A lender would likely approve you up to $280,000
On $84,000 of gross income with $550 of existing monthly debt, the 28/36 rule supports about $1,960 a month toward housing. With $56,000 down at 6.65%, that reaches roughly $280,000 — a $224,000 loan at 20% down. Your resulting debt-to-income ratio would be 35%, and you are currently limited by the housing ratio.