2003 Accord remote problem.
 

Just bought my first car 4 days ago, its a 2003 honda accord.

The Key remote, can unlock the doors when im outside of the car and getting into it, but when I leave my car, the Lock on the remote ANDthe lock on the door dont work. so I have to manually lock all the doors,which I mean isnt a HUGE deal for me, but certainlly would be less of a hassle to get it fixed. my question is what is the problem, can it be fixed, and if so roughly how much would it cost. thanks so much for your help