Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest ten dollars.)
$200 deposited monthly for 15 years at 7% per year

To find the future value (FV) of an ordinary annuity (where deposits are made at the end of each period), we use the formula:

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

Where:
- $ P $ is the deposit amount ($200),
- $ r $ is the interest rate per period,
- $ n $ is the total number of periods.

### Step 1: Identify values
- **Monthly deposit** ($ P $): $200
- **Annual interest rate**: 7%, or 0.07 as a decimal.
- **Compounding periods per year**: 12 (monthly).
- **Number of years**: 15.

### Step 2: Calculate values needed for the formula
1. **Interest rate per period** ($ r $):
   \[
   r = \frac{0.07}{12} = 0.0058333
   \]

2. **Total number of periods** ($ n $):
   \[
   n = 15 \times 12 = 180
   \]

### Step 3: Apply the formula
Now we can substitute the values into the future value formula:

\[
FV = 200 \times \left( \frac{(1 + 0.0058333)^{180} - 1}{0.0058333} \right)
\]

### Step 4: Solve
First, calculate $ (1 + 0.0058333)^{180} $:
\[
(1.0058333)^{180} \approx 2.8497
\]
Now apply the rest of the formula:
\[
FV = 200 \times \left( \frac{2.8497 - 1}{0.0058333} \right)
\]
\[
FV = 200 \times \left( \frac{1.8497}{0.0058333} \right)
\]
\[
FV = 200 \times 316.989 \approx 63,398
\]

### Final Answer:
The future value of the annuity is approximately **$63,400**.

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Would you like more details on how the formula was applied or help with a similar question?

Here are five related questions:
1. How would the future value change if the interest rate was 5% instead of 7%?
2. What would the future value be if deposits were made quarterly instead of monthly?
3. How do you calculate the present value of an annuity?
4. How does compound interest affect annuities compared to simple interest?
5. What if the deposits were made at the beginning of each period (annuity due)?

**Tip:** Increasing the frequency of compounding generally leads to a higher future value, as interest is applied more often.

Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest ten dollars.) $200 deposited monthly for 15 years at 7% per year.

Calculate the future value of an ordinary annuity with $200 deposited monthly for 15 years at an annual interest rate of 7%. This step-by-step guide covers key financial concepts, including compound interest and annuity formulas, suitable for high school or early college students.

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