The Bible says that the wages of sin is death (Romans 6:23). So the question becomes two questions: 1) who has sinned, and 2) what is death? The answer to the first question is given in Romans 3:23 – all have sinned. But what part of us has sinned? Every part of us has sinned; body, soul, and spirit. We cannot say that only our body and soul sinned but our spirit is righteous (or any claim that any part of us is sinless). Therefore, all of us must die to pay for that sin. So we must understand what death is. Death is separation from life. For our bodies and soul, this is what we customarily call physical death. But our spirits must pay the penalty for our sin as well. Our spirits will exist forever after our physical death, so physical death does not result in our spirits` death. Life for our spirits is communion with God, so death for our spirits is separation from God, which is also called "eternal damnation". Therefore, stating that the punishment for sin is death INCLUDES eternal separation from God. It is not a separate and added penalty.
Fortunately for us, God has provided a way (through Jesus) for our spirits' penalty for sin to be paid for us, so we don't have to face eternal separation from God. Jesus had no sin, so when He paid the penalty for sin, God imputed His righteousness to everyone who believes in Jesus. Our body and soul will still die, but our spirits will be able to enjoy communion with God.
