Andrew took a $$12,000$ car loan. He wants to pay off this debt quick, so he chooses to pay it in

just two years. The loan has a $12\%$ nominal interest rate, compounded quarterly.

a$.$ He will make quarterly payments. Draw the cash flow diagram.

b$.$ What is his quarterly payment?

c$.$ Complete the amortization table, showing the amounts for each payment, interest, and

principal.

Andrew decides that he cannot afford the quarterly payment that we found in the previous

question. He decides to change his loan length to $5$ years. He still has an initial loan of $$12,000$

with a $12\%$ nominal rate, compounded quarterly.

a$.$ What is Andrew's new quarterly payment?

b$.$ What is the difference between Andrew's total interest payment for the $5-$year loan and his

total interest for the $2-$year loan?

Andrew received a bonus at the end of year $3!$ He would like to use this bonus to make one

lumpsum payment to pay off his loan at the end of year $3.($Assume his quarterly payment has

been the value found in question $2$ a$.)$

a$.$ Draw a cash flow diagram to show his initial loan, his quarterly payments up until now, and

his potential payoff at the end of year $3.$

b$.$ How much money does Andrew need to pay off his loan at the first quarter of year $4?$