Question

question
a new car is purchased for 20800 dollars. the value of the car depreciates at 10.75% per year. what will the value of the car be, to the nearest cent, after 13 years?
answer attempt 1 out of 2

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 annual depreciation rate (as a decimal), and $t$ is the time in years.

Step2: Convert the rate to a decimal

The depreciation rate is $10.75\%$, so $r = \frac{10.75}{100} = 0.1075$.

Step3: Substitute the values into the formula

We have $P = 20800$, $r = 0.1075$, and $t = 13$. Substituting these into the formula gives $V = 20800(1 - 0.1075)^{13}$.

Step4: Calculate $(1 - 0.1075)$

$1 - 0.1075 = 0.8925$.

Step5: Calculate $0.8925^{13}$

Using a calculator, $0.8925^{13} \approx 0.2607$.

Step6: Calculate the final value

Multiply this by the initial price: $V = 20800 \times 0.2607 \approx 5422.56$.

Answer:

The value of the car after 13 years will be approximately $\$5422.56$.