I'm with Mame on this. It's a question whether you say it like a question or not. In fact how you say it doesn't really count when you're writing because the reader has no idea how you would say it.
I did a bit of research on this. I was able to find a definitive answer in only one place: The Gregg Reference Manual, which is a very helpful, practical guide for style, puncutation, and grammar issues. What does it say? Use the question mark.
Use a period to end a rhetorical question.
14. What's the point of going on.
A rhetorical question usually ends in a question mark (?), but occasionally may end with an exclamation mark (!) or even a full stop (.) according to some writing style guides. For example:
* "What's the point of going on."
* "Isn't that ironic!"
In the 1580s, English printer Henry Denham invented a "rhetorical question mark" for use at the end of a rhetorical question; however, it died out of use in the 1600s. It was the reverse of an ordinary question mark, so that instead of the main opening pointing back into the sentence, it opened away from it.
Some have adapted the question mark into various irony marks, but these are very rarely seen.
You're not following me on this. i
s different than
You're not followng me on this, are you?
Sorry, it was a statement AND then, you questioned him/her.
I vote for the question mark.
Gregg states that end punctuation for a rhetorical question is either a question mark or an exclamation point. The exclamation point is for special emphasis.
f you've found sources that support a period rather than a question mark, why look further? You've found what you need.
Maybe there's no definitive answer and it's just intuitive. For there to not be a question mark at the end of any sentence just feels wrong, for whatever reason.
The point of the question is irrelevant (rhetorical or not). It's a question and deserves a question mark. Your inflection doesn't change, so why would your punctuation? (I just tried it out and my inflection was the same).
You are asking for agreement, not making a statement. Whether you're not really asking for agreement, is not the point. You're still phrasing and inflecting it as a question.
(Then again, I might be tone deaf and don't hear the inflections as accurately as others).