  We investigate a flat FLRW-model in $f(R,T)$-gravity, which includes the
quadratic variation in scalar curvature $R$ and the linear term of the trace of
the stress-energy tensor $T$. In turn, we establish the model has the behaviour
of the late time Universe, which is accelerated expanding and ends up in a big
rip. Using the parametrization of scale factor $a(t)$, we propose a model,
which begins with point-type singularity, i.e., the model starts with a point
of zero volume, infinite energy density and infinite temperature. The model's
behaviour is accelerated expanding at present and $\Lambda$CDM in late times.
Finally, the proposed model behaves like a quintessence dark energy model in
the present time and is consistent with standard cosmology $\Lambda$CDM in late
times.
