John is shopping for a used car
and has found one being offered by
Alice for $12,000, based on $2,000
down and a $10,000 balance to be
paid to Alice over 36 months at
6% (annual) simple interest paid
monthly on the unpaid balance
(John’s monthly payments would be
$10,000/36 + unpaid balance x
0.06/12).
However, if he pays cash,
he can get a reduction of D dollars so
the cash payment would be $12,000
- D.
Although Alice will finance
the car at 6%, she believes she can better invest her money at 10% elsewhere.
If the 36 monthly payments are discounted to the present at a rate of 10%, how big a reduction in the cash price (to the
nearest dollar) can Alice afford to
give John so that buying the car
for a single cash payment and the
net present value of financing over
36 months (plus $2,000 added to
account for the down payment), are
equivalent propositions?
Assume all
months have 30 days, and a year is
360 days.
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car-sharing
