Lenders usually determine whether properties are lendable based on the debt service coverage ratio. 

THEN, I plan to purchase the second home using a FHA or conventional loan (3%-5% down), for which I will likely pay the monthly cost out-of-pocket, maybe with some rental income support if it is a duplex.My concern is, I do not want to spend my savings or weigh down my debt-to-income ratio so much so that I cannot qualify for and pay the down payment and closing for the lending on the second home.Questions: - With the first home being multi-family, 75% of the rental income (or potential rental income initially) will relatively either maintain or boost my debt-to-income ratio from lenders' perspectives, right? 

With a loan, a person takes on a Debt Obligation. 

But the bank still treats it as a secured debt.

Look into a DSCR, Debt Service Coverage Ratio, loan where the rental income can be used to qualify the cash out refinance instead of your personal income.To Your Success! 

You've done a great job with keeping your debt low so I have no concerns about your level of discipline to use/reuse a line of credit.All the best!

And you do not technically have to replace debt. 

If you don't have the extra cash, can you get creative with a private lender or partner stacked on bank debt? 

(Your $12k down and your new $24k debt.)The “trick” in regards to less than 10% down is people think they bought and asset or have equity.

I’ve often seen this happen where initial approval is given, but debt-to-income issues arise once they discover you’re purchasing another property.