I've got one.
It's about 5 ft deep (but not filled to the very top, obviously.)
and 16ft x 10ft, so not a big one by any means. It's oval so you can get a good swim going.
And although it is an above ground pool, you can sink it and indeed we have, so 2/3 of it is underground.
this one
The pools themselves cost about three thousand.
The cost is in the maintenance.
The pump on ours needs replacing and the pipes. The pump alone is going to be about £700.
The pool chemicals you need are a pain in the arse. You need chlorine and ph balancer (+ and - ) and algaecide, and of course you have to have the test strips and test the water daily to make sure it's ok.
Then you have to heat the pool. Because even in summer in this country you cannot go in if it's not been heated. You'll freeze your watsits off.
An electric heater will bankrupt you, so you're best off going for solar panels or pods.
like these
And then you have to clean the pool, because the chemicals will ensure it doesn't go green and slimy, but you still have to get in there and clean it out. So you'll need a skimmer and ideally some sort of bottom feeder 
You'll need a pool cover. And a winter cover. And every year you'll need to winterize your pool with a shedload of chemicals.
I haven't actually ever added up what it costs every year. I think I'm scared to 