Question

a car is purchased for $20,000. after each year, the resale value decreases by 20%. what will the resale value be after 4 years? use the calculator provided and round your answer to the nearest dollar.

Explanation:

Step1: Identify the formula for depreciation

The formula for exponential depreciation is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the initial principal (purchase price), $r$ is the rate of depreciation (as a decimal), and $t$ is the time in years.
Here, $P = 20000$, $r = 0.20$ (since 20% = 0.20), and $t = 4$.

Step2: Substitute the values into the formula

Substitute $P = 20000$, $r = 0.20$, and $t = 4$ into the formula:
$V = 20000(1 - 0.20)^4$

Step3: Calculate the value inside the parentheses

First, calculate $1 - 0.20 = 0.80$.

Step4: Raise the result to the power of 4

Calculate $0.80^4$. We know that $0.80^4 = 0.80\times0.80\times0.80\times0.80 = 0.4096$.

Step5: Multiply by the initial price

Multiply $20000$ by $0.4096$:
$V = 20000\times0.4096 = 8192$

Answer:

The resale value after 4 years is $\$8192$.