iOS: Record audio in other format than caf

I am working on audio recording. I am able to record my audio in caf (Core audio format). Now I want to record sound in .mp3 or .amr.

I tried a lot of google but didn't found anything. I am not sure if my steps following work:

Write that Audio with .caf extention to document dir

Read data from that file

write the file again with .mp3 or .amr extention

I have 100% doubt that this will not going to work as this will just re save file with some other extension. This won't change audio codec.

I thought that for converting any format whether it is audio or video we need to change its codecs and data sequence.

Please also suggest me any player which don't play .caf files not anything else. So I can make sure that my files are converted successfully.

UPDATE Please also let me know that the way I am re-writing data with different extension is correct in the way I am needed?

You might be interested in the iPhoneExtAudioFileConvertTest example.
The MP3 format is however not available due to patents, maybe you can use LAME.