Question

question
a new car is purchased for 21100 dollars. the value of the car depreciates at 10.5% per year. what will the value of the car be, to the nearest cent, after 6 years?
answer

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 rate of depreciation (in decimal), and $t$ is the time in years.
Here, $P = 21100$, $r = 10.5\% = 0.105$, and $t = 6$.

Step2: Substitute the values into the formula

Substitute $P = 21100$, $r = 0.105$, and $t = 6$ into the formula:
$V = 21100(1 - 0.105)^6$
First, calculate $1 - 0.105 = 0.895$.
Then, calculate $0.895^6$. Let's compute that:
$0.895^6 \approx 0.49796$ (using a calculator for the exponentiation)
Then, multiply by 21100:
$V = 21100\times0.49796 \approx 21100\times0.49796$
$21100\times0.49796 = (20000 + 1100)\times0.49796 = 20000\times0.49796 + 1100\times0.49796$
$20000\times0.49796 = 9959.2$
$1100\times0.49796 = 547.756$
Adding these together: $9959.2 + 547.756 = 10506.956$
Rounding to the nearest cent (two decimal places), we get $10506.96$.

Answer:

10506.96