Question

In August 2008, a car manufacturing company was offering the choice of a 3.3% loan for 120 months, or S7000 cash back on the purchase of a $25,998 car (a) If someone took the 3.3% loan offer, how much will the monthly payment be? b) If someone took the $7000 cash back offer and can borrow money from their local credit union at 7.5% interest compounded monthly for ten years, how much will the month (c) Which of the two offers is more favorable? payment be? (a) The monthly payment someone would pay for the 3.3% loan offer would be $ (Round to the nearest cent as needed.) (b) The monthly payment someone would pay for the cash-back offer would be (Round to the nearest cent as needed.) (c) Choose which offer is more favorable. 3.3% loan offer O cash-back offer

Answer 1

Let x_0 be the initial loan amount and r % is the rate of interest per annum loan amount due after one month is (1/12 of year) x_1 = (1 + r/1200) x_0 - b b is monthly payment similarly x_2 = (1 + r/1200) x_1 - b after n months x_n = (1 + r/1200) x_n - 1 - b x_n = (1 + r/1200) (((1 + r/1200) x_n - 2 - b) - b x_n = (1 + r/1200)^2 x_n - 2 - b (1 + (1 + r/1200)) \r\n x_n = (1 + r/1200)^n x_0 - b (1 + (1 + r/1200) + . . . . + (1 + r/1200)^n - 1) x_n = (1 + r/1200)^n x_0 - b (1 + (1 + r/1200)^n - 1)/(1 + r/1200 - 1) when loan gets cleared in n months then x_n = 0 b = (1 + r/1200)^n/((1 + r/1200)^n - 1) (r/1200) x_