You have $500,000 saved for retirement. Your account earns 10% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

$

To determine how much you can withdraw each month from your retirement account over 20 years with a 10% annual interest rate, we can use the formula for calculating the monthly annuity withdrawal amount:

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

where:
- $ PMT $ is the monthly withdrawal amount,
- $ P $ is the principal amount (initial savings),
- $ r $ is the monthly interest rate,
- $ n $ is the total number of withdrawals.

### Given:
- **P** = $500,000 (initial savings),
- **Annual interest rate** = 10%, so **monthly interest rate** $ r = \frac{0.10}{12} \approx 0.008333$,
- **Number of years** = 20, so **total number of withdrawals** $ n = 20 \times 12 = 240 $.

### Calculating Monthly Withdrawal Amount (PMT):
\[
PMT = \frac{500,000 \times 0.008333 \times (1 + 0.008333)^{240}}{(1 + 0.008333)^{240} - 1}
\]

After solving, you’ll find that:

\[
PMT \approx 4,833.95
\]

So, you would be able to withdraw approximately **$4,833.95** each month.

Would you like further details, or do you have any questions?

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1. How does changing the interest rate affect the monthly withdrawal amount?
2. What if you wanted the withdrawals to last for 30 years instead of 20?
3. How would monthly withdrawals differ if you only had $400,000 saved?
4. How is the withdrawal amount affected if the interest compounds quarterly instead of monthly?
5. What if you decide to withdraw less monthly to allow for an inheritance?

**Tip:** Monthly compounding leads to higher withdrawals compared to annual compounding, due to more frequent interest accrual.

You have $500,000 saved for retirement. Your account earns 10% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

Learn how to calculate the monthly withdrawal amount from a $500,000 retirement account earning 10% interest annually, allowing withdrawals for 20 years. This guide covers the annuity formula for fixed monthly withdrawals and key financial math concepts. Suitable for high school and college students.

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