No institute provides education loans by itself, but these institutions have banking partners who provide education loans. There is a huge number of banks that provides education loan, like SBI, Canara Bank, Bank of Baroda, and many more.
The interest rates vary according to the bank. The interest rates start from 6-7% and go up to 11-12%. Every bank has a rating system for institutes, and according to those ratings, they decide the interest rate. For IIMs, Canara Bank provides education loans at 7% per annum. IIMs are listed in category 1 for Canara Bank. Similarly, you can check your institute on its website.