$($a$)$Upon entering college, you purchase the car of your dreams for $$26000.$ You pay $$5200$ down and finance the balance for $4$ years at $7\%$ compounded monthly $.$ Your monthly payments are $$498\mathrm{.}09.$ Set up the spreadsheet to display the outstanding balance for each month for $4$ years. As a checkpoint, you should get $$16931\mathrm{.}98$ just after your $10$th payment.

How much is still owed on the loan just after $30$ payments.$

Find the size of the last payment. $

How much interest in total did you spend on the car? $

$($b$)$If you decided to get a $3$ year loan instead of a $4$ year loan the payments will be $$642\mathrm{.}25.$ What will be the total saving in interest from getting a three year loan instead of a $4$ year loan?$($Note: you do not need a spreadsheet to answer this question.$)$ $

$($c$)$If you decided to get a $5$ year loan,the payments will be $$411\mathrm{.}87.$ Determine the total amount of interest that will be paid on a $5$ year loan $