During 2008 the S&P 500 index depreciated by 37.6%.† Assuming that this trend had continued, how much would an $8,000 investment in an S&P index fund have been worth after 3 years? (Round your answer to the nearest cent.)

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To calculate the value of the investment after 3 years, given a yearly depreciation of 37.6%, we can use the formula for exponential decay:

\[
\text{Future Value} = \text{Present Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}}
\]

### Given:
- **Present Value (initial investment)** = $8,000
- **Depreciation Rate** = 37.6% or 0.376
- **Number of Years** = 3

### Calculation:

1. Substitute the values into the formula:
   \[
   \text{Future Value} = 8000 \times (1 - 0.376)^3
   \]

2. Simplify the depreciation term:
   \[
   1 - 0.376 = 0.624
   \]

3. Raise $0.624$ to the power of 3:
   \[
   0.624^3 \approx 0.2429
   \]

4. Multiply by the initial investment:
   \[
   8000 \times 0.2429 = 1943.20
   \]

### Answer:
After 3 years, the investment would be worth approximately **$1,943.20**.

Would you like further details or have any questions?

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Here are some related questions you may find interesting:
1. What would be the value if the depreciation rate changed to 30%?
2. How would the investment grow if there were a 10% appreciation each year instead?
3. What if the depreciation rate was compounded semi-annually?
4. How much would you need to invest to achieve a future value of $10,000 after 3 years with the same depreciation rate?
5. How does compounding frequency affect the future value of an investment?

**Tip:** When working with percentages in exponential calculations, always convert the percentage to a decimal by dividing by 100.

During 2008 the S&P 500 index depreciated by 37.6%. Assuming that this trend had continued, how much would an $8,000 investment in an S&P index fund have been worth after 3 years? (Round your answer to the nearest cent.)

Learn how to determine the future value of an $8,000 investment depreciating at 37.6% annually over 3 years, using exponential decay calculations. This problem covers key concepts in investment depreciation, exponential functions, and percentage calculations, suitable for high school students in Grades 10-12.

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