When you forgive, the debt doesn't just go away. You absorb the debt. That's why forgiveness is so hard.

(from Weekly Wisdom)

Say you lend a person one thousand dollars, but suppose that when the time comes for the loan to be repaid that person is unable to repay you. If you forgive that person of his debt, then that person no longer owes you anything. By forgiving, you forfeited the money—you absorbed the debt.

How is it that God is able to forgive our sins against him? He absorbed them by sending his son to suffer the penalty for our debts (sins). Christ absorbed the penalty of death so that we don't have to. When God forgave us, he said, "There's no need to repay me." (We couldn't repay God even if we tried, but now we're freed from the burden of trying.)
When you forgive someone, you absorb their debt. That's why forgiveness is so hard.

In Luke 7, Jesus tells this parable to Simon: "Two men owed money to a certain moneylender. One owed him five hundred denarii, and the other fifty. Neither of them had the money to pay him back, so he canceled the debts of both. Now which of them will love him more?" Simon replied, "I suppose the one who had the bigger debt canceled." "You have judged correctly," Jesus said.

Forgiveness is a sign of love. To forgive someone of a massive debt (in this case, five hundred denarii) is a sign of massive love. How is forgiveness a sign of love? Because if you forgive much, then you must absorb much debt (pain, suffering, loss, etc.). Our sin against God is the biggest possible debt we could have; so for God to absorb that is a sign of his endless, measureless love.

When He forgave us, God didn't just ignore our debt; he absorbed our debt.