You are in the process of purchasing a new automobile that will cost you $$25,000.$ The dealership is offering you either a $$1,000$ rebate $($applied toward the purchase price$)$ or $3\mathrm{.}9\%$ financing for $60$ months $($with payments made at the end of the month$).$ You have been pre$-$ approved for an auto loan through your local credit union at an interest rate of $7\mathrm{.}5\%$ for $60$ months.

Required: Should you take the $$1,000$ rebate and finance through your credit union or forgo the rebate and finance through the dealership at the lower $3\mathrm{.}9\%$ APR? $($