Bond Yield Calculator

YTM is the total return anticipated on a bond if it is held until maturity. It accounts for the coupon payments, the time value of money, and any premium or discount to face value. Unlike current yield (which only looks at coupon income), YTM provides a comprehensive measure of expected return.

YTM cannot be solved algebraically — it requires iterative numerical methods. This calculator uses Newton-Raphson iteration with a bisection fallback, converging to 10 decimal places of precision.

Macaulay Duration measures the weighted average time until a bond's cash flows are received. A bond with 7-year Macaulay duration behaves, in price sensitivity terms, like a zero-coupon bond maturing in 7 years.

Modified Duration estimates the percentage price change for a 1% (100 bps) change in yield. A modified duration of 6.5 means the bond price drops approximately 6.5% if yields rise by 100 basis points.

Convexity captures the curvature in the price-yield relationship. For large yield changes, duration alone understates price increases and overstates price decreases. Convexity corrects this asymmetry.

When a bond trades above par (market price > face value), it is a premium bond. This happens when the coupon rate exceeds prevailing market yields. Conversely, a discount bond trades below par when market yields exceed the coupon rate.

For premium bonds, YTM is less than the coupon rate. For discount bonds, YTM exceeds the coupon rate. At par, YTM equals the coupon rate exactly.