**After retiring, you want to be able to withdraw $2100 each month for 24 years. Your account earns 7.2% interest.**

**How much money do you need in your account when you retire?** 

*Do not round numbers while working on the problem.  Only round the final answer.*

*Since we are working with money, round to the cent.*

To determine how much money you need in your account when you retire to withdraw $2,100 each month for 24 years, we again use the formula for the present value of an annuity:

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

Where:
- $PV$ is the present value (the amount you need to have at retirement).
- $P = 2100$ dollars is the payment amount per period.
- $r$ is the monthly interest rate.
- $n$ is the total number of payments (months).

### Step 1: Identify the values
- The annual interest rate is 7.2%, so the monthly interest rate $r$ is:

\[
r = \frac{7.2\%}{12} = \frac{0.072}{12} = 0.006
\]

- The total number of payments $n$ is:

\[
n = 24 \times 12 = 288 \text{ months}
\]

### Step 2: Substitute the values into the formula

\[
PV = 2100 \times \left( \frac{1 - (1 + 0.006)^{-288}}{0.006} \right)
\]

### Step 3: Calculate the present value

I'll compute this now.The amount you need in your account when you retire to be able to withdraw $2,100 each month for 24 years is **$287,504.38**.

Would you like more details on any part of this calculation, or do you have any further questions?

Here are 5 related questions you might consider:
1. How would the required amount change if the interest rate were 8% instead of 7.2%?
2. What if you wanted to withdraw $3,000 each month instead of $2,100?
3. How much would you need to have saved if you wanted to withdraw money for 30 years instead of 24?
4. What is the total interest earned over the 24 years if you start with $287,504.38?
5. How would the amount change if the withdrawals were made yearly instead of monthly?

**Tip:** When planning for retirement, consider inflation, as it can significantly impact your purchasing power over time.

Learn how to calculate the amount needed in your retirement savings to withdraw $2,100 per month over 24 years at a 7.2% interest rate. This problem involves understanding annuities, monthly interest rate calculations, and financial planning for retirement.

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