Question

Downward Motors has offered Vicki either a $2,500 rebate or a 2%, 4-year loan on the new SUV she is purchasing for $33,000 with a $3,000 down payment. Vicki has done her homework and knows that she can get a 6%, 4-year loan at her credit union. Should Vicki take the rebate or the 2% loan from the dealer?

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Answer 1

1.
If Vicki takes Option B (the 2% and 4-year loan) from the dealer, her monthly payments will be
=(33000-3000)*(2%/12)/(1-1/(1+2%/12)^(12*4))
=650.8537092
=651

2.
Under Vicki’s credit condition given by her credit union (6% on a 4-year loan), the present value (PV) of these future payments on Option B is
=651/(6%/12)*(1-1/(1+6%/12)^(12*4))
=27719.78688

3.
If, in the very beginning, Vicki takes Option A (the $2,500 rebate), the present value of payments of buying the SUV are $ .

=33000-3000-2500
=27500

4.
So, Vicki should take Option from the dealer.
Option A