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To solve this problem, we will use the present value formula for compound interest:

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

Where:
- $PV$ is the present value (the amount to be invested now),
- $A$ is the desired future value (accumulated amount),
- $r$ is the annual interest rate (as a decimal),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the time in years.

Given:
- Desired accumulated amount $A = 100,000$,
- Annual interest rate $r = 2\% = 0.02$,
- Compounded quarterly, so $n = 4$,
- Time period $t = 4$ years.

Now we can plug these values into the formula:

\[
PV = \frac{100,000}{(1 + \frac{0.02}{4})^{4 \times 4}}
\]
\[
PV = \frac{100,000}{(1 + 0.005)^{16}} = \frac{100,000}{(1.005)^{16}}
\]

Now, let's calculate the value of $ (1.005)^{16} $.

\[
(1.005)^{16} \approx 1.082857
\]

Thus:

\[
PV = \frac{100,000}{1.082857} \approx 92,333.48
\]

The present value, or the amount to be invested now, is approximately **$92,333.48**.

Would you like more details on this, or do you have any questions? 

Here are some follow-up questions to expand on this topic:
1. How does changing the compounding frequency affect the present value?
2. What happens if the interest rate increases to 3% instead of 2%?
3. How would the present value change if the investment period were 6 years instead of 4?
4. What would be the future value if you invest $92,333.48 for 4 years with the same interest rate?
5. How would continuous compounding alter the calculations for the present value?

**Tip:** Always remember to convert the interest rate from a percentage to a decimal in financial formulas.

The desired accumulated amount is $100,000 after 4 years invested in an account with 2% interest compounded quarterly. What is the present value needed?

Learn how to calculate the present value for an investment of $100,000 with 2% interest compounded quarterly over a 4-year period. Using the compound interest formula, discover the amount needed to invest today to reach your desired future value. Suitable for high school students and financial learners.

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