Hi VT-SDS,
Yes, you will be able to get a loan from banks for your type rating. Your LOI would only be a supporting document. Along with that you would need to furnish security in the form of mortgage ex. house, land etc.
Loans from Nationalized banks instead of private banks is recommended since the rate of interest is slightly low.
However, you would not get 100 % loan. Usually the applicant needs to fund approx 15-25 % of the total amount himself.
Punjab National Bank I have heard recognizes the IndiGo LOI among a few others.
Go for an 'Education loan' rather than a 'Personal loan'. Personal loans are more expensive. Moreover you do not get a moratorium period in a personal loan. Payback starts immediately. In an education loan the bank gives a moratorium period of 1-2 years to start repaying.
You will need to visit atleast 4-5 banks and pick the best option.
All the best !
