'will' (Advanced Grammar In Use Unit 10)

Hello all,

Below is a conversation from the exercise of Unit 10 in Advanced Grammar In Use.

2 Did you know I _______ a new car next week?

a. will buy, b. am going to buy, c. am buying

I see that 'am going to buy' and 'am buying' are acceptable in this sentence. But I was wondering if 'will' is also allowed if we take 'buying a new car next week' as something that is planned.

In Unit 9, A, it says "we can use either 'will' or 'be going to' to talk about something that is planned, or something that we think is likely to happen in the future". The book provides an example: "Where will you stay in Berlin?", which is equivalent to "Where are you going to stay in Berlin?"

Any comments would be greatly appreciated