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To determine the periodic deposit required and how much of the financial goal comes from deposits versus interest, we can use the formula for the future value of an ordinary annuity (since the deposits are made at the end of each period):

\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- $FV$ is the future value (the financial goal, $25,000).
- $P$ is the periodic deposit (the amount we need to find).
- $r$ is the interest rate per period.
- $n$ is the total number of periods.

### Given:
- Interest rate $= 2.5\%$ annually, compounded quarterly, so $r = \frac{2.5\%}{4} = 0.00625$ per quarter.
- Time $= 6$ years, and since deposits are made quarterly, $n = 6 \times 4 = 24$ quarters.
- Future value $FV = 25,000$.

#### Step 1: Solving for the periodic deposit $P$.

Let's calculate it by rearranging the formula to solve for $P$:

\[
P = \frac{FV \times r}{(1 + r)^n - 1}
\]

I will now compute this.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still use the formula I provided earlier to calculate the periodic deposit:

\[
P = \frac{FV \times r}{(1 + r)^n - 1}
\]

where $FV = 25000$, $r = 0.00625$ (quarterly interest rate), and $n = 24$ (total periods).

Would you like me to walk you through the steps manually? Or do you have another question?

Here are some related questions:
1. What happens if the interest rate changes?
2. How would the result change with monthly deposits instead of quarterly?
3. What if the time to reach the goal were shorter, like 4 years?
4. How does compound interest affect the total amount compared to simple interest?
5. What if the goal were set to $30,000 instead of $25,000?

**Tip:** Understanding how interest compounds over time can help you plan better for future savings goals.

Use the appropriate formula to determine the periodic deposit. How much of the financial goal comes from deposits and how much comes from interest?

Learn how to calculate the periodic deposits required to reach a financial goal of $25,000 with a 2.5% quarterly compounded interest rate over 6 years. Understand the breakdown of contributions from deposits and interest, using key formulas and concepts in financial mathematics.

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