Marti is buying a car and is trying to figure out which is the best deal offered by the dealership. The car price is $$36,000$ and she has the choice of:

Cash Option: Paying cash today with a $5\mathrm{.}00\%$ discount $(95\%$ of the car price$).$

Financing Option: She would pay $$1,000$ per month for $36$ months starting at the end of the first month $(0\%$ financing$).$

Marti wants to use an $4\mathrm{.}00\%$ effective annual rate to evaluate the two deals. On a present value basis, which of the two deals is better and by how much?

Group of answer choices

The financing option is better by $$160$

The financing option is better by $$293$

The cash option is better by $$69$

The cash option is better by $$184$