3. [14 marks] (a) [5 marks] Let n be the number of payment periods, i be the interest rate per conversion period and R be the amount of each periodic payment. Let A denote the present value of an ordinary annuity. Show that A Rami 1- (1 + i)-n where an = i (b) [4 marks] Use part (a) to show that the present value of a complex ordinary annuity is 1 Racni Sai where c is the number of interest periods in one payment interval (1 + i)n 1 and Smi i (c) [5 marks] A garage is sold for 2,000 down and 48 monthly pay- ments of 300. If money is worth 8% compounded quarterly, find the cash value of the garage. =