rounding error of implicit and explicit method

Question

To solve the differential equation $y'=f(t,y), y(0)=y_0$ consider a explicit $y_{n+1}=y_n+hf(t_n,y_n)$ and a implicit $y_{n+1}=y_n+hf(t_{n+1},y_{n+1})$ method to solve the ODE. If in the explicit method we have a rounding error of $\epsilon$ in each step of the iteration, then how large is $\epsilon$ in the implicit method? I think it has to be bigger?