Question

Caleb bought a new MacBook for $2,800. He expects its value to depreciate by 3.5% every year. How much will the MacBook be worth after 3 years?

a) $2,590
b) $2,668
c) $2,500
d) $2,482

Answer 1

The MacBook's value after 3 years, with a 3.5% depreciation rate, is calculated using the formula for exponential decay and is approximately $2,512, which is closest to option c) $2,500.

Step-by-step explanation:

Caleb bought a new MacBook for $2,800 and expects its value to depreciate by 3.5% every year. To calculate the value of the MacBook after 3 years, you can use the formula for exponential decay, which is:

Future Value = Present Value × (1 - Depreciation Rate)^Number of Years

Plugging the values into the formula:

Future Value = $2,800 × (1 - 0.035)^3

Future Value = $2,800 × (0.965)^3

Future Value = $2,800 × 0.8971

Future Value = $2,511.88

After rounding to the nearest dollar, the MacBook will be worth approximately $2,512 after 3 years. This means option c) $2,500 is the closest approximation to the correct answer.