Can one mortgage prevent you from getting another?

[Andrew Rogers]

Ok so this may seem really obvious to most people, but I know close to nothing about financing/lending/mortgages. I never learned anything about it in school, never asked my parents, or anything so it's a huge gap in my knowledge and I'm not sure how to look this up. Whenever I listen to the BP podcast or anyting like it and the topic turns to this subject, a lot of it goes right over my head.

To expand on the question in the title: if I get a mortgage for one (investment) property and a couple years later want to buy another property, will banks and other lenders likely look at something like my debt-income ratio and not want to lend to me on another mortgage?

And to expand even more, it would likely be better to explain my plan with some specific examples. I currently still live with my parents for a low amount of rent so have no real estate currently myself. I plan to move out and have my own place (potentially house hacking) within the next 3 or so years. That's still a way's away and I'd like to have at least one property before that time. I'm not in any "rush" to just get something since real estate investing is still very new to me, but I don't want to just wait when I could potentially start sooner.

To throw some numbers out there to make things more tangible, let's say next year I get a single-family home or small duplex investment property for $150,000 with 20% down on a standard mortgage and I make the payments every month with no issues. Then a year or two later, I want to get my place and it'd be a $200,000 house also with 20% down. Would I likely be turned down for that second loan because I still owe a lot on the first? I know it'll likely also depend on the specific lender(s) I'm using, but for most places, would this be an issue at all? I don't want to give away too much personal info but I make more than the US average annual salary but less than 6 figures, have quite a bit in savings, have no other debt, and my credit score is over 700 if that helps as well.