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This is a compound interest problem where we need to determine the present value (lump sum) Emma should invest today to reach $250,000 in 18 years, with an annual interest rate of 11%, compounded monthly.

The formula for compound interest is:

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

Where:
- $ A $ is the future value ($250,000),
- $ P $ is the present value (what we want to find),
- $ r $ is the annual interest rate (11% = 0.11),
- $ n $ is the number of times interest is compounded per year (monthly = 12),
- $ t $ is the number of years (18).

We need to solve for $ P $:

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

Plugging in the values:

\[
P = \frac{250,000}{\left(1 + \frac{0.11}{12}\right)^{12 \times 18}}
\]

Let me calculate that for you.The amount Emma should invest today to have $250,000 in 18 years at an 11% annual interest rate, compounded monthly, is approximately **$34,830.06**.

Would you like any further details or clarifications on this calculation?

Here are 5 related questions:
1. How does the compounding frequency affect the amount to invest?
2. What would the investment amount be if the interest rate were lower, say 8%?
3. How does the time period (18 years) impact the investment?
4. What if Emma wanted to invest in an account compounded quarterly instead of monthly?
5. How much would Emma have to invest for a goal of $500,000 instead of $250,000?

**Tip:** The more frequently interest is compounded, the larger the future amount will grow due to the effects of compound interest.

Attucks College predicts that in 18 years it will take $250,000 to attend the college for four years. Emma has a substantial amount of cash and wishes to invest a lump sum of money for her child's college fund. How much should Emma put aside in an account with an APR of 11% compounded monthly in order to have $250,000 in the account in 18 years? Round your answer to the nearest cent, if necessary.

Learn how to calculate the present value of an investment required to reach a goal of $250,000 in 18 years at an APR of 11% compounded monthly. This problem covers essential concepts of compound interest and exponential growth. Suitable for high school students in Grades 10-12.

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