Context: Yesterday, I decided to visit Uncle Peter next month. This means the decision was made before speaking. Now, I want to inform my friend about this visit. I want to invite my friend to join with me.
(1)I am going to visit Uncle Peter next month. Would you like to go with me?
(2)I am visiting Uncle Peter next month. Would you like to go with me?
(3)I will visit Uncle Peter next month. Would you like to go with me?
(4)I will be visiting Uncle Peter next month. Would you like to go with me?
I think that all 4 sentences works for this context. Right?
I was taught that simple future "will" is only used for a decision right at the time of speaking. But this context refers to a decision before the time of speaking. Does (3) with simple future "wil" sound natural here?