Question

She has negotiated a sales price of $24,145 and she has a $4,000 down payment. She is eligible for the full $750 cash rebate. Her bank has pre-approved her for a 48 month car loan at 3.50%. Assuming Zara wants the cheapest overall price, which option should she take? Should she take the 1.9% financing offer for 66 months from the dealer, or should she borrow the money from her bank at 3.50% to pay off the dealer and receive the $750 cash rebate?

Answer 1

Answer:

The best overall price will be the bank offer because the cash disbursement are lower. Zara is looking for the cheapest overall price, which means the less cash disbursement regardless of the interest.

Explanation:

For the dealer option we need to calculate the cuota for an annuity of 66 month at 1.9% rate which a present value of 24,145 - 4,000 = 20,145

$C * \frac{1-(1+r/12)^{-time} }{rate} = PV$

$C * \frac{1-(1+0.019/12)^{-66} }{0.019/12} = 20,145$

The cuota for the dealer will be 321.69447 = 321.69

321.69 x 66 = 21231.54 overall cash price

Bank couta will be the annuity of 48 months at 3.50%

here we are using the cash rebate so 24,145 - 4,000 - 750 = 19,395

$C * \frac{1-(1+0.035/12)^{-48} }{0.035/12} = 19,395$

Cuota from the Bank 431.01181 = 431.01

431.01 x 48 = 20688.48 overall cash price