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I want to change to a prepay option but they are telling me I have to close the account and restart it in order to achieve this, but isn't that a bad idea? Won't I lose account history and therefore quality score if I do this?
Unfortunately what you've run into is what you'll have to deal with. Google does not currently allow an account to switch between pre and post-pay: [google.com...]
I would assume this is a common switching cost that is often overlooked when switching from agency to agency or from in-house to out of house or vice-versa.
Good luck building up your quality scores!