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The question asks for the future value of a $7,000 investment in an S&P index fund if the depreciation rate of 37.6% per year continued for 9 years.

To solve this, we'll use the formula for exponential decay:

\[
\text{Future Value} = \text{Present Value} \times (1 - \text{depreciation rate})^n
\]

where:
- Present Value = $7,000,
- Depreciation Rate = 37.6%, or 0.376,
- $ n = 9 $ years.

### Calculation:
\[
\text{Future Value} = 7000 \times (1 - 0.376)^9
\]
\[
= 7000 \times (0.624)^9
\]

Now, calculating $ (0.624)^9 $ and then multiplying by 7000.

### Result:
Let me calculate this.The future value of a $7,000 investment in an S&P index fund, depreciating at 37.6% per year over 9 years, would be approximately **$100.41**.

Would you like more details on this calculation, or do you have any other questions?

### Related Questions
1. How would this value change with different depreciation rates?
2. What if the depreciation continued for a different number of years?
3. How would an annual appreciation rate affect the investment instead?
4. What is the formula for exponential growth compared to exponential decay?
5. How is compound interest different from this type of depreciation?

**Tip:** When dealing with percentage-based depreciation, converting the percentage to a decimal and subtracting from 1 helps simplify decay calculations.

During 2008 the S&P 500 index depreciated by 37.6%. Assuming that this trend had continued, how much would a $7,000 investment in an S&P index fund have been worth after 9 years? (Round your answer to the nearest cent.)

Calculate the future value of a $7,000 investment in the S&P 500 index, given a consistent annual depreciation rate of 37.6% over 9 years. This solution uses the exponential decay formula to determine the final amount.

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