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Treasury par yield curve of 12 November 2026: bootstrapped spot rates and implied forward rates

Tool	Yield Curve and Forward Rates
Source	U.S. Department of the Treasury (2026). Daily Treasury Par Yield Curve Rates. Office of Debt Management, Washington, DC, rates of 12 November 2026.
Level	Undergraduate

Problem

The Treasury's par yield curve of 12 November 2026 is given at eight maturities from 3 months to 10 years. Interpolate it to every semi-annual coupon date, bootstrap the discount factors and spot (zero-coupon) rates, and find the forward rate for the second half-year, the 1-year rate 1 year forward and the slope of the curve.

Inputs to Enter

Par yields (%): 3 months 4.32, 6 months 4.42, 1 year 4.65, 2 years 4.86, 3 years 4.90, 5 years 4.95, 7 years 5.02, 10 years 5.10
Semi-annual coupons and compounding (m = 2); forward start 1 year, forward length 1 year

Open the Yield Curve and Forward Rates tool (loaded with this example)

Answers

d_1 = 1 / (1 + 0.0442/2) = 0.978378, spot rate z_1 = 4.420 %
d_2 = (1 − 0.0465/2 · 0.978378) / (1 + 0.0465/2) = 0.955048, z_2 = 2 (0.955048^(−1/2) − 1) = 4.653 %
Forward rate for the second half-year f_2 = 2 (0.978378/0.955048 − 1) = 4.886 %
2-year discount factor 0.908301 (spot 4.867 %); 1-year rate 1 year forward = 2 [(0.955048/0.908301)^(1/2) − 1] = 5.082 %
10 years: par 5.100 %, spot 5.129 %, discount factor 0.602657, last half-year forward 5.431 %
Slope: 10-year minus 2-year 0.24 points, 10-year minus 3-month 0.78 points

Notes

The tool's default inputs are this curve; press Submit. Par yields between the entered maturities are interpolated linearly; the numbers are checked against an independent numpy solution of the par-bond equations (test_yield_curve_forward_rates.php). The example is the tool's own calculation on Treasury data, not a worked example printed by the Treasury.