Question

question
a new car is purchased for 16500 dollars. the value of the car depreciates at 5.75% per year. what will the value of the car be, to the nearest cent, after 5 years?

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 principal (initial value), $r$ is the annual depreciation rate (in decimal), and $t$ is the time in years.

Step2: Convert the rate to decimal

The depreciation rate is $5.75\%$, so $r = \frac{5.75}{100} = 0.0575$.

Step3: Substitute the values into the formula

We have $P = 16500$, $r = 0.0575$, and $t = 5$. So, $V = 16500(1 - 0.0575)^5$.

Step4: Calculate $(1 - 0.0575)$

$1 - 0.0575 = 0.9425$.

Step5: Calculate $(0.9425)^5$

Using a calculator, $(0.9425)^5 \approx 0.7564$.

Step6: Calculate the final value

$V = 16500 \times 0.7564 \approx 12480.60$.

Answer:

The value of the car after 5 years will be approximately $\$12480.60$.