Jesus Christ came into the world to do the will of His Father. We are told in Scripture that the will of the Father was to give to His Son a great multitude of people, and that His Son would die for and redeem those whom God loved without the loss of one. The Bible makes it clear – Jesus Christ would save His people from their sins.
God’s justice demanded an acceptable sacrifice for sins. This sacrifice had to be by blood, and it had to be perfect and pure. Jesus Christ, God’s own Son, came into the world to die and make that sacrifice. Contrary to what is often taught in the world of Christianity, Jesus did not offer, nor does he now offer, himself to man. The sacrifice that Jesus made was an offering to God. God was the One offended, and to Him alone was this offering made. The offering of the life of Jesus was accepted by the Father. The blood of His only begotten Son redeemed us from our sins. The penalty for sin, the wrath of God, was satisfied forever through this one offering. As Jesus gave up the ghost, as He was dying on the cross, He said “It is finished”, and His purpose was fulfilled. God demonstrated his satisfaction with the offering, and His acceptance of the sacrifice by raising Jesus from the dead, who now sits on the right hand of God making intercession for us.
Yes, Christ finished the work He came into the world to do. Every one for whom Christ died will live with Him in Heaven one day. The fact that you see your need of a Savior and the need to repent, that you feel a desire to follow Him and trust Him, is the evidence you have been born again, that He died for you, and He is your Savior.