Question

Heather bought a car for her company that costs $40,000. Each year after she buys it, it is only worth 90% of what it originally was. Write the equation and find the cost of her car after 5 years.

Answer 1

After 5 years, Heather's car, which originally cost $40,000 and depreciates at 10% per year, will be worth approximately $23,619.60.

Step-by-step explanation:

Heather bought a car for her company that costs $40,000, and each year it depreciates to 90% of its value from the previous year. To calculate the cost of the car after 5 years, we'll use an exponential decay model for depreciation. The general formula for depreciation is:

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

In this case, the Present Value is $40,000, the Depreciation Rate is 10% (or 0.10 as a decimal since the car is worth 90% of its previous value each year), and the Number of Years is 5. Plugging these values into the equation, we get:

Future Value = $40,000 × (1 - 0.10)5

Future Value = $40,000 × 0.95

Future Value = $40,000 × 0.59049

Future Value = $23,619.60

Therefore, after 5 years, the cost of Heather's car will be approximately $23,619.60.