Forward Rate Blender

The long spot rate is the time-weighted average of the short spot and the intervening forward rate(s).

\(r(0, T_2)\,T_2 \;=\; r(0, T_1)\,T_1 \;+\; f(0, T_1, T_2)\,(T_2 - T_1)\) (continuous compounding)

Number of periods

\(T_1\) (years) 1.0

\(T_2\) (years) 3.0

Short spot \(r(0, T_1)\) 3.00%

Forward \(f(0, T_1, T_2)\) 5.00%

\(T_3\) (years) 5.0

Forward \(f(0, T_2, T_3)\) 6.00%

Weight on r(0, T₁)

Weight on f(0, T₁, T₂)

Weight on f(0, T₂, T₃)

Z(0, T₁)

Z(0, T₂)

Long spot r(0, T₂)
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