Or do you manually put them in each time?
Banking websites will typically have two or more levels of authentication and will force you to enter random characters of your password. Plus, if the computer is used by more than one person it is highly recommended that you manually enter passwords each time. Even if it is members of your own family as if organisations find out you have been sharing your password and it gets compromised, you won't have a leg to stand on in court.
The computer remembers them. My memory is too bad to keep track. Some of them I write down.
Manually enter them for every site on both my work and personal laptops, my tablet and my phone. It would be to easy to play Hell and Havoc with my life if someone got hold of my passwords
“Better a true enemy than a false friend.”
It is set to save my passwords however I input my banking details from scratch.