I don’t know if it matters if you have equity or not. I think it’s more important to know how much is your payment vs income. If this is your first rental, some lender would let you count the average rent for your house as income and some would not let you until you own the rental for 2+ years. Different lender have different rules regarding this. However, if you say you can afford both payment, then I assume you wouldn’t have problem qualifying if you can’t count the rent toward your income.
