1 Cor. 11:23-26 (ESV)
For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread,  and when he had given thanks, he broke it, and said, "This is my body which is for you. Do this in remembrance of me."  In the same way also he took the cup, after supper, saying, "This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me."  For as often as you eat this bread and drink the cup, you proclaim the Lord's death until he comes.
Permit me to rant. I am beginning to really hate English translations of the Bible. The English speaking world is dominated by reformed theologians, and they cannot abide to let the language of the Bible say what it says. Here I complain about this word covenant. We still talk about the last third of the Bible as the New Testament, but now we talk of the New Testament itself as a covenant. Some may think I quibble here. But the New Testament is not the last third of the book we call the Bible. We call the last third of the Bible the New Testament because it records the New Testament, not the covenant. There is a difference between covenant, and testament. If Christ and or Paul wanted to say covenant they would have used the word syntheke, not diatheke. Syntheke would have denoted covenant, a contract between to living people, each with their own part to do. Diatheke is used for Testament, or what has commonly come to be known as a “will,” as in last will and testament. But the Reformed can’t seem to handle that. They want everything to be a covenant, if we don’t contribute to our justification, they are quick to point that we contribute to our sanctification. A proposition I seriously question. (And when I say reformed, unless otherwise noted, I am using it in my Lutheran freedom and right, inherited through Christ’s last will and testament, to refer to all who are not Lutheran, Catholic, or Eastern Orthodox. If you don’t like being lumped together with Neo Evangelicals and Arminians, get over it, or stop referring to the new covenant.)
You see the benefit of a covenant is earned. A covenant has rules you have to follow for fear of breaking the covenant. A Testament has no such thing. In a Testament a person dies, and those named receive, regardless of who they are and what they have done.
Sure there are laws, and rules recorded in the last third of the Bible along with the New Testament. But breaking these rules does not nullify the gift, the inheritance which is ours in the New Testament. In fact the inheritance we receive on account of the fact that Christ died, is meant to deal precisely with the problem of us breaking those rules. It is the forgiveness of sins, in Christ’s Body and Blood, it is eternal life. We did not nor can we do anything to earn this, to even try is to insult God, and add sin to sin. Christ didn’t come to give us new laws. What was wrong with the ones Moses gave? Nothing, which is why Christ didn’t come to give us new laws, or new rules in a covenant. We were guilty under the old rules; we are guilty under them, so He came to give us forgiveness, and grace. This is our inheritance. This is why it is a testament and not a covenant.