Question

Celine purchased a used car for $2,500. The value of the car depreciates by 14% per year. How much will the car be worth in 5 years? Round to the nearest dollar.

A. $1,250
B. $1,780
C. $1,385
D. $2,850

Answer 1

Using the exponential depreciation formula, Celine's car will be worth approximately $1,109 in 5 years after a 14% annual depreciation rate, which means none of the provided options is correct.

Step-by-step explanation:

To determine how much Celine's car will be worth in 5 years, we must apply the concept of exponential depreciation. The car depreciates by 14% each year. We can calculate this using the formula for exponential decay: V = P(1-r)^t, where V is the future value, P is the present value, r is the rate of depreciation and t is the time in years.

Using the initial value of the car, $2,500, a depreciation rate of 14% (0.14 when expressed as a decimal), and a time span of 5 years, the calculation would be as follows:

V = $2,500(1 - 0.14)^5

V = $2,500(0.86)^5

V = $2,500(0.443705)

V ≈ $1,109.26

After rounding to the nearest dollar, the car will be worth approximately $1,109. So, none of the given multiple-choice options (A, B, C, D) is correct.