Two Jewish Age Concept The Jewish rabbis wrote of "this age and the age to come." (See Eddersheim, Life and Times). "This age" was the one the Old Testament Jews were presently living in (until John the Baptist, John 1:17, Hebrews 10:1). "The age to come " was in reference to the expectant Messianic age which was to be introduced by a Messenger (Elijah; see Malachi 4:5), and by "birth pangs." (Which Jesus referred to in the Olivet Discourse, Mt.24:8) So according to Jewish expectations, Jesus was claiming that the Messianic Age had come!
I know that Messiah (called Christ) is coming. When He comes He will explain everything to us. Then Jesus declared, 'I who speak to you am He!' (John 4:25-26)
New Messianic Age Since Jesus had already informed the disciples of the end of Judaism with its animal sacrificing temple worship (see John 4:21, Luke 16:16, Luke 19:41-44, Mt 24:2), it would be the Messianic Age He would be referring to in this verse under consideration. Jesus, the Messiah, will be "with us" until the very End (through the Holy Spirit presence? John 15-17). This End will be the end of the world (Gk. synteleias)
This "End" is the same one Jesus mentioned in Matthew 13 when He spoke of the End-time Harvest (13:36-43) Same Greek word, meaning "a total completion." Not simply a telos, such as a minor end of an era. Combining two of the translations listed by the Questioner, the Full End of the World, would reflect an accurate understanding of Jesus's intent.
{The Inter-testament and first century rabbis were not monolithic in their teaching on the "two ages," but they generally spoke of the Present Age, and of the coming Age of Messiah. For a thorough description of this, see J. Julius Scott, Jr., Jewish Backgrounds of the New Testament, 1995, chapters 13 and 14. At the end of the Messianic Age there was to be a Resurrection and Judgment.
A lot of the language, used by the Jews about the Messianic Age, is now called "apocalyptic." But Jesus and the Apostles used that terminology in reference to the present Messianic Age, the Kingdom of God Age (containing the Church which is populated by Jew and Gentile without distinction; Ephesians 2:14-18, Luke 3:8) }
Then the End will come, when He hands over the Kingdom to the God and Father, after He has destroyed all dominion, authority, and power. (1 Corinthians 15:24)