Question

1. I will be 14 years old next year.
2. I shall be 14 years old next year.
3. I am going to be 14 years old next year.
4. I intend to be 14 years old next year.

(Are they the same? What is the difference between 'will' and 'be going to'?)

Answer 1

"Will" and "going to" are the same.

"I intend to be 14 years old next year" and "I shall be 14 years old next year" mean the same thing. It's something we'd never really say. It means you want to be 14 and will try to make it happen. It means something like, "I want to be 14 years old next year and I will work to be that old next year."
How can you do that? You either will be 14 or you won't. :-)
A 11 year old won't hope he magically turns 14 next year without needing serious medication. :-)