How likely is it I will be able to get a mortgage for a rental?

[Zackary Mlynarczyk]

I'm 21, a student, I have a consistent work history since I was 18, but not earning much, only ~15k a year, I now have a job earning about 25k/year but it is independent contracting and I deduct quite a bit of that income on my taxes. My credit score is above 740. Soon I will have about 20k cash and I want to finance a rental property with 20% down, I'm looking at properties in the 60-70k range. Will I even be able to find banks willing to loan amounts that low? If so, is there any real chance I would qualify for that loan with my stated income being so low? 

EDIT: I should also add that I have pretty much no expenses as I'm living with parents right now who are awesome and allowing me to continue living here for a few years while I save up for a house or two and graduate college