Question

question
a new car is purchased for 15500 dollars. the value of the car depreciates at 7.5% 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

Substitute $P=15500$, $r=0.075$, $t=6$:
$A = 15500(1 - 0.075)^6$

Step3: Calculate decay factor

Compute $1 - 0.075 = 0.925$, then $0.925^6 \approx 0.6479$

Step4: Compute final value

$A = 15500 \times 0.6479 \approx 10042.45$

Answer:

10042.45 dollars