6. (40 points) 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 3.2% 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 3.2% per year, what is the monthly payment if you're intending to have the loan for 6 years?

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

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?

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?

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 3.2% market interest rate? Why or why not?