Katelynn purchased a used car that was 5 years old for $10,250. After two years, Kelly Blue Book valued the car at $8,075. Determine the car's original value when first bought by the original owners, and calculate the annual depreciation rate.

To determine the car's original value and the annual depreciation rate, we will use the following steps:

Step 1: Calculate the total depreciation over the two years Katelynn owned the car. Total depreciation = Purchase price - Value after two years Total depreciation = $10,250 - $8,075 Total depreciation = $2,175

Step 2: Calculate the annual depreciation over the two years Katelynn owned the car. Annual depreciation = Total depreciation / Number of years Annual depreciation = $2,175 / 2 Annual depreciation = $1,087.50

Step 3: Extend the annual depreciation over the total age of the car to obtain the original value. The car is currently 7 years old (5 years old when purchased + 2 additional years). Total depreciation over 7 years = Annual depreciation * Age of the car Total depreciation over 7 years = $1,087.50 * 7 Total depreciation over 7 years = $7,612.50

Step 4: Calculate the car's original value. Original value = Current value + Total depreciation over 7 years Original value = $8,075 + $7,612.50 Original value = $15,687.50

Therefore, the car's original value when first bought by the original owners was $15,687.50.

To calculate the annual depreciation rate, we use the formula: Annual depreciation rate = (Annual depreciation / Original value) * 100

Annual depreciation rate = ($1,087.50 / $15,687.50) * 100

Annual depreciation rate ≈ 6.93%

Hence, the annual depreciation rate is approximately 6.93%.

Depreciation is the decrease in the value of an asset over time. In the context of a car, depreciation reflects the wear and tear, age, and perceived remaining usefulness of the vehicle. Cars are well-known for depreciating quickly, meaning they lose value as soon as they are driven off the dealership lot.

The "original value" or "purchase price" is what the car was worth when it was brand new. In our calculation, we estimated this by reversing the depreciation process, adding up the amount the car had depreciated from the time Katelynn bought it, and assuming a constant rate of depreciation.

The "annual depreciation rate" is the percentage of value a car loses each year. It's often used to estimate future value and can inform decisions about purchasing a used car or deciding when it might be more economically sensible to replace a vehicle. The annual depreciation rate varies widely between models and makes of cars, being influenced by factors like the car's reliability, demand, and economic conditions.