How would the atonement work in the lives of the people that lived before Christ atoned for our sins?

Dear Gramps,
I was wondering if there were any scriptural references that you knew that could help explain how the atonement worked in the lives of the people that lived before Christ atoned for our sins.  How were they forgiven when the price hadn’t been paid yet.
Naomi, from Sacramento, California

Dear Naomi,
Let’s say that someone you knew had taken something from a store and not paid for it. Quite some time later you found out about it, had compassion on the person and went to the store and paid for it yourself. They committed the unlawful act before the price was paid. Your forgiveness and redemption of the person came only some time after they had committed the offense. It is the same with respect to the payment of the Savior for our sins. For those who lived after he had paid the price for their sins, that payment was just money in the bank to be used when it was needed.
Gramps