John and Mary each take out a 17-year loan of L. John repays his loan using the amortization method, at an annual effective interest rate of i. He makes an annual payment of 500 at the end of each year. Mary repays her loan using the sinking fund method. She pays interest an- nually, also at an annual effective interest rate of i. In addition, Mary makes level annual deposits at the end of each year for 17 years into a sinking fund. The annual effective rate on the sinking fund is 4.62%, and she pays the value of loan after 17 years. Marys total payment each year is equal to 10% of the original loan amount.

(a) Find the interest rate i. (b) Find the amount of the loan. (c) Find the total interest paid by Mary. (d) Find the total interest paid in the tenth year by Mary. (e) Find the principle repaid in the eleventh year by Mary. (f) Find the outstanding balance for Mary after the thirtieth payments.