1. A car dealership will sell you a used car for 5000 if you pay in full immediately. Altern- ately, you may pay 2000 immediately, and further instalments of 2000 one year from now, and also two years from now. [8 marks] [4 marks) (a) Show that the equivalent annual interest rate for this second method is 21.53% (cor- rect to four significant figures.) (b) Show that the equivalent monthly interest rate is 1.638% (again, correct to four sig- nificant figures). (C) Your bank offers to lend you the full 5000, and will ask you to pay it off in equal monthly instalments over two years, at the above monthly interest rate. You are given that, with a monthly interest rate of a, a loan of size C will be paid off in N months using equal instalments of size Ca(1 + a)" R= (1 +a) - 1 What would be the monthly payments, and about how much would you pay in total, if you took up the bank's offer? [8 marks)