A time travel story:

Given that time travel is a one-way proposition, that is that the time traveler does not get to return to their starting point, careful consideration and justification must be given to when and were they will go -- since, as stated before, there will be no going back.

For example, choosing the past will at least make it possible for the traveler to communicate with the future.  Then the question arises, how far back.  Perhaps on back far enough so that their present self could benefit from a killing on the stock market.  Could he loop for a while to accumulate ever greater wealth, and then use that wealth to accomplish something else.

You can only get wealthy in the stock market if you can carry specific knowledge of the future back into the past, and appropriately apply it.

The other thing about time travel in this scenario is that the traveler can only make the "jump" once.  So if the jump was only ten minutes, then it would be wasted.  Just as a jump of ten thousand years would probably be.