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To solve this, we need to use the present value formula for compound interest:

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

Where:
- $PV$ is the present value (the amount you need to invest now),
- $FV$ is the future value (in this case, \$100,000),
- $r$ is the annual interest rate (given as 3% or 0.03),
- $n$ is the number of times the interest is compounded per year (quarterly means $n = 4$),
- $t$ is the number of years (18 years here).

### Substituting the values into the formula:
\[
PV = \frac{100,000}{(1 + \frac{0.03}{4})^{4 \times 18}}
\]

I'll calculate this now.The amount you need to invest now in one lump sum is approximately **$58,392.36**.

Would you like any further details or clarification? Here are 5 related questions that might help you understand this topic better:

1. How does changing the compounding frequency affect the present value?
2. What would happen if the interest rate were higher or lower?
3. How would the present value change if the investment period were shorter or longer?
4. What is the difference between simple interest and compound interest?
5. How is the future value calculated in similar scenarios?

**Tip:** Always check if the interest rate is compounded annually, quarterly, or monthly—it can significantly impact the present value of your investment.

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $100,000 after 18 years with an APR of 3% compounded quarterly. Round your answer to the nearest cent, if necessary.

Learn how to calculate the present value of a lump sum investment required to reach $100,000 after 18 years at a 3% APR, compounded quarterly. This solution covers essential financial concepts and the compound interest formula, suitable for college-level finance or economics students.

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