Many people falsely assume that only New Testament believers are saved by grace whereas Old Testament believers were saved by their obedience to the law of Moses and not by grace. The truth is that both the Old and New Testaments clearly teach that everyone who is saved, throughout all history, is saved the same way: by grace, through faith, on account of Christ alone.
In fact, the New Testament writers argue their case largely by appealing to the Old Testament Scriptures themselves. First, after spending the bulk of three chapters to prove that both Jews and Gentiles are unrighteous, quoting extensively from the Old Testament (Rom. 1-3), the apostle Paul concludes that no one will be declared righteous by observing the law (Rom. 3:20).
Furthermore, Paul points to Abraham, the father of the Jews who lived long before Moses, as his prime test case to prove that salvation comes through faith apart from works that we perform. Paul writes, "If, in fact, Abraham was justified by works, he had something to boast about--but not before God. What does the Scripture say? 'Abraham believed God, and it was credited to him as righteousness' " (Rom. 4:2-3; cf. Gen. 15:6; Gal. 3:6-9).
Finally, Jesus Christ is the fulfillment of all the symbols and predictions of the Old Testament (Luke 24:44; Rom. 3:21-22; Heb. 1:1-3). For example, the Jews celebrated the Passover every year to keep them focused on the One who was to come to die for their sins. As the book of Hebrews says, "The law is only a shadow of the good things that are coming--not the realities themselves. Day after day every priest stands and performs his religious duties; again and again he offers the same sacrifices, which can never take away sins. But when this priest [Christ] had offered for all time one sacrifice for sins, he sat down at the right hand of God because by one sacrifice he has made perfect forever those who are being made holy" (Heb. 10:1, 11-12, 14).
Jesus Christ stands at the apex of history. Just as we look back in history to Christ's sacrifice for our sins on the cross, Old Testament believers looked forward to His sacrifice for them.