When Jesus speaks of peace, he doesn’t mean the absence of troubles in the earthly realm. Jesus means the wonderful, inner peace He wants to give us. As Jesus’ beloved sheep, we can (and should) live without fear because Jesus has completely and fully reconciled us to God. There is no more condemnation for a Jesus-believer.
“Peace I leave with you; my peace I give you. I do not give to you as the world gives. Do not let your hearts be troubled and do not be afraid.” (Jesus in John 14:27; NIV)
God doesn’t even see our sins (Hebrews 8:12, Hebrews 10:17). He once and for all punished Jesus: “… you have put all my sins behind your back.” (Isaiah 38:17; NIV).
There is also a prophetic announcement in Micah for the glorious freedom that we, as followers of Jesus, can gratefully enjoy: “You will again have compassion on us; you will tread our sins underfoot and hurl all our iniquities into the depths of the sea.” (Micah 7:19; NIV)