Living in Rochester NY. Had a one year lease ready to move . This complex is privately owned corp. Its huge. Leaving Rochester office claims it will send security in one month time. Does this complex have the right to keep the interest my security deposit has gained. In the past living at other complexes I have received the interest from security deposits. Unsure this time.

Yes, the landlord owes you the interest. Check out Tenant's Rights Guide for your rights under NY law.

Here is a portion of the info there:

"Landlords, regardless of the number of units in the building, must treat the deposits as trust funds belonging to their tenants and they may not co-mingle deposits with their own money. Landlords of buildings with six or more apartments must put all security deposits in New York bank accounts earning interest at the prevailing rate. Each tenant must be informed in writing of the bank's name and address and the amount of the deposit. Landlords are entitled to annual administrative expenses of 1% of the deposit. All other interest earned on the deposits belongs to the tenants. Tenants must be given the option of having this interest paid to them annually, applied to rent, or paid at the end of the lease term. If the building has fewer than six apartments, a landlord who voluntarily places the security deposits in an interest bearing bank account must also follow these rules. For example: A tenant pays a security deposit of $400. The landlord places the deposit in an interest bearing bank account paying 2.5%. At the end of the year the account will have earned interest of $10.00. The tenant is entitled to $6.00 and the landlord may retain $4.00, 1% of the deposit, as an administrative fee."