According to Newton's Laws of Gravity, a finite universe should eventually collapse on itself. If the universe had an end, then eventually the gravitational pull from stars would cause everything to be pulled into a central point. This central point would also be the spot where the universe once began. This is how it has been theorized that our universe is infinitely expanding].
The great question is: what lies beyond the expanding universe? Is there anything? If time is relative to your position and speed in the universe, then time cannot possibly exist outside of the universe.
It is difficult to comprehend that time has a beginning. Many physicists believe that the universe was all compacted together at one point, and the infamous Big Bang began the universe, expanding and stretching out. This is when it is believed that time began.
The universe is expanding at great speeds, but eventually, it may slow down due to the gravitational pull from stars. Then, the universe will collapse on itself, as mentioned above, possibly returning the universe back to a state of pre Big Bang existence. Then time would end. It is also feasible to think that if the universe did indeed shrink back to nothing, that it would again, Big Bang and expand out for eons and eons. Maybe this phenomenon has already happened, billions of years in the past (not that time is relevant).
Works cited and consulted:
Stephen Hawking, A Brief History of Time
Stephen Hawking, The Cambridge Lectures