Loan source for 2nd investment property

[James Dillard]

I'm looking into buying a 2nd rental property. I have enough equity in my first rental to cash-out refinance a down payment for the second. After speaking with a lender I found that the interest rate would be quite a bit higher (roughly 2%) than if I were to refinance my primary residence which also has a good amount of equity. I feel that the right move would be to refinance my principal residence and leave the equity in my rental property for now, as long as the cash flow from the second property covers the difference in the mortgage on my primary residence. Is this the right train of thought?