Janis would like to borrow $$5000$ for a project. The interest rate is $8\mathrm{.}4\%,$ compounded monthly. She has to pay the money back by making equal monthly payments at the end of every month, for $48$ months. You are required to determine the amount of each monthly payment. Do the following:

$($a$)$ Determine the interest rate per month.

$(2)$

$($b$)$ Determine the value of the loan, $($with interest$),48$ months after it is issued.

$($c$)$ If each monthly payment is $P$ dollars, determine the total value, $($with interest$),$ of the $48$ payments.

$(4)$

$($d$)$ The value of the loan $48$ months later must equal the total value of the payments. Use that condition to calculate $P.$

$(5)$