How to find the discount rate at which two deals are equally attractive?
Presuming the question is about inter-temporal choices and corresponding discount rate (not central banking).
It is rather easy to prove existence of such discount rate.

At one extreme, when discount rate is 100% (carpe diem mode), the person in question (N) will only look at the immediate value and expense. Dealer A effectively sells the car for \$2,000 (in present terms), while Dealer B sells it for \$4,000. So N will choose A.

At the other extreme, when discount rate is 0% (immortal person without any propensity for investment, perhaps?), N will just sum up all the value and expense streams. So A effectively sells the car for \$20,000 (both in present terms and in nominal terms), while B for \$19,500. So N will choose B.

With discounting function being continuous, it follows that somewhere between 100% and 0% there is a discount rate where A and B have the same present value.

PS: I am not sure if I should have posted this as a comment, but it's too long, and actually proves existence of the answer. I may expand this to include the actual solution if the question is updated to specify whether equal payments or equal principal payments or some other amortization schedule is used.