Question

Your parents ask your advice on financing a new car purchase. BMW has been running a...

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)