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To calculate the future value of Margo's retirement account, we can use the **future value of an annuity formula** for monthly contributions compounded monthly. The formula is:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the monthly contribution ($250).
- $r$ is the annual interest rate (6.5% or 0.065).
- $n$ is the number of times the interest is compounded per year (12 for monthly compounding).
- $t$ is the number of years (20 years).

### Step-by-step solution:

1. **Given values:**
   - $ P = 250 $
   - $ r = 0.065 $
   - $ n = 12 $
   - $ t = 20 $

2. **Substitute into the formula:**

\[
FV = 250 \times \frac{(1 + 0.065/12)^{12 \times 20} - 1}{0.065/12}
\]

3. **Simplify the terms:**
   - $ r/n = 0.065/12 = 0.00541667 $
   - $ nt = 12 \times 20 = 240 $

So, the equation becomes:

\[
FV = 250 \times \frac{(1 + 0.00541667)^{240} - 1}{0.00541667}
\]

4. **Calculate:**
   - $ (1 + 0.00541667)^{240} = 3.593776 $
   - $ 3.593776 - 1 = 2.593776 $

Thus,

\[
FV = 250 \times \frac{2.593776}{0.00541667} = 250 \times 478.721
\]

\[
FV = 119,680.25
\]

### Final Answer:
The future value of Margo's account is **\$119,680.25**.

Would you like further details or have any questions?

Here are 5 related questions to expand on the topic:
1. How does changing the interest rate affect the future value of the annuity?
2. What if Margo contributes for 30 years instead of 20 years?
3. How would the future value change if the contributions were made at the end of the month?
4. What is the formula for continuous compounding, and how does it differ from monthly compounding?
5. How would inflation affect the purchasing power of this future amount?

**Tip:** Always double-check your interest rate's compounding frequency to ensure you are using the correct version of the formula.

Margo starts an individual retirement account (IRA) by depositing $250 at the beginning of each month into an account that earns 6.5% interest compounded monthly. If Margo continues this plan for 20 years, what will be the value (in dollars) of her account?

Learn how to calculate the future value of an IRA account with monthly contributions of $250 at an interest rate of 6.5%, compounded monthly. This example provides a detailed step-by-step solution for a retirement account over 20 years.

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