Depends how you want to do it. When you say design, do you mean 'sketch a body for'? If so, get yourself a vehicle design degree.
If you want to make your own car, then it is very much definitely knowledge, and not funding you need. However, let's start with the easy stuff that cash can buy.
Let's say you want to make a mid-engined car which weighs 1000kg, and has 500hp.
First. Design your powertrain. Forget it, it's too hard. So pick pick it off the shelf. Hmmm... cheap 500hp? Chevrolet LS7 engine. Gearbox to suit? Porsche/Getrag six-speed transaxle, plus an invert kit. Brand new, these components will set you back in the order of $30,000, once you include a few hoses, bolts, bellhousing etc.
Now you've got a powertrain. So you have to put it in something. Chassis design. Well, if you can use a sawzall and can weld, you're sorted. Designing a spaceframe chassis is quite hard, but only because you have to choose the compromises. A simple sketch will get you a design which will locate your powertrain, somewhere for the driver to sit, space for fuel tank, radiators, gearlinkages, and of course, four wheels and tyres hung off some suspension components.
Ah. Suspension. This is the fun bit. It has to be very good for a car with 500hp/tonne. And you have to decide whether it is going to be usable on a road or purely for a track. Tough. Plenty of books to help you out there. I'd recommend Milliken and Milliken. This will include a few other topics about vehicle dynamics.
Wheels and tyres... easy. Hubs, carriers, driveshafts, off the shelf if you look hard enough.
But... it has to look good. So, you need a design, and some way of making it.
Forget carbon fibre. Too much like hard work. Perfectly functional bodywork can be made in glass-fibre reinforced plastic. You will need to make your buck, refine it, smooth it, paint it, wax it... then take a female mould of it. Then, from that female mould, you'll make fibreglass parts to form your bidy. You'll need to figure out how many parts, how to fit them together, how ot fit them to the car, how they work with glazing (need a windscreen... unless it's a proper spyder!) door latches, making boot space, how to access the engine... how to fit the lights... and that's not even considering the interior!
So you've done all that. Did you read all the laws which govern how cars should be made and what should be where?
it it a thousand times harder than what I've said above... but it can be done on your own. Look up
http://www.kimini.com/ and see what you can do, and how long it takes. Plenty of links there to keep you busy.
And if you decide it's a bit much - cheat a little and build one yourself from a kit:
Go here:
http://www.ultimasports.co.uk/
Have fun. And if you do it, take the time to do it right.