In EU there's a Directive that requires companies to offer two - not three - years of warranty.
http://ec.europa.eu/consumers/rights/gen_rights_en.htm#gar
Fwiw (not knowing where the OP lives) there are quite big differences between a warranty as it applies under EU consumer laws and AppleCare.
The EU warranty requires that the fault was present at the time of purchase or at the time of delivery/"performance" (depends on each country's laws). In other words, there has to have been a flaw in the product early.
AppleCare, however, does not require this but covers faults that appear later.
Under a consumer warranty the buyer may request certain things to be done to the computer. This is often replacement. However, it is free to the seller/company in charge of the warranty to first try to fix a problem by repairing.
The AppleCare is somewhat more flexible in this respect. In addition to being a service plan, AppleCare is a support plan, meaning that you can call for assistance. This doesn't exist under normal consumer warranties (at least in the EU).
Another benefit of AppleCare is that it is truly world-wide and that both mail-in and on-site service are offered. This is typically not offered by sellers based on the EU warranty.
http://www.apple.com/support/products/mac.html
Not in the EU afaik.
Remember that you can buy AppleCare "anytime within the one-year limited warranty period". So if you're low on money you can wait a bit.
http://www.apple.com/support/products/faqs.html
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