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?

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 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 $t = 13$. Plugging these into the formula: $V = 20800(1 - 0.1075)^{13}$.

Step4: Calculate $(1 - 0.1075)$

$1 - 0.1075 = 0.8925$.

Step5: Calculate $0.8925^{13}$

Using a calculator, $0.8925^{13} \approx 0.2604$.

Step6: Multiply by the initial price

$V = 20800 \times 0.2604 \approx 5416.32$.

Answer:

5416.32