond Yield Measures Explained

• Current yield: Annual coupon ÷ Current price. Simple but ignores capital gain/loss at maturity.
• Yield to maturity (YTM): The single discount rate that makes the present value of all cash flows equal to the current price. The most complete measure of bond return — accounts for coupons, capital gain/loss, and time to maturity.
• Yield to call (YTC): For callable bonds — YTM calculated assuming the bond is called at the next call date at the call price.
• Yield to worst (YTW): The lowest of YTM, all YTC values, and yield to put — the conservative measure used by institutional investors.

Duration and Interest Rate Risk

Duration measures how sensitive a bond's price is to interest rate changes. Modified duration = Macaulay duration / (1 + YTM/periods). Price sensitivity: ΔP/P ≈ −Modified Duration × Δy. A bond with modified duration 7 years will lose approximately 7% of its price if yields rise by 1%. Longer maturity and lower coupon bonds have higher duration — and higher interest rate risk. Convexity captures the curvature in the price-yield relationship; positive convexity means bonds gain more when yields fall than they lose when yields rise by the same amount — a favorable asymmetry. The investment calculators cover the complete fixed-income toolkit.

Premium, Discount, and Par Bonds

When the required yield equals the coupon rate: bond trades at par (face value). When required yield exceeds coupon rate: bond trades at a discount (below face value). When required yield is below coupon rate: bond trades at a premium (above face value). The pull-to-par effect: as maturity approaches, a discount bond's price rises toward face value; a premium bond's price falls toward face value — regardless of yield changes. This predictable price movement is called "accretion of discount" or "amortization of premium."