  We consider the strong solution of the 2D Navier-Stokes equations in a torus
subject to an additive noise. We implement a fully implicit time numerical
scheme and a finite element method in space. We prove that the rate of
convergence of the schemes is $\eta\in[0,1/2)$ in time and 1 in space. Let us
mention that the coefficient $\eta$ is equal to the time regularity of the
solution with values in $\LL^2$. Our method relies on the existence of finite
exponential moments for both the solution and its time approximation. Our main
idea is to use a discrete Gronwall lemma for the error estimate without any
localization.
