You have just been granted a business loan of $1,000,000. The terms of the loan requires that you pay off the loan in quarterly installments over a period of ten years. The bank is charging you an APR of 10%, compounded monthly.

a) Calculate the interest payment and construct a complete amortization schedule that breaks down the interest and principal repayment associated with each interest payment.

b) After five years, you put down a lump sum of $100,000 on the loan. You keep your payments the same as in (a). By how much time have you shortened the life of your loan?

c) Using present value formulas you learned in class, show the interest and principal payment portions of the 32nd payment, and reconcile your result with the amortization schedule constructed in (a).