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The question in the image is asking how much money Madison should invest now in an account with 8% APR compounded monthly in order to have $200,000 in 10 years. This is a typical **future value** problem using compound interest.

We will use the **present value formula** for compound interest:

\[
PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $PV$ is the present value (the amount Madison should invest now).
- $FV = 200,000$ is the future value (the amount Madison wants in 10 years).
- $r = 0.08$ is the annual interest rate (8% APR).
- $n = 12$ is the number of times the interest is compounded per year (monthly compounding).
- $t = 10$ is the number of years.

Let me calculate the amount Madison should invest.Madison should invest approximately **$90,104.69** now in order to have $200,000 in 10 years, with an APR of 8% compounded monthly.

Do you want more details on how this was calculated, or do you have any other questions? Here are a few related questions:

1. How does compounding frequency affect the amount to be invested?
2. What if the interest was compounded annually instead of monthly?
3. How much would Madison need to invest if the APR was lower, say 5%?
4. How does increasing the investment period (e.g., 15 years) affect the required investment?
5. What if Madison made monthly contributions instead of a lump sum investment?

**Tip:** The higher the compounding frequency, the less you need to invest initially to reach the same future goal.

Hale College predicts that in 10 years it will take $200,000 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 8% compounded monthly in order to have $200,000 in 10 years?

Learn how to calculate the lump sum Madison should invest now to save $200,000 for her child's college fund in 10 years. This involves applying the compound interest formula with 8% APR compounded monthly. Suitable for high school students and early college finance learners.

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