Given in the question:
a.) A family buys a car for $20,000.
b.) The value of the car decreases about 18% each year.
c.) After six years the family wants to sell the car.
Should they sell the car for $4000?
Let's determine if the price of the car fits the recommended price using the formula below:
[tex]\text{ y = }Ad^{x^{}}[/tex]Where,
y = the recommended price of the car after 6 years.
A = price of the car when bought
d = (100% - 18%)/100 = 82/100 = 0.82
x = years of use
We get,
[tex]\text{ y = }Ad^{x^{}}[/tex][tex]\text{ y = (\$20,000)(0.82)}^{6^{}}[/tex][tex]\text{= (\$20,000)(0}.30400667142)[/tex][tex]\text{ y =\$}6,080.13342848\text{ }\approx\text{ \$6,080.13}[/tex]The computed depreciated value of the car is $6,080.13.
Therefore, we recommend that they should sell the car at a higher price but not more than $6,080.13 since it's still within the recommended depreciated value.
