You have $400,000 saved for retirement. Your account earns 8% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 15 years?

To determine how much you can withdraw each month for 15 years from an account with $400,000 and an 8% annual interest rate, we can use the **annuity formula**:

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

Where:
- $ PMT $ is the monthly withdrawal amount (the amount we're solving for),
- $ P $ is the principal (the initial amount saved, $400,000),
- $ r $ is the monthly interest rate,
- $ n $ is the total number of monthly withdrawals (the number of months over 15 years).

### Step 1: Identify key values.
- Principal $ P = 400,000 $
- Annual interest rate = 8%, so monthly interest rate $ r = \frac{8\%}{12} = 0.0066667 $
- Total number of months $ n = 15 \times 12 = 180 $ months.

### Step 2: Apply the formula.
Now, we can plug these values into the annuity formula:

\[
PMT = \frac{400,000 \cdot 0.0066667}{1 - (1 + 0.0066667)^{-180}}
\]

### Step 3: Calculate the monthly withdrawal.
Let me compute this step for you:

\[
PMT = \frac{400,000 \cdot 0.0066667}{1 - (1.0066667)^{-180}}
\]
\[
PMT = \frac{2666.67}{1 - 0.3118} = \frac{2666.67}{0.6882} = 3875.96
\]

### Final Answer:
You can withdraw approximately **$3,875.96 per month** for 15 years.

Would you like a more detailed breakdown of the calculation, or do you have any further questions?

Here are 5 questions related to the topic:
1. What happens if the interest rate changes during the 15 years?
2. How would the withdrawal change if you wanted to take out money for 20 years instead of 15?
3. What if you want to leave some amount at the end of the 15 years?
4. How would taxes impact your withdrawals?
5. How does inflation affect the real value of your withdrawals over time?

**Tip**: If you plan to withdraw over a longer period or adjust for inflation, it's crucial to re-evaluate the withdrawal amount regularly.

Learn how to calculate monthly withdrawals from a $400,000 retirement account earning 8% interest over 15 years. Using the annuity formula, this example covers key concepts like compound interest and retirement planning. Suitable for high school students or anyone looking to understand financial math.

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