Question

A car is purchased for $22,000. After each year, the resale value decreases by 35%. What will the resale value be after 4 years? Round your answer to the nearest dollar

Answer 1

Given the initial value of the car at $22,000 and the annual depreciation value at 35%. To calculate the resale value of the car after a given number of years, we shall apply the exponential decay formula;

`f(x)=a(1-r)^x`

This can also be written as;

`y=a(1-r)^t`

The value of x in the first equation is the same as the value of t in the second equation. x is the number of years, and t is also the same, the number of years.

Therefore, with the values already given, we would have;

`\begin{gathered} \text{Where;} \\ a=\text{initial value}=22000 \\ r=\text{rate of depreciation}=0.35\text{ (35\%)} \\ t=\text{time in years}=4 \end{gathered}`

The resale value after 4 years would now be;

`\begin{gathered} y=a(1-r)^t \\ y=22000(1-0.35)^4 \\ y=22000(0.65)^4 \\ y=3927.1375 \\ \text{Rounded to the nearest dollar;} \\ y=3,927 \end{gathered}`

ANSWER:

The resale value after 4 years would be $3,927