Present simple in the future tense [duplicate]
In my understanding, "planning to" just expresses the desire and the preliminary arrangements being made to do something.
On the other hand "going to" is used when the plan of doing something is completed and the action will be carried out soon.
For example, when I say "I am planning to buy a new car", the ultimate decision is not made. Here I am expressing my desire. However, when I say "I am going to buy a new car" the planning stage is over and I have made the final decision to buy a new car.
I use present continuous and say "I am buying a new car next week", only when I have made the decision, arranged the money and fixed even the time of buying the car. The action is immediate and certain.
Do you think you will visit them next week?
Do you plan to visit them next week?
It would be unusual for a speaker to respond to those questions with the OP's suggested examples: I think I will visit them next week, and I plan to visit them next week. Questions that begin with an auxiliary verb usually require a yes or no type of answer, in this situation the person expresses their decision made (at that moment) in the PRESENT.
i) Yes, I will / Definitely (A DEFINITE “YES”)
ii) I think so. (A HESITANT“YES”)
iii) I might. (A PROBABLE “YES”)
iv) I don't know, I haven't decided yet. (UNCERTAINTY)
v) No, I don't think so. (A PROBABLE “NO”)
vi) No, I won't / No, I don't (A DEFINITE “NO”)
The next question begins with the auxiliary verb will
- Will you visit them next week?
Any of the short answers i) to vi), excluding Yes, I do and No, I don't, would be appropriate.
Are you going to visit them next week?
Are you visiting them next week?
Are you going to be visiting them next week?
There is no real discernible difference in meaning between 4, 5 and 6, it is a matter of personal choice whether you say or write one or the other. All three questions imply an action that is premeditated. The BE + VERB + ING (Present Continuous) is used to express a fixed, or planned arrangement in the future. BE+ GOING TO + VERB is commonly used for predictions, intentions, and also arrangements in the future. The BE + GOING TO + VERB + -ING (Future Continuous with "Be Going To") is used for actions in progress in the future.
The short answers express the speaker's decision made in the PAST.
i) Yes, I am
ii) I don't know yet.
iii) No, I'm not
- Are you planning to visit them next week?
- Are you planning to be visiting them next week?
Question 7 is the Present Continuous form of question 2. Question 8 is the Future Continuous with "present continuous". Here the verb plan has a similar meaning to think + about; e.g. Are you thinking about visiting them next week? Any of the answers from i) to iii) (above) would be appropriate.