I have read on an English site as below:
The future continuous can be used to ask questions in a polite and indirect manner when we want to know what someone's plans are.
Example: Excuse me. Will you be using this chair? ( = If you're not using it, may I take it?)
(1) Will you be using this chair?
(2) Will you use this chair?
(3) Are you going to use this chair?
As the explanation from that site, then (1) is considered more polite than (2) and (3).
Could you give me the reason the future continuous sound more polite than other future tenses when asking about someone's plan?
Similarly, a cashier would say:
(1) How will you be paying? In cash or by credit card?
(2) How are you paying? In cash or by credit card?
(3) How are you going to pay? In cash or by credit card?
(4) How will you pay? In cash or by credit card?
In this situation, Is (1) considered the most polite way to use? and why?