Question

A car was valued at 38,000 in the year 2007. If its value depreciates by 10% each year, what will be its value in the year 2023?

a) $15,120
b) $15,860
c) $16,540
d) $17,320

Answer 1

The value of the car in the year 2023 is calculated using the formula for exponential decay, resulting in approximately $15,120 after a 10% annual depreciation over 16 years.

Step-by-step explanation:

The value of a car that depreciates by 10% each year can be calculated using the formula for exponential decay: V = P(1 - r)^n where V is the final value, P is the initial value, r is the depreciation rate (expressed as a decimal), and n is the number of years.

In this case, the car's initial value (P) in 2007 is $38,000, the depreciation rate (r) is 10% or 0.1, and the number of years (n) from 2007 to 2023 is 16 years.

Substituting these values into the decay formula gives us: V = 38000(1 - 0.1)^16 = 38000(0.9)^16

Calculating this, the value of the car in 2023 comes out to be approximately $15,120. Therefore, the correct answer is option (a) $15,120.