You are interested in purchasing a $2023$ Subaru Outback. Suppose the model you are looking at comes to $$45,987\mathrm{.}87$ after taxes. You have a down payment that knocks the price down so that you only need to finance $$40,000.$ The terms ofyour loan are: $5\mathrm{.}5\%$ per year; compounded monthly, for $8$ years.aCalculate your monthly payment, R$.$ Call the set of terms for your loan as outlined in the problem above, with monthly payment R$,$ PLAN $1.$bAccording to PLAN $1,$ calculate the sum of all n payments of $R$.$According to PLAN $1,$ how much interest do you pay over the eight years?According to the terms of your loan, there is no penalty if you pay off your loan early. After reviewing your budget, you think you may be able to swing Z$=$$$850\mathrm{.}00$ as your periodic payment; instead of the payment calculated in question $1$a$.$ Call the set of terms for your loan as outlined in the problem above, with monthly payment Z$,$ PLAN $2.$dConstruct an Amortization Schedule for either PLAN $1($Monthly Payment R$)$ or for PLAN $2($Monthly Payment Z$).$ You must complete rows $0$ through $24$ of the Amortization Schedule, which is representative of the first two years of your loan. Please note that the loan will not yet be paid off, so B$24$ will not be O$.$Make a conjecture about how many total rows of the schedule may be needed to amortize the loan under PLAN $2.$ Justify your answer.