A loan of $28000 is taken out with interest charged at the rate of 10.96% per annum, compounding quarterly. Equal payments are to be made twice per year, at the end of each six-month period, for 5 years. (a) Find the quarterly interest rate, expressing your answer as a percentage. (b) Briefly explain why there will be ten payments. (c) Let M be the amount of each half-yearly payment, and let A, be the amount owing after n payments. By finding A, A2 and A3, and by noticing the pattern that occurs, show that A10 = 28000 (1.0274)20M (1.027418 +1.027416 + 1.027414 + ... +1.0274 + 1). (d) By letting A10 = 0 and solving for M, find the amount of each half-yearly payment. (e) How much is paid in total? (f) How much interest is charged on the loan?