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The problem presented asks how much Emma should invest today to accumulate $350,000 in 18 years with an APR of 12%, compounded monthly.

This is a classic problem of determining the present value (PV) for future savings using compound interest. The formula to use is:

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

Where:
- $PV$ = Present value (the amount to invest today)
- $FV$ = Future value ($350,000)
- $r$ = Annual interest rate (12% or 0.12)
- $n$ = Number of compounding periods per year (monthly compounding means $n = 12$)
- $t$ = Number of years (18 years)

Let me calculate that for you.Emma should invest approximately **$40,799.17** today in order to have $350,000 in 18 years, assuming an APR of 12% compounded monthly.

Would you like a more detailed explanation of the process?

Here are 5 related questions you might want to explore:
1. How does the compounding frequency affect the final amount?
2. What if Emma invested monthly instead of a lump sum?
3. How would a lower APR affect the amount Emma needs to invest?
4. How much would Emma need if the compounding period were annual?
5. How would taxes affect the interest earned?

**Tip:** Always double-check whether your interest rate is compounded annually, monthly, or daily as this affects the final outcome significantly!

Arnett College predicts that in 18 years it will take $350,000 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 12% 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 to accumulate $350,000 in 18 years at 12% APR, compounded monthly. This financial mathematics problem uses the compound interest formula to determine the present value of a future investment.

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