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.)

$

To find out how much an $8,000 investment in an S&P index fund would be worth after 3 years with an annual depreciation of 37.6%, we can use the formula for compound depreciation:

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

where:
- $ V $ = future value of the investment
- $ P $ = initial investment amount ($8,000)
- $ r $ = annual depreciation rate (37.6% or 0.376)
- $ n $ = number of years (3)

Plugging in the values:

\[
V = 8000 \times (1 - 0.376)^3
\]
\[
V = 8000 \times (0.624)^3
\]
\[
V = 8000 \times 0.244140624
\]
\[
V \approx 1953.13
\]

Thus, after 3 years, the investment would be worth approximately **$1,953.13**.

Would you like more details on this calculation or have any questions? Here are some related questions to consider:

1. How does the S&P 500 typically perform after significant declines?
2. What are the historical average returns of the S&P 500 over the long term?
3. How would a different rate of depreciation affect the investment's value?
4. What are the implications of investing in index funds during a market downturn?
5. How does inflation affect the real value of investments over time?

**Tip:** Consider diversifying your investments to mitigate risks during market downturns.

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.)

Discover how to calculate the future value of an $8,000 investment in an S&P index fund after a 37.6% annual depreciation over 3 years. This guide covers compound depreciation and provides a detailed solution, showing the investment would be worth approximately $1,953.13.

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