I am in gold business, I could not sell the gold on credit and some of my customer don't have enough money, the prefer installments, so could I arrange for them cash loan to be paid back in same amount in predefined time, by which they will use to buy gold from me?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is not permissible to lend money to your customers in order for them to buy goods from you, whether it is gold or not. The evidence about this is the narration of the Prophet which reads: "It is not permissible to lend money to someone in order that he will buy from you." [An-Nasaa'ee and At-Tirmithi] This narration is also interpreted to mean to lend money to someone and to sell him goods for a higher price than their actual price. This is forbidden as this loan is a way of advertising for one's goods with this money. Any loan that brings a benefit is forbidden.  However, if someone obtains a loan from a third person with whom you have no relationship, then there is no harm in this, Inshaa' Allaah.

Allaah knows best.