Dr. Monzer Kahf, a prominent Muslim economist and counselor has this to say on student loans with an interest rate linked to inflation: In lending, the Shari’ah requires that a loan be due in the same currency by which it was given. At the time of payment it may be paid in any other currency, as long as it is paid at the exchange rate of the day of payment. You cannot change what is due from a person, and any increase in what is due from a person is Riba.
This was easy to apply when gold and silver were the base of all currencies. The problem started when cheating in the percentage of pure silver in currencies began. When this occured, you had the same Dirham, but not the same quantity of silver in it. Then we got paper currencies whose value (purchasing power) varies with changes in many variables, which the two parties of a loan usually don’t have any control over. So then what do we do?
We have to distinguish between two cases, a large or big difference in the value of currency between the date the loan is given and the date it is paid, and a small difference. People usually tolerate small changes in the value of money (as we notice that they continue keeping cash and checking accounts when the inflation rate is small). In the case of a small difference in the value of money, the great majority of Muslim scholars emphasize the principle that if a loan is paid in the same currency, it must be the same number of units regardless of the change in prices. (We must note here that even gold and silver, when they were common currencies, also had small changes in their prices from time to time.) Any increment in this case is Riba, and forbidden.
In the case of big disparity in the value of money between the day a loan is given and the day it is paid back, there are three opinions:
1) The majority of scholars say that the same principles apply, yet, they say that any substantial injustice to either party, in a loan, must be dealt with through certain compromises, even if such compromises are imposed by the government. These injustices must be treated on a case-by-case basis because each case is not always in the same situation or in the same circumstances, and sometimes part of it involves the normal expected and or unexpected risk people usually undertake.
this group objects to any general measure, like indexation of loans and bank checking accounts. They argue that at a time of high inflation Riba-minded people love indexation because the real rate of interest is sometimes negative, i.e., inflation is more than the nominal interest rate.
2) Some scholars argue that unless the currencies are cancelled absolutely, payment of loans must be in accordance with the number of units only, regardless of value.
3) And some argue for general indexation.
now we come to your specific question, increments in a student loan, which charges an interest rate equal to the rate of inflation, are a form of Riba. It is covered by the definition of Riba in Duyun (loans) i.e. any conditioned increment in a loan. Yet, one may argue that while Riba is the price of money through time, the compensation of inflation is not a price of money; it is rather the cost of lending.
the OIC Fiqh Academy , in five of its annual meetings, could not solve this controversy, and I don’t think it is going to. I think it is a Riba, although it less severe than normal increments that are not tied to inflation.

As for the permissibility of taking a Riba-based loan for study, Dr. Muzammil Siddiqi, former president of the Islamic Society of North America (ISNA), says: Like all other loans, Student loans are also permissible as long as they don’t involve interest. However, if a student is in dire need to pursue his/her studies and no loans are available without interest, then in that case, under the rule of necessity, it will be permissible for the student to take the minimum loan and he/she should pay it back as soon as possible. This is of course, in the case when pursuing that field of education is also very important for the future of the Muslim student. But if a study is not necessary and it is only as a matter of enhancement of one’s knowledge, then one should not take loans with interest.