Question

A car is purchased for $40,000. if the car loses 22% of its value after each year, approximately how much is the car worth exactly 8 years after it was purchased?

Answer 1

The value of a car purchased for $40,000 that depreciates by 22% annually would be approximately $6,722.80 eight years later, calculated using an exponential decay formula.

Step-by-step explanation:

The question is about calculating the depreciation of a car's value over time using a constant rate of depreciation. If a car is purchased for $40,000 and loses 22% of its value each year, we can calculate its value after 8 years by applying the formula for exponential decay:

V = P(1 - r)^n

Where:

• V is the value of the car after n years,
• P is the initial purchase price,
• r is the annual rate of depreciation,
• n is the number of years.

Substituting the values into the formula:

V = $40,000(1 - 0.22)^8

V = $40,000(0.78)^8

V ≈ $40,000(0.16807)

V ≈ $6,722.80

So, approximately 8 years after it was purchased, the car would be worth around $6,722.80.