Q4 (9 points) 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) [2 points] Find the payment amount to the nearest cent. b) [2 points] Find the outstanding loan balance at time 5.25 years. c) [1 point] Find the amount of overpayment in the last payment and the appropriate final smaller payment. d) [1 point] Show that the outstanding loan balance at time 5.25 years can be calculated with the prospective method adjusted for the final smaller payment. e) [3 points] Find the minimum number of payments needed for the total principal repaid to exceed the total interest paid. Hint: once you set up an equation, you can solve using trial and error or a computation engine such as WolframAlpha