While modelling our late time cosmically accelerated universe, it is popular to involve different dark energy models, the equation of state of which can be taken as a function of the redshift and some unknown parameters. Barboza and Alcaniz have proposed one of a such kind of dark energy's EoS model. We use some new parametrizations like Feng, Shen, Li, Li I and II and Polynomial parametrizations to get more accurate concepts about the fate of our expanding universe. We try to find how the hypothesis of the fate of our universe behaves in the above background of dark energy models. Possibilities of occurrences of future cosmic singularities are studied.