You take out a car loan of $10,000 at 12% with monthly compounding. The loan is to be paid off in monthly installments over a 50-month period. (a) Construct the amortization schedule for the loan and provide the monthly payment, interest payment, principal payment and outstanding balance for the 15th payment period the 25th payment period, and the 45th payment period (outstanding balance for the end of the periods). (b) After 15 months you decide to pay off the entire loan. What is the balance that needs to be paid off? (c) How much interest is saved by paying off the loan after 15 months? (d) Suppose instead of paying off the loan in 15 months, you increase your payments by a fixed amount$100 per month (beginning at the 15th period) for the remaining period of the loan. When is the loan paid off (what payment period)? (e) How much interest is saved in this scenario? (f) Would it be more suitable to pay off the loan at the end of the 15th month, or increase the payments by $100 beginning at the end of the 15th month