I have a personal account and later I created a business page linked to it.
I want to keep only the business/fan page and delete the account (profile) created earlier. Is it possible? If so, how?
Someone (a flesh-and-blood person) needs to own the business/fan page. If you don't want to be that someone any more, then you need to find someone else who is going to take on the role.
On the other hand, if you still want to be the flesh-and-blood person who administers the page, but you just don't want to use Facebook youself any more then just: