Predestination
In John 4.34, Jesus said before He was crucified:
My meat is to do the will of him that sent me, and to finish his work. (John 4:34)
What is precisely the will of Him Who sent Jesus to live among us? The answer is in John 6:38-40:
I have come down from heaven, not to do my own will, but the will of the one who sent me. And this is the will of the one who sent me that I should not lose anything that he has given me, but should raise it to life on the last day. This is my Father’s will: That everyone who sees the Son and believes in him should have eternal life, and I will raise him to life on the last day.
In verse 44, we read how the Father chooses those He will give the Son – via His sovereignty in salvation:
No one can come to me unless the Father who sent me draws him, and I will raise him to life on the last day.
In John 17:1–2, we read that the Father gave the authority to the Son to judge all those the Father gave the Son:
After Jesus had said this, he looked up to heaven and said, Father, the hour has come. Glorify your Son, so that the Son may glorify you. For you have given him authority over all humanity so that he might give eternal life to all those you gave him.
The phrase “the hour has come” in the first verse above is a reminder of Jesus’ acceptance of the will of the Father for the Him to be crucified for our sins so that we may have eternal life. Jesus had the option to reject the will of the Father, for it is a dispositional or preferred will of the Father.
The above verses reveal a two-step process that leads to eternal life via the Father’s will for His Son. Firstly, the Father exercises His sovereignty to choose those He wants to have eternal life through His Son, and secondly, it is through the free will of those chosen to believe in His Son to have eternal life. So both God’s sovereignty in salvation and the free will of an individual determine whether the person will achieve eternal life.
Purgatory
There is a famous story in the Bible that clearly indicates that purgatory is not necessary for salvation. On Mount Calvary, one of the two thieves - sinners till the end of their lives - cried out to Jesus:
And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily I say unto thee, Today shalt thou be with me in paradise. (Luke 23: 42 – 43)
The Greek for “today” is σήμερον, sémeron, which according to Strong’s Concordance, also means “now”. Jesus answering in the affirmative implies He had had His Father’s confirmation of salvation for both of them at that instant, whilst they were still alive.
It is our complete faith in Christ that saves us, as per the exhortations of Paul the Apostle (Romans 10:8–10, New KJV):
But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith which we preach): that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. (Romans 10:8–10)