Julia purchases a Nissan Sentra a The dealer charges for the

Julia purchases a Nissan Sentra. a) The dealer charges for the car include the invoice price of $24, 500, the sales tax of 6.25% of the invoice price, plus a non-taxed fixed license plate fee of $45. What is the total of these charges ? b) Her dad makes a down payment on the car. After paying that she has to take out a car loan of $18, 500. If she obtains a loan at 53% for 4 years with monthly payments what will her monthly payment be? What is the total she will pay on the loan during the 4 years?

Solution

8(a). The amount of sales tax on the Nissan Sentra car costing $ 24500 is $ 24500*6.25% = $1531.25. The total amount of the charges is invoice price+sales tax+fixed licensed plate fee=$24500+$1531.25+$45 = $ 26076.25.

(b).Julia takes a loan of $ 18500 at 5.3 % for 4 years. Her monthly payment can be determined by the formula p = Pr(1+r)ⁿ ) /[(1+r)ⁿ – 1], where p is the fixed monthly payment, P is the amount of the loan,r is the monthly interest rate and n is the number of months. Here, P = $18500, r = (5.3/100)*1/12 = 53/12000 and n = 4*12 = 48. Then p = 18500(53/12000)(1+53/12000)⁴⁸/[(1+53/12000)⁴⁸-1] = (37*53/24) ( 12053/12000)⁴⁸/[( 12053/12000)⁴⁸ -1] = (37*53/24)(1.235570995/0. 235570995) = $ 428.56   ( on rounding off to the nearest cent).Thus, the monthly installment will be $ 428.56.

(c ). The total amount paid by Julia during 4 years will be $428.56 *48 = $20570.88.