Question

a new car is purchased for 22300 dollars. the value of the car depreciates at 10.25% per year. what will the value of the car be, to the nearest cent, after 6 years?

Explanation:

Step1: Define depreciation formula

The formula for annual depreciation is $A = P(1 - r)^t$, where $P$ = initial value, $r$ = annual depreciation rate, $t$ = time in years, $A$ = final value.

Step2: Identify given values

$P = 22300$, $r = 0.1025$, $t = 6$

Step3: Substitute values into formula

$A = 22300(1 - 0.1025)^6$

Step4: Calculate the decay factor

$1 - 0.1025 = 0.8975$

Step5: Compute the power term

$0.8975^6 \approx 0.52047$

Step6: Find final value

$A = 22300 \times 0.52047 \approx 11606.48$

Answer:

11606.48 dollars