Fan won't shut off after disired temperature reached

How is the fan set? I can set mine to run all the time or only just before and just after the compressor kicks in.

Thermostat may be broke. Are familiar with the thermostat (is this your home)?

I have a setting for fan all the time (both when the compressor runs and when it doesn't) and a setting for fan only when the compressor runs.

You can use either one.

That's how it's designed.

My furnace has the same option.

I don't need to install thermostats to know how they work - for that matter I couldn't build a car but I drive one.