a new car is purchased for 17300 dollars. the value of the car depreciates at 9.25% per year. what will the…

a new car is purchased for 17300 dollars. the value of the car depreciates at 9.25% per year. what will the value of the car be, to the nearest cent, after 15 years?

a new car is purchased for 17300 dollars. the value of the car depreciates at 9.25% 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, and $t$ is the time in years. Here, $P=$17300$, $r = 0.0925$, and $t = 15$.

Step2: Substitute the values into the formula

$A=17300\times(1 - 0.0925)^{15}$. First, calculate $1-0.0925 = 0.9075$. Then, find $(0.9075)^{15}$. Using a calculator, $(0.9075)^{15}\approx0.25777$.

Step3: Calculate the final value

$A = 17300\times0.25777$. $A\approx4459.421$. Rounding to the nearest cent, $A\approx4459.42$.

Answer:

$4459.42$