Define the annual percentage rate $($APR$).$ Suppose you borrow $$3,621\mathrm{.}15$ and take out a loan with an $8\%$ nominal interest rate. You must repay the loan with $48$ monthly payments of $$90$ each. In addition, you must pay an initial loan processing fee of $$100.$ What is the APR for this loan? show all the steps with excel as well as all the steps you would do with the calculator and all of the steps you would do if you were to use formulas. Be as detailed as possible.