Taking a riba-based loan in order to rent an apartment

Firstly: 

We ask Allah, may He be exalted, to bestow His bounty upon
you and make you independent of means with that which He has permitted, and
to protect you from riba, whether the amount involved is small or great. 

Secondly: 

Riba is a major sin, concerning which there is a stern
warning as is quite clear. The basic principle is that it is prohibited in
all forms.

In Fataawa al-Lajnah ad-Daa’imah (13/385) it says:

What is the Islamic ruling on taking a loan from the bank
with interest (riba) in order to build a modest house? 

Answer: 

It is prohibited to take loans from the bank or elsewhere
with interest, whether the loan is taken to build a house or to be used on
buying food, clothing or medical treatment costs, or it is taken in order to
do business with it and earn profit on it, or for other purposes, because of
the general meaning of the verses that prohibit riba, and the general
meaning of the hadiths which indicate that it is prohibited. By the same
token, it is not permissible to deposit money in banks and the like in
interest-bearing accounts. End quote. 

No exception is made from that, except cases of clear
necessity, such as if a person cannot find food or drink or clothing or
accommodation except by taking a riba-based loan, as explained previously in
the answers to questions no. 123563,
94823.

Necessity with regard to accommodation can be met by renting,
not by owning. 

So strive hard to look for permissible work which will enable
you to provide such accommodation. 

If you cannot find any work, then it is permissible for you
to take a riba-based loan in order to rent accommodation that will meet your
needs, without going to extremes in that, because necessity is to be
properly estimated. 

Al-‘Allaamah ash-Shinqeeti (may Allah have mercy on him)
said:

There is no difference of opinion among the scholars that
necessity is connected to specific situations that require rulings different
from those which apply in situations where one has options. So for every
Muslim who was forced into something in a true sense of the word, lenience
should be prescribed in his situation. 

Allah, may He be glorified and exalted, made exceptions in
cases of compulsion (when one has no choice except one option in five verses
in His Book, where He listed the four prohibited things which are most
emphatically prohibited, namely dead meat (meat that was not slaughtered in
the prescribed manner), blood, pork and that which is slaughtered for anyone
or anything than Allah. Every time Allah mentions the prohibition on these
things, He makes an exception for cases of necessity. Thus in the case of
necessity these things are not haraam. 

Allah, may He be exalted, says in Soorat al-An‘aam
(interpretation of the meaning):

“Say (O
Muhammad (blessings and peace of Allah be upon him)): ‘I find not in that
which has been inspired to me anything forbidden to be eaten by one who
wishes to eat it, unless it be Maytah (a dead animal) or blood poured forth
(by slaughtering or the like), or the flesh of swine (pork, etc.) for that
surely is impure, or impious (unlawful) meat (of an animal) which is
slaughtered as a sacrifice for others than Allah (or has been slaughtered
for idols, etc., or on which Allah’s Name has not been mentioned while
slaughtering). But whosoever is forced by necessity without wilful
disobedience, nor transgressing due limits, (for him) certainly, your Lord
is Oft-Forgiving, Most Merciful.””

[al-An‘aam 6:145]. 

And He says, also in al-An‘aam (interpretation of the
meaning):

“And why should you not eat of that (meat) on which Allah’s
Name has been pronounced (at the time of slaughtering the animal), while He
has explained to you in detail what is forbidden to you, except under
compulsion of necessity?”

[al-An ‘aam 6:119]. 

And He, may He be exalted, says in an-Nahl (interpretation of
the meaning):

“He has forbidden you only Al-Maytah (meat of a dead animal),
blood, the flesh of swine, and any animal which is slaughtered as a
sacrifice for others than Allah (or has been slaughtered for idols etc. or
on which Allah’s Name has not been mentioned while slaughtering). But if one
is forced by necessity, without wilful disobedience, and not transgressing,
then, Allah is Oft-Forgiving, Most Merciful”

[an-Nahl 16:115]. 

And He, may He be exalted, says in al-Baqarah (interpretation
of the meaning):

“He has forbidden you only the Maytatah (dead animals), and
blood, and the flesh of swine, and that which is slaughtered as a sacrifice
for others than Allah (or has been slaughtered for idols, etc., on which
Allah’s Name has not been mentioned while slaughtering). But if one is
forced by necessity without wilful disobedience nor transgressing due
limits, then there is no sin on him. Truly, Allah is Oft-Forgiving, Most
Merciful”

[al-Baqarah 2:173]. 

And He, may He be exalted, says in al-Maa’idah
(interpretation of the meaning):

“Forbidden to you (for food) are: Al-Maytatah (the dead
animals – cattle-beast not slaughtered), blood, the flesh of swine, and the
meat of that which has been slaughtered as a sacrifice for others than
Allah, … But as for him who is forced by severe hunger, with no
inclination to sin (such can eat these above-mentioned meats), then surely,
Allah is Oft-Forgiving, Most Merciful.”

[al-Maa’idah 5:3].

See: al-Qawaa‘id an-Nooraniyyah by Shaykh al-Islam
(205); al-‘Uqood by Shaykh al-Islam (37); Madaarij as-Saalikeen
by Ibn al-Qayyim (1/376-377) 

And Allah knows best.