According to Paul, Jesus achieves salvation by representation. Jesus’ sacrifice atones for those who have faith in it. When one acknowledges one’s own inadequacy at following the Law and accepts Christ’s sacrifice as sufficient, in and of itself, for redeeming fallen man (that works cannot and do not add anything to salvation), one is saved.

Man, by nature, is fallen and sinful. Right-off-the-bat, man has already violated the Law of God and can, thus, never keep the Law perfectly. Any hope of gaining righteousness by doing any good deed is utterly futile, because man can never change the fact that he has not kept the law perfectly. Thus, salvation must be achieved by something other than following the Law.

Since man does not keep the Law perfectly, man’s punishment is Hell. This damnation to Hell is the righteous and just judgment of God, because the wages of sin is death, and if God didn’t punish sin with death, He would not be just. But because God loved man, He offered His Son up as a sacrifice to satisfy His own judgment on the select group of people, who have faith in Christ’s sacrifice.

God doesn’t simply forget about the sins of some to let them into Heaven. Their sins still have to be paid for. So, instead of sentencing some people to eternal damnation, He punishes Christ for their sins in their stead.

Christ is the center of salvation, because all God is concerned with (as far as people getting to Heaven is concerned) is whether or not there is still sin accounted to a person. Either a person has faith in Jesus’ sacrifice and his sins are thus paid for by Christ, or a person doesn’t have faith in Christ’s sacrifice, alone, and his sins are still accounted to him. Works have nothing whatsoever to do with it. Doing good works is nothing, because as soon as a man sins once in his life, works can no longer be considered in gaining access to Heaven.

When a man has faith in Christ’s sacrifice alone for his salvation, that man’s wickedness is then accounted to Christ, and Christ’s righteousness is accounted to the man. God’s justice simply demands that the sins be paid for—it doesn’t necessarily have to be the man who actually committed the sins who pays for them. Since Christ lived a life completely perfect under the Law, He had the ability and authority to do this “sin-for-righteousness swapping.”