Problem $6\mathrm{.}3$: You have been shopping for a nice new mattress and found just the one you want from Dreamland Mattresses. The price $of$ the mattress $is$ $$2,499\mathrm{.}00$ and they offer financing with a annual rate $of9\mathrm{.}0\%$ compounded monthly.

$a.$ How long $(in$ years$)$ will $it$ take you $to$ pay off the loan $if$ you make payments $of$ $$65$ per month? Make sure $to$ show you answer $to$ two decimals.

$b.$ How much will you pay $in$ interest over the life $of$ this loan?