If a lender purchase a house for $100,000 and add their profit $25,000 and sell this to a customer for $125,000 in installments, is this Halal
In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
In principle, if one purchases a house for $100,000, then sells it to a customer for $125,000 on installments, this is a permissible transaction. It is important to note that the price of the house must be stipulated. In the case of default by the buyer in the payment of the price at the due date, the price cannot be increased.
Note: Such a transaction in Islamic Finance is known as Murabahah Home Financing. In terms of Islamic Finance, the Murabahah transaction is inclusive of certain intricacies known to the Ulama. Such a transaction has been allowed by Ulama with some conditions. Unless these conditions are fully observed, Murabahah is not permissible. Therefore, a blanket ruling of permissibility cannot be given. Each Murabahah contract would have to be analyzed independently.
And Allah Ta’āla Knows Best
(Mufti) Abdul Azeem bin Abdur Rahman
The Shar’a ruling herein given is based specifically on the question posed and should be read in conjunction with the question.
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 An Introduction to Islamic Finance, Page 76
 An Introduction to Islamic Finance, Page 72-73