Consent in banking transactions
The provisions of the Indian Contract Act, 1872 relating to "consensus ad idem" which is a term meaning "meeting of minds" interpreted in contract law as "agreement on the same thing in the same sense" apply here.
You must note the provision for "Free Consent" which lists matters such as coercion, undue influence, fraud, misrepresentation, and mistake that vitiate the consent of a party in a contract and render it void or voidable in specific instances.
The information about the loan/banking product when given fully, and in accordance with banking regulations, satisfies the requirement for "consensus ad idem" as you are complying with the statutory obligations under banking regulations to provide such information which enables the customer to make the decision.
Thus, for instance, NBFC's are bound by the RBI Master Circular - Fair Practices Code which provides for provision of information on various aspects of the lending instrument to the borrowers. Circulars such as these are ostensibly intended to insure that the customer has full information about the product so as to ensure "consensus ad idem".
Standard Form of Contract
The Supreme Court of India has cited Chitty's Law of Contracts to give relief on the basis of such contracts, where it has cited this discussion/definition.
The use of standard form contracts.
The process or mass production and distribution, which has largely supplemented if it has not supplanted individual effort, has introduced the mass contract - uniform documents which must be accepted by all who deal with large-scale organisations.
When you ask a customer at your branch to sign on the dotted line of a loan agreement, you are in effect asking them to sign a standard form of contract. This is a contract which is used by corporates to give a "standard" set of terms and conditions, which are not substantively negotiable except for certain amendable provisions, such as the term and other negotiable components in your contract.
Under the Information Technology Act, 2000, the provision on what constitutes a valid "Electronic Signature" is important to note for the purposes of your question. (Electronic Signature is a broader category than the hash-able "digital signatures" with the latter falling within the definition of the former). Section 3-A says that it must be a technique that is either reliable or is listed in the Second Schedule.
This provision enables the electronic signature of loan agreements in any of the ways specified in the provision.
Hence, the effect of all of the above is that when a person signs your standard form contract, they are bound to return the loan amount with whatever interest as per the terms. They consent to do so when they "execute" the contract, as any standard loan agreement has a repayment schedule. This execution, which takes effect by the signing may be physically, or by way of digital signing methods deployed by digital lending apps.