Praise be to Allah.
If what is meant is that you are buying the car from the company by instalments, whereby you give a first payment of approximately ten thousand, then you pay monthly instalments, there is nothing wrong with that, because it is a valid transaction, which means that the car will enter your possession with the first payment, but the company has the right to stop you selling it, which means that it is held in pledge for them until you have paid off all the instalments.
This contract has nothing to do with hire-purchase, but it is not clear why they are taking the payments that you mention, which is approximately two thousand and eight hundred riyals.
If the contract is a contract for renting the car, paying such and such every month, with a promise that you will take possession of the car at the end of that period, this is permissible so long as the rental contract is a genuine contract and is not a cover for selling in which liability for the rented item (the car) is borne by the entity that is renting it out (the company), and not by the one who is renting it, as is basic maintenance apart from running costs throughout the rental period. This is different than a sale, because in a sale the liability and basic maintenance pass to the buyer because he takes possession of the item as soon as the contract is done.
It is permissible for the rental contract to be accompanied by a separate contract of giving, conditional on the entire rent being paid off, in which it is stated that the item is being rented for a specific fee and for a specific length of time, then it states that it will be given, such as if it says: The two parties have agreed that the first party (the company, for example) will give the car to the second party (the customer) when the time period ends and he has paid off all the instalments that he owes.
The Islamic Fiqh Council has issued a statement on hire-purchase agreements, and has explained the various forms (of such contracts) that are permissible or not permissible. They have stated that it is permissible for a rental contract to be accompanied by “a contract giving the item to the renter, subject to the condition that he pay the rent in full. That may be in a separate contract or a promise to give it after he pays off the rent in full.” End quote. See also the text of the statement in full in Fiqh al-Nawaazil by Dr. Muhammad Hasan al-Jeezaani (3/301).
If the company has stipulated that the liability and basic maintenance of the car – apart from running costs – are to be borne by the renter, then it is an invalid contract and is not really a rental, and it is not permissible for you to enter into this transaction.
There also remains a problem with the first payment and with the fees that are approximately two thousand and eight hundred. If the first payment is counted as part of the rent, there is nothing wrong with that, otherwise it is essential to explain the reason why this amount is to be paid.
As for the fees, we do not know their conditions
What we advise you to do is to buy a car by instalments directly from the seller or by means of what is known as muraabahah, so you buy it through al-Rajihi Bank, after the bank buys it from the seller. This is safer and more beneficial for you, and you will become the owner of the car when the transaction is done, unlike the case with a hire-purchase agreement, where you will still be renting until the end of the period, and the company may or may not fulfil its promise at the end, and there is the possibility that you may fall into haraam if you do not fulfil the conditions of this transaction.
And Allaah knows best.