School me on Mortgage Lending

[Franky Juwana]

I have a dilemma and need y'all experts opinion. 

I currently living in an 1br apartment which costs me $1390/month. I'm buying a 4br 1 1/2 bath single family home which now waiting for closing for $294.000 which PITI would come out around $2500/month with 5% down with FHA loan.

Originally we are going to live in it, but after reading real estate book and active in bigger pockets, I have a different idea which is to rent the house for 4 br around $2850-$3000.

I know it's not 70% rule but I didn't think we're going to do this before.

Now, my question is, if after I close around July, Can I apply another mortgage in October to buy our second home which this one we are going to live in it.   Will the bank see if my 1st home payment is being covered by my tenant? and will it effect my debt of ratio for us applying the second mortgage in short period of time because even with the first house, our debt ratio is kinda tight. 

Thanks y'all