What is the ruling on buying necessities in installments, and is it permissible to take an additional amount in exchange for the installments, or is it forbidden?

This question describes two types of purchases:

1. First Method: Immediate purchase with the condition of taking an additional amount for every thousand, to be repaid with the installments.

Permissible Scenario: The merchant genuinely purchases the commodity and it enters into their guarantee and ownership, then they sell it to you in installments at a higher price.

Prohibited Scenario: The merchant does not actually purchase the commodity, but instead pays its price to the seller on behalf of the buyer to reclaim it with an increase (an interest-bearing loan).

2. Second Method: Requesting a partial payment and mortgaging gold for the remainder in interest-free installments.

This method is permissible, provided that the lender does not benefit from the mortgage in any way, for every benefit drawn from a loan is usury (riba).