Is 3.17 the magic number?

[Fritz Schneider]

Hi, new investor here trying to make sense of the world. Feel free to point me to things I should have read that explain this that I may have missed. 

Background: I own one rental property and am looking to buy a second. I'm speaking with lenders and from what I understand they generally count 75% of gross rents toward income and require that DTI be <= .42. Suppose I'm at .42. I think this means that I need to find a property for which the debt service ratio is 1 / (.75*.42) =~ 3.17. That is, for every $1 debt that I'd add with the new property it must generate at least $3.17 in gross rents. Verify that the math is right by working backwards: if I receive $317 in rent it's discounted by the lender by 75% leaving $237. If my debt is $100 than that's (roughly) a .42 debt to service ratio.

This seems like a tough constraint. Is it the case that most small investors are constrained in this way? How do investors achieve greater leverage?  

I think the answer is some combination of non-qualifying loans and that there is some inflection point beyond which you're no longer an amateur and so your finances are evaluated differently, but I'm having a hard time understanding how it works. 

Thanks!