You are considering buying a new car for $$37,000.$ If you purchase the car you will pay $$7,000$ of the purchase price as a

down payment. Below are two options to choose from.

Option $1$: Pay off the amount borrowed to purchase the car with a $5$ year loan, and the annual percentage rate $($APR$)$ will

be $0\%.$

Option $2$: Receive a $$2,000$ instant rebate. This will lower your loan amount. Pay off the amount borrowed to purchase the

car with a $5$ year loan, and the annual percentage rate $($APR$)$ will be $3\mathrm{.}9\%.$

$($A$)$ Which option should you choose? Why?

$($B$)$ How much should the rebate be in order to make the two options equal?