Puzzle: How much money to bring

Solve this one:

You were going to enter into a 20 stories building…

In every floor there is a guard…

To every guard you will pay a half of the money you brought, then the guard will gave you change of Php1.00.

Question: what is the minimum money that you would bring so that you can reach the top floor of the building having  Php2.00 left?

Who am I?

LETS SEE HOW FAST YOU CAN SOLVE THIS:

I am a five letter word.

If my first letter is removed i come above you

If my first two letters are removed I am still around you

HINT:  I am used for your comfort