$1.$ You need to borrow $$5000$ to buy a used car. The local bank will lend you the money with $10\mathrm{.}5\%$ interest compounded monthly. You plan to pay the loan of in one lump payment after two years.

$($a$)$ Find the periodic interest rate.

$($b$)$ How much will you have to pay back after the two years is up$?$

$($c$)$ How much interest are you paying $($in dollars$)?$