A lender would likely approve you up to $242,777
On $78,000 of gross income with $550 of existing monthly debt, the 28/36 rule supports about $1,790 a month toward housing. With $47,000 down at 6.65%, that reaches roughly $242,777 — a $195,777 loan at 19.4% down. Your resulting debt-to-income ratio would be 36%, and you are currently limited by the total debt.