Jesus spoke significantly of both, and yet there is never a mention of a third place, an interim location where man undergoes further purification. The concept of purgatory implies that Christ’s work on the cross was incomplete and insufficient to save us from judgement for our sins. We know, however, that the full redemptive work of Christ was accomplished on the cross, just as Christ Himself declared, “It is finished” (John 19:30).
For believers, the end of this life will be the beginning of our eternal life with the LORD. We can see this in Jesus’ parable about the rich man and Lazarus in Luke 16:19-31, whereby Lazarus was taken immediately upon his death to “Abraham’s side,” a common figure-of-speech for Heaven, and the rich man was immediately cast into torment in Hades. Paul assures believers in 2 Corinthians 5:6-8 that to be “away from the body” is to be “at home with the Lord.” Those who have been saved by faith in Jesus Christ may rest assured that their debt has been paid by Christ Himself, and that their death will find them standing before God justified and glorified, and welcomed into His kingdom.
 “When the Son of Man comes in his glory, and all the angels with him, then he will sit on his glorious throne.  Before him will be gathered all the nations, and he will separate people one from another as a shepherd separates the sheep from the goats.  And he will place the sheep on his right, but the goats on the left.  Then the King will say to those on his right, ‘Come, you who are blessed by my Father, inherit the kingdom prepared for you from the foundation of the world. (Matthew 25:31-34 ESV)
Some additional CARM articles that speak to this topic and may be of help: