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The problem shown in the image asks for the future value (FV) of an annuity with regular deposits of $1,800 quarterly over 20 years at 2% annual interest. Let's solve this step by step.

### Formula for the Future Value (FV) of an Annuity:
The formula for the future value of an annuity with regular deposits is:

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

Where:
- $P$ = Regular deposit amount
- $r$ = Interest rate per period
- $n$ = Total number of periods

### Given Information:
- Regular deposit ($P$) = $1,800
- Annual interest rate = 2%
- Time = 20 years
- Compounding quarterly (so 4 periods per year)

### Step 1: Adjust the interest rate and periods for quarterly compounding.
- Interest rate per period ($r$) = $\frac{2\%}{4} = 0.005$
- Total number of periods ($n$) = $20 \times 4 = 80$ quarters

### Step 2: Apply the values to the formula.
\[
FV = 1,800 \times \frac{(1 + 0.005)^{80} - 1}{0.005}
\]

Let's calculate this.

\[
(1 + 0.005)^{80} = (1.005)^{80} \approx 1.48985
\]
Now calculate:

\[
FV = 1,800 \times \frac{1.48985 - 1}{0.005} = 1,800 \times \frac{0.48985}{0.005} = 1,800 \times 97.97 \approx 176,346
\]

### Final Answer:
The future value (FV) is approximately **$176,346.00**.

Would you like further details or have any questions? Here are some related questions:

1. How does the compounding frequency affect the future value?
2. What happens if the interest rate changes from 2% to 3%?
3. How would the future value change if the deposits were made monthly instead of quarterly?
4. Can this formula be applied to continuous compounding?
5. What are the differences between an ordinary annuity and an annuity due?

**Tip:** Always adjust both the interest rate and the number of periods to match the compounding frequency when using annuity formulas.

Find the accumulated FV in the given annuity account. Assume end-of-period deposits and compounding at the same intervals as deposits. $1,800 is deposited quarterly for 20 years at 2% per year.

Learn how to calculate the future value of an annuity account with quarterly deposits of $1,800 for 20 years at 2% annual interest. This solution uses the Future Value (FV) formula for an annuity with compounding interest. Suitable for finance and math students.

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