Chapter 7.7, Problem 33PPE

To determine

To explain: If the family should sell car for 4000 dollars.

Answer to Problem 33PPE

The family shouldn’t sell the car for 4,000 dollars

Explanation of Solution

Given information:

Family buys a car for 20,000 dollars

The value of the car decreases 20% each year

Calculation:

The formula for the depreciation is:

  $A=P{\left(1\pm r\right)}^t$

Now,

  $\begin{array}{l}P=20,000\\ r=\frac{20}{100}=0.2\end{array}$

Put the values in formula:

  $\begin{array}{l}A=P{\left(1\pm r\right)}^t\\ A=20,000{\left(1-0.2\right)}^t\end{array}$

Negative because the value of car decreasing each year

Value of car after 6 years

  $\begin{array}{l}A=20,000{\left(1-0.2\right)}^6\\ A=20,000{\left(0.8\right)}^6\\ A=5,242.88\end{array}$

Hence, the family shouldn’t sell the car for 4,000 dollars as after 6 years the actual value will be 5,242 dollars approximately