Question

a new car is purchased for 22400 dollars. the value of the car depreciates at 6.75% per year. what will the value of the car be, to the nearest cent, after 9 years?

Explanation:

Step1: Define depreciation formula

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

• $P = 22400$ (initial value),
• $r = 0.0675$ (annual depreciation rate),
• $t = 9$ (number of years).

Step2: Substitute values into formula

$A = 22400(1 - 0.0675)^9$

Step3: Calculate the decay factor

$1 - 0.0675 = 0.9325$
$A = 22400(0.9325)^9$

Step4: Compute the power term

$0.9325^9 \approx 0.5661$

Step5: Calculate final value

$A \approx 22400 \times 0.5661$
$A \approx 12680.64$

Answer:

12680.64 dollars