a new car is purchased for 23700 dollars. the value of the car depreciates at 13.5% per year. what will the…

a new car is purchased for 23700 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 10 years?

a new car is purchased for 23700 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 10 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.

Step2: Convert the rate to a decimal

Given $r = 13.5%=0.135$, $P = 23700$, and $t = 10$.

Step3: Substitute the values into the formula

$A=23700\times(1 - 0.135)^{10}=23700\times(0.865)^{10}$.

Step4: Calculate $(0.865)^{10}$

Using a calculator, $(0.865)^{10}\approx0.22137$.

Step5: Calculate the final value of the car

$A = 23700\times0.22137\approx5246.47$.

Answer:

$5246.47$