If you purchase the $3600 plan, that's $100 a month....If you finance the extended warranty, it cost even more in interest.
I would recommend that you put the $100 a month in an interest bearing savings account and at the end of the 3 years, you will have over $3600. If you bought the vehicle new, your standard warranty would be coming to an end when the extended warranty would be needed, and now you have $3600 available for any contingencies that may come up.
If the vehicle did not have any major issues during the factory warranty period, then you are probably not likely to have any serious issues. If you had a lot of issues with the vehicle during the factory warranty, you might look at getting rid of the vehicle ASAP and you will have $3600+ to put down on your next vehicle
If I don't feel comfortable with the quality of any new vehicle I buy, I will look to getting rid of it shortly after the factory warranty expires. Of course, I have owned cars that went through the factory warranty period without incident, but after the warranty expired, they started to have issues.....again, if they were my primary vehicle, I got rid of them as fast as possible.
....Rich