Discount factor taking into account yield curve shape

I have always been told that the discount factor formula is just: $$DF(T) = \frac{1}{(1+L_{t_0})^T}$$ where $L_{t_0}$ is the LIBOR rate on one period (the first one I guess) and $T$ the number of periods.

But shouldn't we take into account the yield curve shape, and use instead forward rates: $$DF(T)=\frac{1}{(1+L_{t_0})\times \prod_{i=1}^T[1+F(t_i,t_{i+1})]}$$ where $F(t_i,t_{i+1})$ is the forward LIBOR rate between start of period i $t_i$ and its end $t_{i+1}$?

Why haven't I encountered this? Is it wrong?