This song is easy and catchy as hell, and this IS the right way to 
play it.
The A chord used is what I call the Green Day A. U simply Barre an 
open A muting the little E string

INTRO- listen to song for strumming pattern and stratches

A (a bunch of times) E (the barre chord on the 7th fret twice) then
A one last time

VERSE all chords are barre
A                             D 
Wherever you go you know I'll be there
A                           E
If you go far you know i'll be there
         A                D
I'll go anywhere, so I'll see ya there
A                              E
You place a name you know I'll be there
A                               D
You name the time you know I'll be there
        A                 E
I'll go anywhere, so I'll see ya there

CHORUS use open E and D on the first line, then return to barre
A E     F#m               E
I don't care if you don't mind
D    A  E             D
I'll be there not far behind
D A    E             D                       A    E   A
I will dare, keep in mind, I'll be there for you

VERSE 2
p.m. A............................release
When there's a truth you know i'll be there
D                              A
Amongst the lies you know i'll be there
        E                     A
I'll go anywhere, so I'll see ya there

CHORUS- Same

BRIDGE

After the chorus finishes start the li'l A  E, using open E

F#m E A

D C#m A

F#m E A

D Dmaj7 D E

on the b string play the 9th then 10th fret

LAST VERSE
 n.c.                           A
If you should fall you kno i'll be there
D                              A
To catch the call you kno i'll be there
        E                    A
I'll go newhere, so i'll see ya there

LAST CHORUS

same again only on the last "I don't care" dont hop back do D,
Stay on E

OUTRO
A    E            A
I'll be there for you
A    E            A    E  A
I'll be there for you

That's it, ne questions feel free to email me