Chord transposing help?

Question

I need to transpose this song into the key of C.
The song is house of the rising sun, here are the verse chords.
Am C D F
Am C E E
Am C D F
Am E Am E
Anyway the chords are repetitive throughout the song, so you get the idea. My music instructor told me that I needed to transpose this song to the key of C for a better match to my voice.
I'm pretty sure that Am transposes to C# Barr chord but the rest?
This is my first attempt at this so your help and any explanations would be greatly appreciated. Peace!
I think the song just needs to be carried up three keys. Thanks.

There is also a D chord. If you could also include this in you transposing.

Yea you may be right about the transposing of Am. I had the same idea as far as the capo but he insist that this is vital in the long run to learn. So he gave me this song to do. Thanks for the answer.

Answer 1

Key of Cm

Cm Eb F Ab
Cm Eb G G
Cm Eb F Ab
Cm G Cm G

Key of C# minor (If you started with C#m)

C#m E F# A
C#m E G# G#
C#m E F# A
C#m G# C# G#

Edit: If you want to be able to transpose, learn your intervals, that will help, but it does take time to learn. The more you practice at it the better you will get.

Answer 2

if you just want to play it and sing it, and he's not testing you on transposing chords... try using a capo. put it at the 3rd fret and just play the chords like normal Am CDF and so on..
It's much easier using a capo instead of trying to figure out the chords.
It also gives your guitar a little bit different sound.

And, wouldn't the Am become a Cm? especially if you're just going up 3 frets.