Inputs
Key Results
Price–Yield Curve
Curve shows price versus yield around the entered YTM holding coupon schedule constant. Useful to visualize rate sensitivity and convexity.
Example Data Table
Click “Use” to load a preset into the input panel.
| Face | Coupon % | YTM % | Years | Freq | |
|---|---|---|---|---|---|
| 1000 | 5 | 6 | 5 | 2 | |
| 1000 | 3 | 2.5 | 10 | 2 | |
| 1000 | 0 | 4 | 3 | 1 |
Formula Used
Let F be face value, c the annual coupon rate, y the annual yield to maturity, m payments per year, and N = m × years the number of coupon periods. The per‑period coupon is C = F × c / m. The present value (price) is
P = Σ (t=1..N) [ CFₜ / (1 + y/m)ᵗ ], where CFₜ = C for t < N, and CF_N = C + F.
The Macaulay Duration (in years) is
D_Mac = (1/P) × Σ (t=1..N) [ (t/m) × CFₜ / (1 + y/m)ᵗ ]
The Modified Duration is
D_Mod = D_Mac / (1 + y/m)
The Modified Convexity (in years²) with discrete compounding is
C_Mod = (1/P) × Σ (t=1..N) [ CFₜ × t × (t + 1) / (1 + y/m)^(t+2) ] / m²
Small price change approximation for a yield shift Δy (in decimal):
ΔP / P ≈ - D_Mod × Δy + 0.5 × C_Mod × (Δy)²
How to Use
- Enter face value, coupon rate, yield to maturity, years, and pick payments per year.
- Press Calculate to compute price, Macaulay duration, modified duration, convexity, and DV01.
- Review the cash flow schedule and the PV weight chart to see timing of value.
- Use the price–yield curve to visualize sensitivity and curvature around the current yield.
- Export the schedule as CSV or PDF for audit, sharing, or further analysis.
Notes: Compounding assumes nominal APR with m compounding periods. Clean price equals PV of future cash flows from next coupon date (no accrued interest modeling).