Question

a new car is purchased for 18000 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 14 years?

Explanation:

Step1: Define depreciation formula

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

• $P = 18000$ (initial value),
• $r = 0.135$ (annual depreciation rate),
• $t = 14$ (number of years).

Step2: Substitute values into formula

$A = 18000(1 - 0.135)^{14}$

Step3: Calculate the decay factor

$1 - 0.135 = 0.865$, so $A = 18000(0.865)^{14}$

Step4: Compute $(0.865)^{14}$

$(0.865)^{14} \approx 0.14547$

Step5: Find final value

$A \approx 18000 \times 0.14547$

Answer:

$2618.46$ dollars