Suppose Mark buys a $$27,000$ car. She puts $15\%$ down and finances the rest at $12\mathrm{.}7\%$

$($a$)$ According to his original plan to pay off the loan in $4$ years, what would her monthly payments be $($this part uses the loan formula as before$)?$

$($b$)$ Suppose Angelica decides to pay $$800$ per month instead. How many months $n$ will it take to pay off her loan?

The purpose of this question is to illustrate how "tax$-$deferred" payroll deductions work. Suppose Cameron $$45,000$ per year before taxes and is thinking about contributing to an IRA.

$($a$)$ If Cameron is taxed at a rate of $12\%$ by the federal government ${?}^2,$ and at a rate of $4\mathrm{.}75\%$ by the state of North Carolina ${?}^3($so a combined rate of $16\mathrm{.}75\%),$ about how much would Taylor take home per month after taxes?

$($b$)$ If Cameron were to contribute $$525$ per month to a Roth IRA $($this is an after$-$tax account$),$ how much would Cameron have left each month to pay for other things?

$($c$)$ What if Cameron puts the $$525$ per month into a Traditional IRA, so this money is deducted on each paycheck before taxes are calculated. How much would Cameron take home per month in this scenario?