Car Prices in
2012
The National Automobile Dealers Association reported that the average retail selling price of a new vehicle was
$
30
,
303
in
2012
. A person purchased a new car at the average price and financed the entire amount. Suppose that the person can only afford to pay
$
500
per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of
3
⋅
5
%
. (Source: The National Automobile Dealers Association, www.nada.com.)
a. Set up a differential equation that is satisfied by the amount
f
(
t
)
of money owed on the car loan at time
t
.
b. How long will it take to pay off the car loan?