At the end of a year, a car is worth 5% less than its value at the beginning. If it was worth $10,000 in January, what is its value in December?

• A. $9500
• B. $9000
• C. $9700
• D. $10000

Answer: (A)

To determine the car's value at the end of the year after a depreciation of 5%, you start by calculating 5% of the initial value. The initial value of the car is $10,000.

First, calculate 5% of $10,000:

[

5% , \text{of} , 10,000 = \frac{5}{100} \times 10,000 = 500

]

This amount, $500, represents how much the car's value decreases during the year. To find the value at the end of the year, subtract this depreciation from the initial value:

[

10,000 - 500 = 9,500

]

Therefore, the car is worth $9,500 at the end of December. This aligns perfectly with the understanding of depreciation as a percentage reduction on the initial value. When a car's value declines by a percentage, it is crucial to calculate that percentage based on the original value to determine the new value accurately.

Consequently, the appropriate value for the car in December is indeed $9,500.