I would beware of anyone advising you that a no doc loan is available for investment property. In today’s economic marketplace investment properties are very high risk, requiring more verified down payment, more restrictive debt to income ratios on verified income, additional insurance requirements for rent loss, post closing reserve requirements and income operating statement/rent comparable addendum’s in addition to the standard appraisal report which adds to your closing costs. In distressed markets lenders may not do investment properties at all. I put a website below that may offer additional information on investment loan purchases.
But there is nothing that says you can’t purchase both at the same time. Just giving you food for thought, hope it helps and good luck!
First off, ‘no doc’ loans do not exist anymore. You will either need to go ‘stated’ which means stating a reasonable income and qualify on your assets ie retirement, savings. Or you will need to go full doc. If you are self employed, a minimum of 2 years will be required to do a mortgage loan.