a new car is purchased for 23200 dollars. the value of the car depreciates at 13.25% per year. what will the…

a new car is purchased for 23200 dollars. the value of the car depreciates at 13.25% per year. what will the value of the car be, to the nearest cent, after 7 years?

a new car is purchased for 23200 dollars. the value of the car depreciates at 13.25% per year. what will the value of the car be, to the nearest cent, after 7 years?

Answer

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay (depreciation) 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 $r = 13.25%=0.1325$, $P = 23200$, and $t = 7$.

Step3: Substitute the values into the formula

$A=23200\times(1 - 0.1325)^7$. First, calculate $1 - 0.1325=0.8675$. Then, calculate $(0.8675)^7$. $(0.8675)^7=0.8675\times0.8675\times0.8675\times0.8675\times0.8675\times0.8675\times0.8675\approx0.39777$. Next, calculate $A = 23200\times0.39777$. $A\approx9228.264$.

Answer:

$9228.26$