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To solve this, we need to calculate the future value of an ordinary annuity. The formula to find the future value ($FV$) of an ordinary annuity is:

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

Where:
- $P$ is the annual payment ($200),
- $r$ is the interest rate per period (15% or 0.15),
- $n$ is the number of periods (5 years).

Let's calculate this step by step:

\[
FV = 200 \times \left( \frac{(1 + 0.15)^5 - 1}{0.15} \right)
\]

First, calculate $ (1 + 0.15)^5 $:

\[
(1 + 0.15)^5 = 2.011357
\]

Now, subtract 1:

\[
2.011357 - 1 = 1.011357
\]

Next, divide by 0.15:

\[
\frac{1.011357}{0.15} = 6.74238
\]

Finally, multiply by the annual payment of $200:

\[
200 \times 6.74238 = 1,348.48
\]

So, the future value is approximately **$1,348**. The correct answer is **$1,348**.

Do you need further clarification or more details?

### 5 Follow-up Questions:
1. How would the future value change if the interest rate were 10% instead of 15%?
2. What happens to the future value if the annuity period increases to 10 years?
3. Can you explain how an ordinary annuity differs from an annuity due in this calculation?
4. How is the present value of an ordinary annuity calculated?
5. What if the payments were made quarterly instead of annually? How would that affect the calculation?

**Tip:** Understanding how interest rates and time periods affect annuities helps in making better financial decisions!

What is the future value of a 5-year ordinary annuity with annual payments of $200, invested at a 15% interest rate?

Calculate the future value of a 5-year ordinary annuity with annual payments of $200 and an interest rate of 15%. This finance problem involves concepts of compound interest and annuities, suitable for college-level students.

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