Formal vs. informal letters

Keep me posted.
Informal Neutral Formal
Asking for action
Can you see to it? Could you please act quickly to .. I would be grateful if you could
Promising action
I'll make sure We'll replace it We will of course
Don't worry. I'll get onto it. I'm sure we can find a solution.

I can assure you that

Asking to be contacted/updated
Please let me know what you plan to do.

Please could you keep me informed of

Sorry about that. I’m very sorry about Please accept our sincere apologies