Is sunlight alone enough to kill all mold on a towel?

I have a light biege towel that has developed dark spots in several areas which I believe may be mold. I ran it through the wash and it had no noticeable effect on the spots. The towel is hung on a rack in a bathroom with very little ventilation. I have a window that gets direct sunlight during the late afternoon. Would hanging the towel here kill all the mold or do I need to also wash with amonia or vinegar? If sunlight alone works; how many hours should it take? Will the mold spots start disappearing or would I still need to launder to get spots out even after the mold is dead?