a new car is purchased for 16500 dollars. the value of the car depreciates at 5.75% per year. what will the…

a new car is purchased for 16500 dollars. the value of the car depreciates at 5.75% per year. what will the value of the car be, to the nearest cent, after 5 years?

a new car is purchased for 16500 dollars. the value of the car depreciates at 5.75% per year. what will the value of the car be, to the nearest cent, after 5 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 time in years.

Step2: Convert the rate to a decimal

Given $r = 5.75%=0.0575$, $P = 16500$, and $t = 5$.

Step3: Substitute the values into the formula

$A=16500\times(1 - 0.0575)^5$. First, calculate $1-0.0575 = 0.9425$. Then, $(0.9425)^5=0.9425\times0.9425\times0.9425\times0.9425\times0.9425\approx0.74777$. Next, $A = 16500\times0.74777\approx12338.21$.

Answer:

$12338.21$