You are about to buy a $$40,000$ car. The dealership gives you two alternative offers for financing the purchase: a$.5-$year loan, equal monthly payments, $0\%$ APR b$.5-$year loan, equal monthly payments, $1\mathrm{.}9\%$ APR, with $$2,000$ cash back today Which of the above two offers should you accept and why? $($Show complete work and formulas$)$