Saving faith is not intellectual assent alone, but it includes it. It is belief from the heart (Act 8:37), And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
The word heart refers to the center of all physical and spiritual life. It includes the soul, mind, and will. It is the seat and arbiter of our thoughts, passions, desires, appetites, affections, purposes, effort, understanding, intelligence, and emotions.
It produces trust, an assured reliance; one in which confidence is placed; a dependence on something future or contingent.
It produces hope.
Rom 10:9, “That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.”
Thank you. That is so much more concise than what I posted.