Question

question a new car is purchased for 25000 dollars. the value of the car depreciates at 8.25% per year. what will the value of the car be, to the nearest cent, after 15 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 (in decimal), and $t$ is the time in years.
Here, $P = 25000$, $r = 0.0825$ (since 8.25% = 0.0825), and $t = 15$.

Step2: Substitute the values into the formula

Substitute $P = 25000$, $r = 0.0825$, and $t = 15$ into the formula:
$$V = 25000(1 - 0.0825)^{15}$$
First, calculate $(1 - 0.0825) = 0.9175$.
Then, calculate $0.9175^{15}$. Using a calculator, $0.9175^{15} \approx 0.2860$.

Step3: Calculate the final value

Multiply $25000$ by $0.2860$:
$$V = 25000 \times 0.2860 = 7150.00$$ (rounded to the nearest cent)

Answer:

The value of the car after 15 years will be $\$7150.00$.