#### Answer

$\$14,300$

#### Work Step by Step

An automobile was purchased for $\$23,000$.
$7$ years later, it's worth $\$2700$.
The difference in the prices is:
$23,000-2700=20,300$ dollars.
Assuming the car's value depreciated steadily, it depreciated at the rate of:
$20,300\div7=2900$ dollars per year.
This would make the car's price after 3 years:
$23,000-3*2900=23,000-8700=14,300$ dollars.