Rental agreements are normally made for 11 months to save on stamp duty & other registration costs, because any rental agreement for 12 or more months have to be compulsorily registered.
Normally, rental agreements consist of provisions for termination of the agreement before the 11 month period, whereby the landlord or the tenant can terminate the agreement before 11 months by giving sufficient notice period to the other party (usually 1 month) in writing. In your case, if no such clause termination clause is there in the rent agreement, I think it is correct to say that you need to pay rent for 11 months, regardless of your staying for 11 months or not. Pls explore the risk of the landlord NOT returning the security deposit even after you have the house painted.