Jesus drank the wine and said, "It is finished!". Then he bowed his head and gave up his spirit. (John 19:30)
Excavators had found a ledger in Jerusalem which belongs to the period during which Jesus was among us in this world. In it were the words "It is finished". These words are noted to indicate that a debtor has paid their debt in full and that the debt is finished.
"It is finished" were the last words of Lord Jesus on the cross. He had paid for all our debts of sin through his death on the cross and he has made us free from our debts.
The synonymous use of debts and sins can also be seen in the King James' version of the Lord's prayer, where we say "Forgive us our debts, as we forgive our debtors".