Bond Pricing & YTM
Calculate bond price, yield to maturity, Macaulay duration, and convexity for any fixed-coupon bond. Supports semi-annual and annual coupons — useful for fixed income analysis.
Price
$1,039.91
YTM
4.5000%
Macaulay duration
8.0356 yr
Modified duration
7.8587
Convexity
74.5506
How to use the bond pricing & ytm
Pick whether you have YTM (and want price) or vice versa. Enter face value, coupon rate, years to maturity, and coupon frequency. Duration (Macaulay & modified) and convexity are computed for the resulting yield.
Formula & explanation
Price = Σ (C / (1 + y/f)^t) + F / (1 + y/f)^N where N = years × frequency. Modified duration ≈ Macaulay / (1 + y/f). Convexity ≈ Σ t(t+1) × cf_t / (price × (1+y)^2 × f²).
Examples
1,000 face, 5% coupon (semi-annual), 10 years to maturity, 4.5% YTM → price ≈ 1,039.96.
Frequently asked questions
- Why does the price drop when yields rise?
- Future cash flows are discounted at a higher rate, so present value is lower. Modified duration estimates the percent price change for a 1% yield move.
- What's convexity used for?
- It's the second-order correction to duration's linear approximation. Higher convexity = more curvature, generally desirable for bondholders.
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