You are considering the purchase of a used car priced at $$10,000.$ The car

dealer requires that you make a down payment of $$2,000,$ but offers to

finance a loan of $$8,000$ to cover the remainder. The loan would be an

amortized installment loan with equal monthly payments over $5$ years

starting next month, charging an interest rate of $8\%$ expressed as an APR

with monthly compounding.

a$.$ What is the periodic interest rate most appropriate for this problem

$($expressed as a percentage with $3$ decimal places$)?$

b$.$ What is the present value of the promised payments on the loan

discounted at the quoted interest rate $($expressed as a dollar amount

with two decimal places$)?$

c$.$ What is the total number of payments you will make repaying the loan

$($expressed as a whole number$)?$

d$.$ What is the monthly payment you will be required to make on the

loan $($expressed as a dollar amount with two decimal places$)?$