I don't think you should be paying for it at all! Warranty or not you are protected under the sale of goods act unless you were told about this fault before buying. If as in your case you find a major fault within a few days or weeks of purchase you are very much entitled to expect a repair.
Check ou this post:
Sale Of Goods Act (buying A Vehicle) - Your Rights
Here are a few other guidlines for you.....
1. What should you expect?
Dealerships must abide by the law and sell good quality vehicles that are correctly described. They should offer some kind of warranty and be using services such as HPI and the National Mileage Register to check the vehicles they are selling. Before you buy, ask to see the dealer's HPI certificate. If they can't provide this proof, then get a check done yourself to be on the safe side.
2. Codes of practice
For added reassurance, find out which of your local dealers belongs to a trade association that requires the firm to abide by a code of practice. Contact the
Retail Motor Industry Federation (RMIF) or
Scottish Motor Trade Association (SMTA) for a list of members.
3. The laws
Dealers have to comply with a whole range of legislation, some of which is specifically targeted at the motor trade, including (links open in a new window):
4. What is 'satisfactory' quality? Sale of Goods legislation rules that the car must meet the standard that a reasonable person would regard as acceptable, bearing in mind the way it was described, how much it cost, and any other relevant circumstances. Apart from usual wear and tear, a used vehicle must be free from defects - except ones pointed out to you and those which should have been uncovered by an inspection (but only if one has been done). Legislation also requires dealers to sell cars only where they have
good title.
5. What does 'as described' mean?
Under the Trade Descriptions Act 1968, all descriptions applied to a vehicle must be true. For instance, a car cannot be advertised as having had one careful owner if it has actually had three.
6. What does 'reasonably fit for the purpose' mean?
If you have said that you will be using a vehicle for towing a caravan, for example, it must be fit for that purpose - unless the dealer has specified otherwise. Ask for written confirmation of the purpose as proof. For extra reassurance, HPI offers a unique outfit matching service to ensure the car you want to buy can legally tow your caravan. For a fee, you can check the match at
www.towsafe.co.uk.
7. Does a car have to be roadworthy?
It's not illegal for a dealer to sell you a car that has been a
total loss, provided that you have been made aware of the fact. However, the Road Traffic Acts provide that any vehicle sold for road use must be in roadworthy condition. If the seller cannot provide a
Thatcham-approved inspection report, copies of most inspections are available from HPI at an additional cost.
8. What should you do if you are unhappy with the vehicle you have purchased?
Return to the dealer and, if he refuses to take action, contact the following organisations for advice (links open in a new window):
bought a second hand car and now with problems 
