The purpose of this question is to illustrate how "tax$-$deferred" payroll deductions work. Suppose Taylor earns $$40,000$ per year before taxes and is thinking about contributing to an IRA.

$($a$)$ If Taylor is taxed at a rate of $12\%$ by the federal government ${?}^1,$ and at a rate of $4\mathrm{.}75\%$ by the state of North Carolina ${?}^2($so a combined rate of $16\mathrm{.}75\%),$ about how much would Taylor take home per month after taxes?

$($b$)$ If Taylor were to contribute $$500$ per month to a Roth IRA $($this is an after$-$tax account$),$ how much would Taylor have left each month to pay for other things?

$($c$)$ What if Taylor puts the $$500$ per month into a Traditional IRA, so this money is deducted on each paycheck before taxes are calculated. How much would Taylor take home per month in this scenario?