He is going to rent a house and what he has paid will be returned to him at the end of the lease

Firstly: 

It is not permissible to do the deal in this manner. This is a form of loaning with interest, which is haraam. 

The reason for that is that a loan means giving money or property to someone to benefit from it and then give it back. 

The money that is given to the landlord will be returned after the agreed lease period ends, so this money is a loan, and the lender benefits from this loan by making use of the house until his money is returned to him. So this deal is in fact a loan which brings a benefit, and the scholars are agreed that every loan which brings a benefit to the lender is haraam, because it is a type of riba. 

Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (6/436): 

Every loan in which it is stipulated that something extra be given (when paying back) is haraam, with no dispute. Ibn al-Mundhir said: They are unanimously agreed that if the lender stipulates that the borrower should give something extra or give him a gift, and he gives the loan on that basis, then taking the extra amount is riba. It was narrated from Ubayy ibn Ka’b, Ibn ‘Abbaas and Ibn Mas’ood that they forbade loans that bring benefits. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in al-Sharh al-Mumti’, 4/64: 

An example of benefits as a condition of a loan is when a man comes to another man and says: “I want you to lend me one hundred thousand,” and he says, “But I will live in your house for a month.” Here the loan brings a benefit to the lender so it is haraam and is not permissible. 

The basic principle concerning loans is that they are an act of kindness towards the borrower, but if conditions are introduced it becomes a kind of business deal, and if it is a kind of business deal then it involves riba al-fadl and riba al-nasee’ah. So for example if someone borrows one hundred thousand from me and I stipulate that I will live in his house for a month, then it is as if I sold him one hundred thousand in return for something extra, which is my living in the house for a month. This is riba nasee’ah because it is a delay in handing over what has been borrowed, and it is riba al-fadl because it involves giving something extra. 

Hence the scholars said that every loan that brings a benefit is riba. End quote. 

It says in al-Mawsoo’ah al-Fiqhiyyah (3/266): 

The conditions of a loan being valid: 

The first condition: the lender should not benefit. If the lender benefits form giving the loan either by stipulating conditions in the contract or otherwise, then if it is by stipulating conditions then it is haraam without any scholarly dispute on that point… end quote. 

Secondly: 

Attention should be paid to what a contract really involves in spite of what it is called. In fact this contract – as stated above – is a loan that brings benefits, and this is a kind of riba. The fact that people call it renting does not alter the fact at all, and does not change the ruling thereon. The Prophet SAWS (peace and blessings of Allaah be upon him) told us that some people among his ummah would drink khamr (alcohol) and call it by another name. 

So beware of making halaal things that are haraam. Paying a small amount as rent does not make this haraam action permissible, because the larger amount that is paid is still a loan that brings a benefit. 

The owner of the money has not paid the larger amount of money (the loan) which will come back to him for any purpose other than to make use of the house, and the owner of the house has not given the house to the other person to use except in return for the loan. 

Nothing is hidden from Allaah, and He has punished the one who makes haraam things halaal by means of trickery with a swift punishment, as happened in the story of the Sabbath-breakers (see al-Nisa’ 4:47 and al-A’raaf 7:163). 

And Allaah knows best.