A lender would likely approve you up to $292,256
On $82,000 of gross income with $550 of existing monthly debt, the 28/36 rule supports about $1,910 a month toward housing. With $46,000 down at 6.65%, that reaches roughly $292,256 — a $246,256 loan at 15.7% down. Your resulting debt-to-income ratio would be 36%, and you are currently limited by the total debt.