Is expiation obligatory upon one who swore an oath—in a state of intense anger—that he would not take a loan, then wished to help his brother who needs his signature to approve a loan secured by the house?

One should help a brother in need of marriage, as this is a form of cooperation in righteousness and piety, and it increases love. It is obligatory to ensure that the loan he will take is not usurious (riba-based); if it is, then it is impermissible to assist him. However, if it is a good loan (qard hasan), then there is no objection to helping him. You do not owe any expiation unless you swore an oath not to help him and then you helped him. In that case, an expiation for breaking an oath becomes obligatory, which is feeding ten poor people, or clothing them, or emancipating a slave. If one cannot find any of these, then he must fast for three days.