$($i$)$ You took a $$2,000$ one$-$year loan to be paid back in $12$ installments. The interest rate is $9\%.$ Calculate the monthly payment and total cost.

$($ii$)$ Suppose the lender of $$2,000$ uses add$-$on interest method $($Rule $78$ loan$)$ and also charges $9\%,$ what is the monthly payment and the total cost.

$($iii$)$ Explain why the monthly payment and total cost are lower in $($i$)$ than it is in $($ii$)$ even when the interest charged is the same.

$($iv$)$ If you decide to pay off the loan after $6$ payments, how much would you save in interest in the Rule $78$ loan?