Bond
Bond Duration Calculator
Maturity is not duration: compare recovery timing and rate sensitivity.
Coupon-date valuation · fixed coupons · linear price estimate
Results
Enter bond terms to explore the results.
Understand this calculation
Duration is measured in years and differs from maturity. Earlier coupons shorten the weighted recovery time. The price estimate is linear; use convexity and exact repricing for larger changes.
See calculation method and assumptions
Formula
D_Mac = Σ[(t/m) × CF_t/(1+y/m)^t] / P; D_Mod = D_Mac/(1+y/m); ΔP/P ≈ −D_Mod × ΔyMacaulay duration is the present-value-weighted time to cash flows. Modified duration measures price sensitivity to a small yield change.
Variables, rates and periods
- Face / Price
- Face is principal repaid at maturity; Price is the bond's value today.
- Coupon
- Coupon per period = face value × annual coupon rate / payments per year.
- YTM / y
- Nominal annual yield to maturity, entered as a percentage; discounting uses its decimal value divided by payments per year.
- m / N
- m is coupon payments per year; N = years to maturity × m. Coupons are paid at period end.
- D / Δy
- D is duration in years; Δy is the decimal change in nominal annual yield, 50 bps = 0.005.
Model assumptions
- Valuation is on a coupon date.
- Fixed coupons and face redemption;
- nominal annual yield is divided by frequency.
- No default or options.
- Maturity must span whole coupon periods.
Compare Macaulay and modified duration to estimate the price effect of a small yield change.
Worked example
- Compare ten-year maturity with duration.
- Convert 50 bps to 0.005 and multiply by negative modified duration.
- Use price sensitivity analysis for exact repricing under larger shifts.
Frequently asked questions
Why use duration for small changes?
Duration approximates the slope of the price curve, excluding curvature. Larger changes may increase approximation error.