Question

A new car is purchased for $35, 000 and over time its value depreciates by

one half every 6 years. What is the value of the car 14 years after it was
purchased, to the nearest hundred dollars?

Answer 1

Using the half-life depreciation model, after 14 years, the car's value would be approximately $8,700, assuming discrete half-life periods.

Step-by-step explanation:

A car is purchased for $35,000 and depreciates by one half every 6 years. To calculate the car's value 14 years after purchase:

Determine the number of half-life periods in 14 years: 14 years ÷ 6 years per period = 2.33 periods (approximately).

Round down to the nearest whole number since depreciation happens at the end of each period: 2 periods.

Apply the depreciation formula: Initial Value × (1/2)^number of periods = $35,000 × (1/2)^2 = $35,000 × 1/4.

Calculate the result: $35,000 × 1/4 = $8,750.

However, since we rounded down the periods, after 2 periods (12 years), the car would have already been valued at $8,750. In the next 2 years, the car value would keep depreciating, but not to half since we're not completing another full period. Therefore, the value after 14 years would be slightly less than $8,750. To answer precisely would require a more complex formula that accounts for continuous depreciation, which isn't provided in the question. So, to the nearest hundred dollars, we approximate the value after 14 years as $8,700.

Answer 2

The value after 14 year is 8750 dollar