Question

a new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per year. what will the value of the car be, to the nearest cent, after 8 years?

Explanation:

Step1: Recall the depreciation formula

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.

Step2: Convert the rate to decimal

The depreciation rate $r = 9.75\% = \frac{9.75}{100}= 0.0975$.

Step3: Identify the values of P, r, and t

Here, $P = 16600$ dollars, $r = 0.0975$, and $t = 8$ years.

Step4: Substitute into the formula

Substitute the values into the formula: $V = 16600(1 - 0.0975)^8$.
First, calculate $(1 - 0.0975)= 0.9025$.
Then, calculate $0.9025^8$. Using a calculator, $0.9025^8\approx0.4632$.
Now, calculate $V = 16600\times0.4632\approx7689.12$.

Answer:

The value of the car after 8 years will be approximately $\$7689.12$.