"Why does the Old Testament show a God of wrath and the New Testament a God of mercy?"

The God of the New Testament is the same as the God of the Old Testament. The Bible says that He never changes. He is just as merciful in the Old Testament as He is in the New Testament. Read Nehemiah 9 for a summary of how God mercifully forgave Israel, again and again, after they repeatedly sinned and turned their back on Him. The psalms often speak of God’s mercy poured out on sinners.

He is also just as wrath-filled in the New Testament as He is in the Old. He killed a husband and wife in the Book of Acts, simply because they told one lie. Jesus warned that He was to be feared because He has the power to cast the body and soul into hell. The apostle Paul said that he persuaded men to come to the Savior because he knew the "terror of the Lord." Read the dreadful judgments of the New Testament’s Book of Revelation. That will put the "fear of God" in you, which incidentally is "the beginning of wisdom."

Perhaps the most fearful display of His wrath is seen in the cross of Jesus Christ. His fury so came upon the Messiah that it seems God enshrouded the face of Jesus in darkness so that creation couldn’t gaze upon His unspeakable agony. Whether we like it or not, our God is a consuming fire of holiness (Hebrews 12:29). He isn’t going to change, so we had better ...before the Day of Judgment. If we repent, God, in His mercy, will forgive us and grant us eternal life in heaven with Him.