A loan of $12,000 is repaid with quarterly payments (at the end of each period) for 20 years. Assume the interest rate is 5% nominal annual rate compounded quarterly.

a) Find the payment amount to the nearest cent. Use this rounded amount in the remaining parts.

b) Find the outstanding loan balance at the time of 5.25 years.

c) Find the amount of overpayment in the last payment and the appropriate final smaller payment.

d) Show that the outstanding loan balance at a time of 5.25 years can be calculated with the prospective method adjusted for the final smaller payment.

e) Find the minimum number of payments needed for the total principal repaid to exceed the total interest paid.