How to find the discount rate at which two deals are equally attractive? Dealer A will sell me a car for \$20,000 with \$2,000 down and the remaining $18,000 paid back over 36 months at a rate of 8% compounded monthly.

Dealer B will sell me the same car for \$19,500 with \$4,000 down and the remaining $15,500 paid back over 36 months at a rate of 10% compounded monthly.

(I assume these interest rates are APRs, since having them be monthly rates results in you paying more in interest than the price of the car.)

I'm asked to find the discount rate at which these deals are equally attractive. I assume this means the rate at which if I were to forgo buying a car and deposit amounts equal to the payments instead, I would end up having the same present value for both deals.

But when I try to calculate this I run into problems. I calculated the monthly payments for both deals, but then when I try to equate their present values and solve for the discount rate, I get that there is no positive discount rate for which these two deals are equally attractive. I've checked my math over and over and I'm sure it's correct so I must be thinking about the problem incorrectly. Anyone have any ideas?
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.