A new car was bought for 24 000 euro. It decreased in value by 20 % in the first year. If it's value at the end of the second year was 16 128 euro , by what percentage did it's value decrease during the second year?

Let's break this down step-by-step to find the percentage decrease in value during the second year.

### Step 1: Calculate the car's value at the end of the first year
The car initially costs 24,000 euros and decreases in value by 20% in the first year.

\[
\text{Decrease in value} = 20\% \times 24,000 = 0.20 \times 24,000 = 4,800 \text{ euros}
\]

Now, subtract this decrease from the initial price:

\[
\text{Value at the end of the first year} = 24,000 - 4,800 = 19,200 \text{ euros}
\]

### Step 2: Calculate the decrease in value during the second year
The car's value at the end of the second year is given as 16,128 euros. The value at the end of the first year was 19,200 euros, so the decrease in value during the second year is:

\[
\text{Decrease in value} = 19,200 - 16,128 = 3,072 \text{ euros}
\]

### Step 3: Find the percentage decrease during the second year
Now, we need to calculate what percentage this decrease (3,072 euros) is of the car's value at the end of the first year (19,200 euros):

\[
\text{Percentage decrease} = \left(\frac{3,072}{19,200}\right) \times 100
\]

Let's compute this:

\[
\text{Percentage decrease} = \left(\frac{3,072}{19,200}\right) \times 100 \approx 16\%
\]

So, the car's value decreased by **16%** during the second year.

Would you like more details or have any questions?

### Related Questions
1. How much would the car be worth at the end of the third year if it decreases by 16% again?
2. What is the total percentage decrease in the car's value over the two years?
3. If the car's value continues to decrease by 16% annually, what will its value be after five years?
4. How would the calculation change if the car decreased by a fixed amount each year rather than a percentage?
5. Can you explain how compound percentage decreases work?

### Tip
When dealing with percentage decreases, always use the original amount for each specific year to calculate the decrease accurately.

A new car was bought for 24 000 euro. It decreased in value by 20 % in the first year. If its value at the end of the second year was 16 128 euro, by what percentage did its value decrease during the second year?

Learn how to calculate the percentage decrease in a car's value during its second year. Starting at 24,000 euros with a 20% depreciation in the first year, find out how the value further decreases to 16,128 euros by the second year. A step-by-step solution with core algebraic concepts and percentage calculations, suitable for Grades 6-9.

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