I think that anything priced under $40K will be a hole in the wall. And many down payment assistance programs require a good inspection of the property. There was one house that we looked at that had a cracked concrete slab in the backyard and the realtor said that the CHFA program probably wouldn't go forth without that fixed. Luckily, we didn't like that home at all.
I agree with the others that you should work on your career first and go back to school if needed. I know you want a home of your own but you should be patient to get something you are happy with versus the only property affordable. This isn't the same as a car purchase. I would try also to look for options through Section 8 in your state as you may be able to get something 100K or higher with Section 8 assistance. You need to have enough income to take care of repairs and a $40K home is likely a hole in the wall that would require a lot of repairs and being a single mom on your income, I don't think that is a good fit for you as you would only have enough to pay the mortgage and that is it. You want a home that is safe for your baby.
You could also look for sale by owner properties where you pay the seller and he pays the mortgage and as the balance goes down on the loan and your income goes up, later on you can qualify for a mortgage for that property. Or try a rent to own property. But going out there looking for a mortgage right now on anything that is affordable, is not the best plan of attack.
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