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To find the car's value in 2013 given that it depreciates by 15% each year, we can use the formula for exponential depreciation:

\[
V = P \times (1 - r)^n
\]

Where:
- \( V \) is the final value of the car,
- \( P \) is the initial value of the car,
- \( r \) is the annual depreciation rate, and
- \( n \) is the number of years.

Given:
- Initial value \( P = £3200 \),
- Depreciation rate \( r = 0.15 \),
- Number of years \( n = 2013 - 2008 = 5 \).

Substitute the values into the formula:

\[
V = 3200 \times (1 - 0.15)^5
\]
\[
V = 3200 \times 0.85^5
\]

I'll calculate this value.The car's value in 2013 is approximately £1419.86.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What would be the car's value in 2015 if the depreciation continued at the same rate?
2. How much total value did the car lose from 2008 to 2013?
3. If the car had depreciated at 10% annually instead, what would its value be in 2013?
4. What is the formula for compound depreciation over time?
5. How long would it take for the car's value to drop below £500 with a 15% annual depreciation?

**Tip:** Depreciation is a common concept in finance, particularly when calculating the value of assets like cars and machinery over time. Understanding exponential decay is key to mastering these calculations.

In 2008, the value of a car was £3200. The value of the car then depreciated by 15% every year. What was the car's value in 2013? Give your answer to the nearest penny.

Learn how to calculate the value of a car after 5 years with a 15% annual depreciation rate. Starting with an initial value of £3200 in 2008, this step-by-step guide shows how to find the car's value in 2013 using exponential decay formulas.

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