A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to half its original value in 4 years. IF you bought a car 8 years ago, and it's now worth $5,000, how much did you pay for the car originally?

now it is worth 5000

4 years ago it was worth 10000
8 years ago it was worth 20000

To determine the original price of the car, we can use the concept of depreciation. Depreciation is the reduction in value of an asset over time. In this case, we know that the car depreciates to half its original value in 4 years.

Let's break down the problem:

1. The car depreciates to half its original value in 4 years.
This means that after 4 years, the car is worth half of its original price.

2. You bought the car 8 years ago and it is currently worth $5,000.
Since the car has depreciated for 8 years, we need to find the original price of the car.

To calculate the original price, we can use the formula:

Original Price = Current Value / (1 - Depreciation Rate)

The depreciation rate can be calculated using the half-life of the car's value (4 years). The half-life formula is:

Depreciation Rate = 1 / (2 ^ (Time / Half-life))

Substituting the given values:

Half-life = 4 years
Time = 8 years

Depreciation Rate = 1 / (2 ^ (8 / 4))
Depreciation Rate = 1 / (2 ^ 2)
Depreciation Rate = 1 / 4
Depreciation Rate = 0.25

Now, we can calculate the original price:

Original Price = $5,000 / (1 - 0.25)
Original Price = $5,000 / 0.75
Original Price = $6,666.67 (rounded to the nearest cent)

Therefore, the original price of the car was approximately $6,666.67.