Question

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?

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: Plug in given values

$P = 15300$, $r = 0.1425$, $t = 6$
$A = 15300(1 - 0.1425)^6$

Step3: Calculate remaining value factor

$1 - 0.1425 = 0.8575$
$0.8575^6 \approx 0.40047$

Step4: Compute final value

$A = 15300 \times 0.40047 \approx 6127.19$

Answer:

6127.19 dollars