You$$re given a $6-$year auto loan from your credit union. Suppose the car costs $$56,000$ and your down payment is $$6,500.$ The current market interest rate is $3\mathrm{.}2\%$ for the short$-$term loans with the same creditability as yours. Answer the following questions:

a$)$ Given that the APR $($namely the Annual Percentage Rate. That is$,$ the stated interest agreed on the loan$)$ of the loan is $3\mathrm{.}2\%$ per year, what is the monthly payment if you$$re intending to have the loan for $6$ years?

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b$)$ What is the effective annual rate if the loan is compounded monthly? $$

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$$c$)$ Suppose the credit union says that if you$$d like to retire the loan earlier, say at the end of the $3$rd year, you need to pay $($say$)$ $$26,000$ for the rest of the loan, would you take it given that you have no difficulty generating the cash flow? Why or why not?

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d$)$ Suppose the original agreement that you signed with the credit union is to have a $3-$year loan and pay back the loan with $$24,000$ at the end of year $3,$ how much will be your monthly payment if this is how you finance the purchase?

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e$)$ Suppose that the left$-$over principal of the loan is $$36,000$ at the end of the second year after two years of payments given in a$),$ what is the Internal Rate of Return $($IRR$)$ for this loan now?$$ Is this rate different from the $3\mathrm{.}2\%$ market interest rate? Why or why not?