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 7 years? (Round your answer to the nearest cent.)
$ 

To calculate the value of a $7,000 investment in an S&P 500 index fund after 7 years of continuous depreciation at a rate of 37.6% per year, we can use the formula for exponential decay:

\[
V = P \times (1 + r)^t
\]

where:
- $ V $ is the future value of the investment,
- $ P $ is the initial investment ($7,000),
- $ r $ is the rate of depreciation (which will be negative for depreciation, so $ r = -0.376 $),
- $ t $ is the number of years (7 years).

Plugging in the values:

\[
V = 7000 \times (1 - 0.376)^7
\]
\[
V = 7000 \times (0.624)^7
\]
\[
V \approx 7000 \times 0.0632
\]
\[
V \approx 442.54
\]

Thus, after 7 years, the investment would be worth approximately **$442.54**.

### Questions for Further Exploration:
1. What factors contributed to the S&P 500's decline in 2008?
2. How does the historical performance of the S&P 500 compare to other investment options over the same period?
3. What strategies can investors use to mitigate losses during market downturns?
4. How do dividends affect the total return on an investment in an index fund?
5. What is the impact of inflation on the real value of investments over time?

### Tip:
Consider diversifying your investments to reduce risk, especially in volatile markets.

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 7 years? (Round your answer to the nearest cent.)

Discover how to calculate the future value of a $7,000 investment in an S&P 500 index fund after 7 years of 37.6% annual depreciation, resulting in an approximate value of $442.54. Ideal for high school students learning about exponential decay.

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