Reaper saves the audio as a .wav file. The repeak file is something that Reaper uses internally. You might want to check your project settings to see where it's actually storing the recorded audio, because if the only files you're seeing are .repeak files, then something is configured incorrectly.
I was creating my own SAMPLES directory by copying files from the Home Recording samples. Problem was Windows "show file extensions" was unchecked. So "Tom 2.wav.repeaks" was listed as "Tom 2.wav" I was looking for .wav files but those aren't them. "Tom2" didn't look right until I could see the extensions.
I've been looking at file type extensions for better than 20 years. Why MS decided the default should be to hide them in Win 7 is something Bill Gates should answer for in karma court.