13. You are considering a 10-year loan for $100,000 at a monthly nominal rate of 7.5%.

(a) Calculate the monthly payment for this loan.

(b) Calculate the outstanding balance of this loan over the first year immediately following each of the required 12 payments as well as the changes in these balances, called loan amortizations. (Hint: recall that the loan balance equals the present value of remaining payments)

(c) Confirm that the ratio of successive amortizations are in constant ratio of 1 þ 0:075 12 .

(d) Derive algebraically the general formula for the loan amortizations and confirm that the ratio of successive values is a constant 1 þ i 12 .

(e) Demonstrate that given the formula derived for the values of the amortizations, they indeed add up to the original loan value, L.