Some say the deposit, which I don't understand and others say off the payments.

I would offer an incentive for signing a longer term lease- $50 less a month than your new month to month price maybe.At closing, make sure they transfer the security deposit and prorated rent for whatever was collected that month.Kelly

Can a Security Deposit Be Used For Unpaid Rent in Chicago?

Have them deposit in a bank account.Have them mail to you.

I have had tens of thousands of dollars of damage caused by 'good dogs' and "wonderful, loving" cats-some so severe that it was almost better off to demolish the property.Even if I accepted a substantial ( and by substantial, I mean $10k or more) pet deposit  I still run the risk of exceeding that if enough damage is done. 

Also, do I have to keep tenant security deposits and last month's rent in a separate trust account?

The deputy has been depositing the money into his personal checking account to take $50 out for himself for managing the property and sending the remainder the owner out of state.  

Gross Potential Income $132,000 - Vacancy ($10,560) 8% - Concessions, Loss to Lease, Bad Debt $0 Effective Gross Income $121,440 Other Income (Laundry) $2,500 Total Net Income $123,940 EXPENSES Real Estate Taxes $12,500 Insurance $0 Contract Services $2,190 Trash Removal $0 Electric $0 Gas $0 Water and Sewer OR All Utilities $37,500 Legal $1,000 Management Fee 8.00% $9,915 Repairs and Maintenance  $7,500 General/Admin $1,100 Payroll $0 Other $500 Deposit to Replacement Reserve $3,000 Total Expenses $75,205 Net Operating Income (NOI) $48,735 Debt Service Principal $7,384 Interest $24,857 Total Debt Service $32,242 Total Distributions to Members $16,493 Member Contribution $234,163 ROE 7.044% Member Cash on Cash Return 7.04%

The contract also states "This offer shall remain open___ o'clock___   ______and if not accepted by said time this offer shall be deemed rescinded and all deposits shall be refunded."  

The key is to start with a sufficient security deposit and clear expectations defined in the rental agreement.