Question

During the first year, a new car depreciates in value by 20% and during the second

year, the car depreciates in value by 15% of its value at the beginning of that year..
What is the cost of a new car if its value at the end of the second year is €15 640?

Answer 1

To calculate the cost of a new car at the beginning of the first year, we need to work backward from the value at the end of the second year.

Let's assume the cost of the new car at the beginning of the first year is **C** euros.

During the first year, the car depreciates by 20%, which means its value at the end of the first year is **0.8C** euros.

During the second year, the car depreciates by 15% of its value at the beginning of that year, which is **0.85 × 0.8C = 0.68C** euros.

Given that the value at the end of the second year is €15,640, we can set up an equation:

**0.68C = 15,640**

Solving for **C**, we find:

**C = €15,640 / 0.68 ≈ €22,976.47**

Therefore, the cost of a new car at the beginning of the first year is approximately **€22,976.47**