Automatically update Contact status when Account status is changed

Automatically update Contact status when Account status is changed

I currently have a field for "Status" in my Accounts, which denotes whether the client is active or inactive. I'd like to be able to have that same field (synced) in the related Contacts so that I can send a targeted email to active contacts only. It seems like I should be able to do this with a workflow or even a new field that utilizes a lookup list, but my experimentation with both those options has not been successful.

For clarity, if I update ABC Company to Inactive Client, I'd like Bob Smith from ABC Company to automatically have his contact record also reflect Inactive Client.

What I don't want is to have to update individual contacts every time I change the status on an account - that's just redundant work. Any suggestions?