"I exist" is a statement belonging to the conceptual reality. So the answer to 'why' is any purpose you like to think as your purpose for living.But if you are looking for an answer from ultimate reality, this is an invalid question as it is based on 2 false assumptions.1. Asserting an entity called 'I' without any evidence in reality.2. Asserting an inherent purpose to nature without any evidence in reality.
I suggest studying the PatIccasamuppada(dependent origination).