A Car's Depreciation Calculation

A car was purchased at $20,000 and loses value at a rate of 7% per year. What will be the value of the car after 5 years?

Final Answer:

The value of the car after 5 years will be approximately $14,612.44, and the closest option is $14,000 (Option 1).

Explanation:

The depreciation of the car can be modeled using the formula for exponential decay: \(V(t) = V_0 \cdot (1 - r)^t\), where:

- \(V(t)\) is the value after (t) years,

- \(V_0\) is the initial value,

- (r) is the rate of decay per year (expressed as a decimal), and

- (t) is the time in years.

In this scenario, \(V_0 = $20,000\), r = 7% (or 0.07), and t = 5 years. Plugging these values into the formula, we get:

\[V(5) = 20000 \cdot (1 - 0.07)^5\]

Calculating this expression gives us approximately $14,612.44. Therefore, after 5 years, the car's value will be around $14,612.44, which is closest to $14,000 (Option 1) among the given options.

This calculation reflects the impact of annual depreciation, where the car loses 7% of its value each year. Understanding such depreciation is essential for financial planning and assessing the long-term cost of owning a car.