Is it permissible to buy goods and pay their price, then sell them by installment at the same time, and is it permissible to appoint the installment buyer to purchase and then sell them to himself on condition that the amount be paid by installment?

It is permissible for someone who has bought and taken possession of a commodity to sell it in installments. As for authorizing a person to buy a commodity and then authorizing them to sell it to themselves, there is a difference of opinion among scholars.

The majority of jurists prohibit this if the authorization is absolute. They justify the prohibition by stating that custom dictates a sale should be to someone other than the agent, to avoid suspicion falling upon the agent, and because offer and acceptance cannot properly occur within a single person.

However, if the principal authorizes the agent to sell to themselves, there is also a difference of opinion on this matter: Hanafis and Shafi'is prohibit it according to the relied-upon view in their madhhabs, while Hanbalis permit it.

The preponderant view is that it is permissible for the agent to sell to themselves if the principal authorizes them to do so, especially if the price is specified; this is because the suspicion that was the reason for the prohibition is then absent.