Stating one price for a product if paid for in cash and another price if paid for in installments
Question

Is it permissible to state one price for a product if the purchaser is going to pay for it in cash, and another price if the purchaser is going to pay for it in installments? For example, this car costs fifty thousand in cash and sixty thousand by installments?.
Praise be to Allah.If the vendor says: this car costs fifty thousand if paid for in cash and sixty thousand if paid for in installments, one of two scenarios must apply: 
1 – The seller and purchaser part having agreed on one price and method of payment. In this case the transaction is valid. 
2 – If they separate without having agreed on the price. This transaction is haraam and is not valid. 
Al-Baghawi (may Allah have mercy on him) said in Sharh al-Sunnah – concerning this second type of transaction – This is invalid according to the majority of scholars, because it is not known which of them has stated the price. 
This is how many of the scholars interpreted the Prophet’s prohibition on doing two transactions in one. 
Al-Tirmidhi (1152) narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) forbade two transactions in one. This was classed as saheeh by al-Albani in Saheeh al-Tirmidhi, 985. 
Al-Tirmidhi said: this is what the scholars based their views on. Some scholars interpreted it by saying that two transactions in one means that the seller says, “I will sell you this garment for ten in cash or for twenty in installments, but when they part they have not agreed on either of the transactions. If they part having agreed on one of them, there is nothing wrong with that, if the contract is based on one of them. 
Al-Nasaa’i (may Allah have mercy on him) said: Two transactions in one means that a person says, “I will sell you this product for one hundred dirhams in cash or for two hundred dirhams in installments.” 
Al-Shawkaani said in Nayl al-Awtaar: The reason why two transactions in one is forbidden is that the price is not fixed because one thing is sold for two prices.  
The Standing Committee was asked: 
What is your opinion about selling a car of ten thousand in cash or twelve thousand in installments? 
They replied: 
If a person sells a car to another for ten thousand riyals, for example, if he pays cash, or for twelve thousand riyals if payment is deferred, and they part after the transaction is made without having agreed on either of the two options – the cash price or the price for delayed payment – this transaction is not permissible and it is not valid, because of the ambiguity concerning the final transaction and whether the price is to be paid now or later. This is how many of the scholars have understood the Prophet’s prohibition on making two transactions in one. This was narrated by Ahmad, al-Nasaa’i and al-Tirmidhi, and classed as saheeh by the latter. But if they agree before they separate  upon the price and one of the methods of payment, either the price in cash or the price if payment is deferred, and they separate having agreed upon the specific details, then the transaction is permissible and is valid because the price and conditions are known."(Fatawa al-Lajnah al-Daa’imah, 13/192 )
In another question: 
If the vendor says, “This product costs ten riyals if payment is deferred and five riyals if paid in cash, what is the ruling on that? 
The Committee replied: 
If the situation is as you described, then the transaction is not permissible, because it is a kind of two transactions in one. It was proven that the Prophet (peace and blessings of Allah be upon him) forbade two transactions in one, because that involves ambiguity that may lead to conflicts and disputes."(Fatawa al-Lajnah, 13/197)
Among the decisions of the Fiqh Council is the following: 
It is permissible to increase the price for deferred payment as opposed to immediate payment. It is also permissible to state the price if paid in cash and another price if payment is made in installments at known times. But the transaction is not valid unless the two parties decide as to whether this is to be paid in cash or paid later. If there is some confusion as to whether the payment is to be in cash or paid later, then there is no firm agreement on one particular price, so this is not permissible according to sharee‘ah. 
And Allah knows best.