MEGA Elementary Education Multi-Content Practice Test

What expression calculates the car's value 12 years after purchase with a 15% annual depreciation?

1. 20,000 - 12 x 3,000

2. 20,000 - 12 x ((3,000 + 2,550 + 2,167 + 1,842)/4)

3. 20,000 - 20,000(0.15)^12

4. 20,000(1 - 0.15)^12

The correct answer is: 20,000(1 - 0.15)^12

To determine the car's value 12 years after purchase, given a 15% annual depreciation, we need to understand how depreciation affects the car's value over time. The formula for calculating the depreciated value of an asset over multiple years is based on exponential decay. In this context, we can represent the car's initial value, which is $20,000, and the annual depreciation rate, which is 15% (or 0.15 in decimal form). When an asset depreciates by a fixed percentage each year, you can find its value after a number of years using the formula: Final Value = Initial Value × (1 - Depreciation Rate) ^ Number of Years In this case, we plug in the values: Final Value = $20,000 × (1 - 0.15)^12. This effectively allows us to calculate the car's value after 12 years, as it repeatedly applies the 15% depreciation to the remaining value each year. Using this formula captures the essence of compound depreciation due to the percentage decline, making it the correct expression to evaluate the car's worth after the specified time.