Arnett College predicts that in 1818 years it will take $350,000$⁢350,000 to attend the college for four years. Madison has a substantial amount of cash and wishes to invest a lump sum of money for her child’s college fund. How much should Madison put aside in an account with an APR of 7%7% compounded monthly in order to have $350,000$⁢350,000 in the account in 1818 years? Round your answer to the nearest cent, if necessary.

We can solve this problem using the formula for the future value of an investment compounded periodically. The formula is:

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

Where:
- $A$ is the future value of the investment, which is $350,000$.
- $P$ is the present value or the amount Madison needs to invest.
- $r$ is the annual interest rate (7% or 0.07).
- $n$ is the number of times the interest is compounded per year (monthly compounding means $n = 12$).
- $t$ is the time in years, which is 18.

We are solving for $P$. Rearranging the formula to solve for $P$, we get:

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

Now, substituting the values:

\[
P = \frac{350,000}{(1 + \frac{0.07}{12})^{12 \times 18}}
\]

Let's calculate this step-by-step.Madison should invest approximately \$99,643.01 in an account with a 7% APR compounded monthly to have \$350,000 in 18 years.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the required investment change if the interest rate was compounded annually instead of monthly?
2. What if the interest rate was 6% instead of 7%? How would that affect the initial investment?
3. How long would it take for the investment to double at 7% compounded monthly?
4. What would be the future value if Madison invests only $80,000 today with the same interest rate?
5. How does the compounding frequency (monthly, quarterly, etc.) affect the amount Madison needs to invest?

**Tip:** Compounding more frequently results in higher returns, but also requires a smaller initial investment for the same future value.

Arnett College predicts that in 18 years it will take $350,000 to attend the college for four years. Madison has a substantial amount of cash and wishes to invest a lump sum of money for her child’s college fund. How much should Madison put aside in an account with an APR of 7% compounded monthly in order to have $350,000 in the account in 18 years? Round your answer to the nearest cent, if necessary.

Learn how to calculate the lump sum investment needed for a $350,000 college fund in 18 years with a 7% APR compounded monthly. This problem uses the compound interest formula to determine the present value and is suitable for students in Grades 10-12.

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