All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
For this transaction called "rent (or lease) to own" to be permissible, it is a condition that the rent contract should be different from the sale contract and each one should be independent from the other in a point of view of time (i.e. the two contracts may not be concluded in one contract at the same time). For instance the contract of sale should be done after the rent contract, and it is permissible to have a promise of ownership at the end of the rent period provided that it is not an obligation to fulfil the promise.
Secondly, the rent contract should be real and not as a means to cover the sale. This could be known if the price determined for the rent is the real rent and if the rulings of rent are applied during the entire period of rent. Also, the rulings of sale should start at the beginning of the sale contract and the conditions of both contracts should not be applicable on the same property at the same time. For more benefit, please refer to Fatwa 81863.
The Islamic Fiqh Committee Resolution (number 44/56) reads: "It is permissible to conduct a rent contract whereby the tenant can benefit from the rented place (be it a car, a house or else) in return for a definite price during a definite period of time. Therefore, the owner may give to the tenant the option of owning the rented place at any time he wishes, provided that the sale should be dealt with at its time with a new contract and according to the market price."
Therefore, if the contract which you mentioned in the question corresponds with the above, then this contract is permissible.
As regards the security (deposit) which the owner puts on the tenant, then if this amount is for the purpose of protecting the right of the owner (bank) concerning the rent or in case of neglect or transgression of the tenant about the rented item, then this is permissible. However, if the case is not for what has been mentioned, then the deposit is not permissible because it is the owner who guarantees the rented item and not the tenant.
Allaah Knows best.