Question

a new car is purchased for 16400 dollars. the value of the car depreciates at 12.5% per year. what will the value of the car be, to the nearest cent, after 8 years?

Explanation:

Step1: Define depreciation formula

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

• $P = 16400$ (initial value),
• $r = 0.125$ (annual depreciation rate),
• $t = 8$ (number of years).

Step2: Substitute values into formula

$A = 16400(1 - 0.125)^8$

Step3: Calculate the decay factor

$1 - 0.125 = 0.875$, so $A = 16400(0.875)^8$

Step4: Compute $(0.875)^8$

$(0.875)^8 \approx 0.349918$

Step5: Multiply by initial value

$A \approx 16400 \times 0.349918$

Answer:

$5738.66$ dollars