Question

Your parents ask your advice on financing a new car purchase. BMW has been running a national sales promotion that gives buyers of a new car (BMW 435ix) the choice of a $2,000 rebate or 0.6% APR financing for 60 months. In addition, the local BMW dealer is offering 2.8% APR financing for 60 months on all car purchases through a local bank, which could be used if your parents decide to take the rebate and use it as an additional down payment on their BMW 435ix. Your parents found a well-equipped BMW for a price of $52,000 and have $3,000 as a down payment. Should your parents take the $2,000 rebate with 2.8% APR financing or the 0.6% APR financing and no rebate? Show your work and justify your decision.

Answer 1

Option 1: $ 2000 rebate and 2.8% APR Loan.

Purchase Price = $ 52000, Original Down Payment = $ 3000 and Rebate = $ 2000

Borrowing = 52000 - 3000 - 2000 = $ 47000

Effective Monthly Rate = (2.8 / 12) = 0.233 % and Tenure of Borrowing = 60 months

Let the monthly loan repayments be $P

Therefore, 47000 = P x (1/0.00233) x [1-{1/(1.00233)^(60)}]

47000 = P x 55.934

P = 47000 / 55.934 = $ 840.274

Option 2: No Rebate and 0.6% financing

Purchase Price = $ 52000 and Original Down Payment = $ 3000

Borrowing = 52000 - 3000 = $ 49000

Tenure = 60 months and Effective Monthly Rate = (0.6 / 12) = 0.05 %

Let the monthly loan repayments be $ K

Therefore, 49000 = K x (1/0.0005) x [1-{1/(1.0005)^(60)}]

49000 = K x 59.094

K = 49000 / 59.094 = $ 829.182

As the monthly loan repayments under Option 2 is lowe than that under Option 1, one should opt for Option 2 (APR of 0.6 % and no rebate)