Diana wants to borrow $$23000$ to buy a vehicle. A bank is willing to give her the loan under the following conditions:

She must make equal payments at the end of each month for $5$ years.

She will have to pay interest at the rate of $12\mathrm{.}6\%$ per year but calculated monthly

You have to help her determine her monthly payment. Do the following:

$($a$)$ Calculate the monthly interest rate

$($b$)$ Calculate the value of the loan $60$ months after she gets it

$($c$)$ If the mothly payment is $$P$ per month, write down an expression for the total value of the $60$ payments.

$($d$)$ Form an equation by arguing that the total value of the $60$ payments shound be equal to the value of the loan $60$ months after it was released.

$($e$)$ Solve the equation for $P.$