All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.

Since the Messenger of Allah (PBUH) said: "When someone with whose religion and character you are satisfied asks your daughter in marriage, accede to his request. If you do not do so there will be temptation in the earth and extensive corruption."

Marrying such a person is permissible because he is a Muslim, and Allah may bless him with another job in which no usury/interest is involved. And Allah The Most Exalted Knows Best.