Question

a new car is purchased for 17900 dollars. the value of the car depreciates at 12.25% per year. what will the value of the car be, to the nearest cent, after 10 years?

Explanation:

Step1: Define depreciation formula

The formula for exponential depreciation is $A = P(1 - r)^t$, where:

• $P = 17900$ (initial value),
• $r = 0.1225$ (annual depreciation rate),
• $t = 10$ (time in years).

Step2: Substitute values into formula

$A = 17900(1 - 0.1225)^{10}$

Step3: Calculate the decay factor

$1 - 0.1225 = 0.8775$
$0.8775^{10} \approx 0.2705$

Step4: Compute final value

$A = 17900 \times 0.2705$
$A \approx 4841.95$

Answer:

$\$4841.95$