In your account or on your account?

Please help. I am confused when to use in your account or on your account. What’s the right term to use?

To my knowledge:

“On somebody’s account” means “because of somebody”.
I won’t be coming to the meeting today, but please, don’t cancel the meeting on my account.

“In somebody’s account” means simply “in somebody’s bank account”.
I have only $2 in my account so I won’t be buying the hacksaw any time soon.

Thank you.