Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 11%. The amount of money you will have in 50 years is closest to which of the following?
$110,739

$166,109

$184,565

$221,478

To determine the amount of money you will have in 50 years, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the number of years the money is invested or borrowed for.

In this problem:
- $ P = 1000 $ (the initial investment),
- $ r = 0.11 $ (the rate of return as a decimal),
- $ n = 1 $ (assuming the interest is compounded annually),
- $ t = 50 $ years.

The formula simplifies to:

\[
A = 1000 \times \left(1 + 0.11\right)^{50}
\]

Now, let's calculate the final amount $ A $.

\[
A = 1000 \times \left(1.11\right)^{50}
\]

Let's compute this value.The amount of money you will have in 50 years is approximately **$184,565**.

So, the correct answer is closest to **$184,565**.

Would you like more details or have any other questions?

Here are five related questions for further exploration:

1. How would the final amount change if the interest were compounded quarterly?
2. What would be the amount after 30 years with the same rate of return?
3. How does the compound interest formula differ when interest is compounded monthly?
4. What would the investment amount be after 50 years if the rate of return was 8% instead of 11%?
5. What is the difference between compound interest and simple interest?

**Tip:** When dealing with investments, always consider the compounding frequency, as it can significantly impact the final amount.

Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 11%. The amount of money you will have in 50 years is closest to which of the following? $110,739, $166,109, $184,565, or $221,478.

Discover how to calculate the future value of a $1000 investment with an 11% annual return over 50 years using compound interest. Learn key concepts in exponential growth and understand the impact of compounding over time. Suitable for students in Grades 10-12.

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