In this work, we aim to study the consequences of presently observed accelerated expansion of the universe by assuming power-law based Starobinsky type metric $f(R)$ gravity as the theory of gravity. We, here, focused on evolution of the universe by studying different cosmological parameters like Hubble parameter, Deceleration parameter and Jerk parameter etc. From our analysis, we found that the phenomenological constant of Starobinsky model $(M^{2})$ has a very small value $0.6538t_{0}^{-2}$ , where $t_{0}$ is the present age of the universe. Again, from the nature of variation of deceleration parameter and jerk parameter, we concluded that the universe has been undergoing an accelerated phase of expansion from $0.711t_{0}$ and this will continue even upto the distant future.
