Answer is an offer. For making offers, use 'will'
Explanation
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Answer is a promise. You use 'will' or 'won't'
Offer with questions: 'Shall...?'
In this case, it is an offer. For offers use 'will'
Answer is about plans or future arrangement. You may use 'going to' or 'present continuous'
Plans or future arrangements: 'going to' or 'present continuous'.
Prediction: 'will' or 'going to'
For predictions use either 'will' or 'going to'.
The answer is a prediction. You can make predictions with 'will' or 'going to'.