What is a fair price to pay to have the termites in my house exterminated?
I'm sorry, but there's no simple answer to your question. It is like asking 'how much will my next car cost?': there are just too many big variables for any single answer to be useful.
Price depends very much on what steps need to be taken and this in turn depends on the type of termites, the location, the construction and a whole lot of other factors.
Let's assume you live i the USA in a typical (not huge) house. You might be super lucky and get a a small infestation of subterraneans killed for $400 but chances are you are looking at something in the range of $2,000 to $4,000. If they are drywoods, a fumigation may even run to a bit more.
It may be necessary to put in barrier chemicals or to have an ongoing monitoring system as it is unlikely that termites won't try to attack again. There's usually no value in words like "exterminate" or "eradicate" except in the short-term. If you find termites, you need to control them and to take steps to manage the ongoing risk.
Only by getting the place properly inspected can you find out what needs to be done.