question\na new car is purchased for 25000 dollars. the value of the car depreciates at 8.25% per year. what…

question\na 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?

question\na 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?

Answer

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation as a decimal, and $t$ is the number of years. Here, $P=$25000$, $r = 0.0825$, and $t = 15$.

Step2: Substitute the values into the formula

$A=25000\times(1 - 0.0825)^{15}$. First, calculate $1-0.0825 = 0.9175$. Then, find $(0.9175)^{15}$. Using a calculator, $(0.9175)^{15}\approx0.28477$.

Step3: Calculate the final value

$A = 25000\times0.28477=$7119.25$.

Answer:

$7119.25$