The truck dealership is offering $0\%$ financing or a factory cash$-$back rebate of $$6,000.$ The purchase price with $0\%$ financing is $$45,000$ with $60$ monthly payments of $$750.$ Your local bank will provide you with a $100\%$ financing to purchase the truck. The truck loan would include an interest rate of $4\mathrm{.}9\%$ over $60$ months. The bank would charge a $$400$ loan origination fee. Please calculate annual percentage rate $($APR$)($Please show your work$)?$ Which financing offer has the lowest APR? How much will you pay for the truck with the zero percent offer? How much will you pay for the truck with the bank financing offer? $($Please use Excel for this problem and show you work$).($Hint what is the real value of the truck$)$