You have $500,000 saved for retirement. Your account earns 4.0% interest. How much will you be able to pull out annually, if you want to be able to take withdrawals for 25 years?

To calculate how much you can withdraw annually over 25 years from a retirement account with a starting balance of $500,000 and an annual interest rate of 4.0%, we can use the formula for the annuity withdrawal amount:

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

where:
- $ A $ = Annual withdrawal amount
- $ P $ = Initial principal (account balance), which is $500,000
- $ r $ = Annual interest rate, which is 4.0% or 0.04
- $ n $ = Number of years for withdrawals, which is 25

### Step-by-Step Solution

1. **Convert the interest rate to a decimal**: 
   \[
   r = \frac{4}{100} = 0.04
   \]

2. **Plug values into the formula**:
   \[
   A = \frac{500,000 \times 0.04}{1 - (1 + 0.04)^{-25}}
   \]

3. **Calculate the terms**:
   - Compute $ (1 + r)^{-n} $:
     \[
     (1 + 0.04)^{-25} \approx 0.3751
     \]
   - Calculate $ 1 - (1 + r)^{-n} $:
     \[
     1 - 0.3751 \approx 0.6249
     \]
   - Finally, calculate the withdrawal amount:
     \[
     A = \frac{500,000 \times 0.04}{0.6249} \approx 32,012.81
     \]

### Solution

The annual amount you can withdraw from your account is approximately **$32,012.81** for 25 years, assuming a 4.0% annual interest rate.

Would you like a more detailed breakdown or have any questions?

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Here are five related questions you might find interesting:

1. How would the annual withdrawal amount change if the interest rate was 5% instead of 4%?
2. What would happen to the annual withdrawal amount if the period was extended to 30 years?
3. How much would be left in the account after 15 years of withdrawals?
4. How would inflation impact the purchasing power of these annual withdrawals over time?
5. What initial principal would you need to withdraw $40,000 annually at a 4% interest rate?

**Tip:** When planning withdrawals, consider adjusting for inflation to maintain the same purchasing power over time.

Find out how much you can withdraw annually from a $500,000 retirement account with a 4.0% interest rate over 25 years. This solution covers the annuity withdrawal formula and time value of money principles, providing a step-by-step guide for financial planning.

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