a new car is purchased for 15300 dollars. the value of the car depreciates at 14.25% per year. what will the…

a new car is purchased for 15300 dollars. the value of the car depreciates at 14.25% per year. what will the value of the car be, to the nearest cent, after 6 years?

a new car is purchased for 15300 dollars. the value of the car depreciates at 14.25% per year. what will the value of the car be, to the nearest cent, after 6 years?

Answer

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time in years.

Step2: Convert the percentage to a decimal

Given $r = 14.25%=0.1425$, $P = 15300$, and $t = 6$.

Step3: Substitute the values into the formula

$A=15300\times(1 - 0.1425)^6$. First, calculate $1-0.1425 = 0.8575$. Then, calculate $(0.8575)^6$. $(0.8575)^6=0.8575\times0.8575\times0.8575\times0.8575\times0.8575\times0.8575\approx0.40477$. Next, calculate $A = 15300\times0.40477$. $A=15300\times0.40477 = 6193.981$.

Step4: Round to the nearest cent

Rounding $6193.981$ to the nearest cent gives $6193.98$.

Answer:

$6193.98$