THE FIRST THING we need to know about Paul’s answer as recorded in Acts 16 is that is was only the beginning of the answer…
When he told the jailer, “Believe on the Lord Jesus Christ” he did not stop there. A doctor, when asked, “What shall I do about my disease may reply, “Just trust in me and I will take care of you.” All understand that to be the beginning of an answer that involves putting yourself into the doctor’s care, following his directions, and taking his prescriptions. There is no instance in or out of the Bible of anyone ever being blessed by faith, cured by faith or saved by faith until that faith led them to obey. Even denominational theologians admit that belief that offers salvation always involves a trusting reliance on him, not merely intellectual assent. The problem is, they do not seem to know what “trusting reliance” involves.
It is easy to see here that the response was one that was always true in every case of conversion. They heard the gospel (v. 32, cf., Romans 10:17). They responded to that story in penitent faith (v. 33, Mark 16:16; Acts 2:38). They were baptized immediately (cf. Acts 22:16; 8:37-38). Can one imagine a person who thinks baptism is not important being baptized at that hour of the night under those circumstances? When verse 34 indicates that they “rejoiced, having believed” it again shows that this faith was not simply intellectual assent, but trusting reliance on and submission to the commands of Jesus. (T. Pierce Brown)
“And he brought them out and said, “Sirs, what must I do to be saved?” So they said, ‘Believe on the Lord Jesus Christ, and you will be saved, you and your household.’ Then they spoke the word of the Lord to him and to all who were in his house. And he took them the same hour of the night and washed their stripes. And immediately he and all his family were baptized. Now when he had brought them into his house, he set food before them; and he rejoiced, having believed in God will all his household.” Acts 16:30-34
–Mike Benson