Question

Sarah wants to purchase a new car that lists for $30,000. The manufacturer currently offers two incentive programs. She may finance the full price of the car through the manufacturer at 0% for 5 years. Alternatively, she may arrange his own financing and receive a $3,000 discount off the price of the car.

Sarah’s bank will finance the car at 4.5 percent for 5 years.

Which financing option should she choose? Justify your answer.

Answer 1

Monthly payment for manufacturer’s offer = Cost of car /Number of payments

                                                                  = $ 30,000/12 x 5

                                                                   = $ 30,000/60 = $ 500

We can use formula for EMI to compute monthly payment for Bank’s offer as:

EMI = P x r x (1+r) n/(1+r) n – 1

P = Principal of loan = $ 30,000 - $ 3,000 = $ 27,000

r = Rate per period = 0.045/12 = 0.00375 p.m.

n = Number of periods = 5 years x 12 months = 60 periods

EMI = $ 27,000 x 0.00375 x (1+ 0.00375)60/ [(1+ 0.00375)60-1]

       = $ 27,000 x 0.00375 x (1.00375)60/ [(1.00375)60-1]

       = $ 27,000 x 0.00375 x 1.25179582052417/ (1.25179582052417-1)

       = $ 126.744326828072/ 0.25179582052417

       = $ 503.3615195 or $ 503.36

Sarah should choose to finance from the car’s manufacturer as the EMI from manufacturer is less than the EMI of the bank’s offer.