Its probably due to insufficient hygiene of that area, especially if you haven't had a dentist clean your teeth over those years. There are probably only two options you have, which is to basically keep the tooth knowing that there will be occassional problems and potential for infection and pain, or to remove the tooth and replace it with either a bridge/implant or close that space with orthodontics. Or you can remove the tooth and leave it alone and let it drift into that spot potentially, although there's no guarantee that it'll close up.
The space between those two teeth may be too small to place a bridge or implant, in which case removing the teeth and leaving it alone may be fine. Its in the back area so its not a cosmetic area luckily.
If you were to keep it and maintain your hygiene, you may avoid having problems but there's always a potential for it to become infected and painful. Also, you may develop an abscess which can be dangerous, especially if you don't see your dentist regularly for check ups. Sometimes abscesses have minor pain and then suddenly become painful and swelling within a few days. It can be life threatening.
I would consult with your dentist but I would recommend removing the tooth.
I can't comment on cost cause each dentist charges differently for all procedures and different areas of the country may have different standards. Usually billing for a non-insurance (or cash) patient is determined by what is UCR (Usual, Customary and Reasonable fee guide).