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 15months, 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?

 

 

 2. Now consider that instead of an amortized loan, you repaid the loan in above (a) using a sinking fund approach (where you can earn a 5% monthly compounded rate for the sinking fund deposits, and the loan rate is the same as in above (a)). 

(a) Construct the sinking fund schedule for the loan and provide the sinking fund deposit, interest earned on the sinking fund, fund increase and fund balance for the 15th period the 25th period, and the 45th period (fund balance for the end of the periods). 

(b) Compare the total interest paid (interest paid on the loan) for both the amortized loan (1(a)) and sinking fund loan. Is one method financially superior to the other?

 (c) What determines the more financially beneficial approach? 

(d) What interest rate would equalize the two methods