0. John buys a car for $45,000 by making level payments at the end of each month for six years. John is charged an annual nominal interest rate of 6% compounded monthly in his loan. John repays the loan exactly as scheduled (he does not make any extra or early or late payments). (please do not use a spreadsheet.

   1. (a) Find the amount of each monthly payment.

   2. (b) Find the total amount of payments made by John.

   3. (c) Find the total interest paid by John during the duration of the loan.

   4. (d) Calculate the outstanding loan balance immediately after the 12th payment has been made using the retrospective method.

   5. (e) Calculate the outstanding loan balance immediately after the 24th payment has been made using the prospective method.

   6. (f) Calculate the amount of interest and the amount of principal repaid in the 25-th payment.