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A simple trick is being used to come up with the right discount factors. Since $D_T=\frac{1}{1+r_1}\frac{1}{1+r_2}\frac{1}{1+r_3}\cdots\frac{1}{1+r_T}$ and $D_S=\frac{1}{1+r_1}\frac{1}{1+r_2}$ we can form the desired discount factor from two days hence to date $T$ as follows $\frac{D_T}{D_S}=\frac{1}{1+r_3}\cdots\frac{1}{1+r_T}$ (which we might call $D_{...

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