Is it permissible to rent out a mortgaged house?
Question

                I belong to ARAMCO. This company offers a free-of-interest mortgage to build a house. Instalments will be automatically discounted from my salary every month for about fifteen years. The company provides the land for free.

Is it permissible for me to live in a floor and rent the other floor of the house? Knowing that it is owned by the company until mortgage is paid. 

The article (9) of the agreement with the company says:  

“You are not allowed to rent, sell or pledge the house under any case before the whole mortgage is paid, unless you get a written permission from the company. The company also has the right to take any suitable action it sees fit in case the contract is violated.”.
Praise be to Allah.
    This means that the mortgaged land is in pledge to the 
    company until the loan is paid off. The scholars differed as to whether it 
    is permissible for the one who is keeping something as a pledge to rent out 
    the property in question without the permission of the one who gave it to 
    him in pledge. 

    Some of them are of the view that this is not permissible. 
    This is the view of Imam Abu Haneefah and Imam Ahmad. 

    Others are of the view that it is permissible to rent it out 
    for a period that ends before the debt becomes due. This is the view of Imam 
    Maalik and Imam al-Shaafa’i. 

    Ibn Qudaamah (may Allaah have mercy on him) said in 
    al-Mughni (4/254): The one who is keeping the property in pledge does 
    not have the right to benefit from the property, by using it, dwelling in it 
    etc, and he does not have the right to dispose of it by renting it out, 
    lending it or otherwise, without the permission of the one who gave him the 
    pledge. This is the view of al-Thawri and ashaab al-ra’y. Maalik, Ibn Abi 
    Layla, al-Shaafa’i and Ibn al-Mundhir said: The one who is keeping the 
    pledged property has the right to rent it out or lend it for a period that 
    ends before the debt becomes due. End quote. 

    Undoubtedly the purpose of a mortgage or pledge is to 
    guarantee repayment of the debt, and the company has the right to sell the 
    mortgaged property and take the loan from its price if the time for paying 
    off comes and the debtor refuses to pay the debt or is unable to do so. 

    This guarantee is diminished if the house is rented out, 
    because it is difficult to evict the tenant, and that may take years, in 
    addition to the money and effort it will cost. 

    Hence the company has the right to stipulate that the 
    borrower is not allowed to rent out the house, because even if this renting 
    does not affect the rights of the company, it undoubtedly affects the 
    guarantee of repayment of the debt, and the Prophet  (peace and 
    blessings of Allaah be upon him) said: “The Muslims are bound by their 
    conditions, except a condition that makes a haraam thing permissible or 
    makes a halaal thing forbidden.” Narrated by al-Tirmidhi (1352) and Abu 
    Dawood (3594); classed as saheeh by al-Albaani in Saheeh al-Tirmidhi. 

    If the borrower has agreed to this condition then he must 
    abide by it. 

    And Allaah knows best.