What does the Bible teach about hope?
The Bible teaches that from the moment of conversion, God assures us that we already have eternal life.
Very truly I tell you, the one who believes has eternal life.
We have this hope as an anchor for the soul, firm and secure. It enters the inner sanctuary behind the curtain, where our forerunner, Jesus, has entered on our behalf.
Dictionary of "Mormonese"
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What does Mormonism teach about hope?
In Mormonism, it’s impossible to know one’s eternal destiny until Judgment Day, where Mormons will find out if they are worthy enough.
As we repent of our sins, giving up every impure thought and act, the Holy Ghost will change our hearts so we no longer have even the desire to sin (see Mosiah 5:2). Then when we are judged, we will be found ready to enter into God’s presence.
Gospel Principles, Chapter 46: The Final Judgment
We have sure hope because we have eternal life with God, right now.
Mormons hope that they will be judged worthy enough on Judgment Day.