Jennifer is the owner of a video game and entertainment software retail store. She is currently planning to retire in 30 years and wishes to withdraw $10,000/month for 20 years from her retirement account starting at that time. How much must she contribute each month for 30 years into a retirement account earning interest at the rate of 2%/year compounded monthly to meet her retirement goal? (Round your answer to the nearest cent.)


This is a two-part problem where Jennifer wants to make monthly contributions to her retirement account for 30 years and then withdraw monthly for 20 years during retirement. Here's the approach:

### Step 1: Calculate the amount needed in the retirement account at the beginning of retirement (i.e., after 30 years).
Jennifer wants to withdraw $10,000 per month for 20 years. This is an ordinary annuity problem where she withdraws money monthly.

The formula for the future value of an annuity is:

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

Where:
- $FV$ is the future value of the annuity (the total amount needed at retirement),
- $P$ is the monthly withdrawal amount ($10,000),
- $i$ is the monthly interest rate (2% annual interest compounded monthly, so $ i = \frac{0.02}{12} = 0.0016667 $),
- $n$ is the number of months Jennifer will be withdrawing money (20 years = 240 months).

Substitute the values:

\[
FV = 10,000 \times \frac{1 - (1 + 0.0016667)^{-240}}{0.0016667}
\]

### Step 2: Calculate how much Jennifer must contribute each month for 30 years.
Now, we treat the amount needed at retirement as the future value of an ordinary annuity. The formula for the future value of an annuity (this time for contributions) is:

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

Where:
- $FV$ is the amount needed at the beginning of retirement (from Step 1),
- $P$ is the monthly contribution (what we need to find),
- $i$ is the monthly interest rate (still 0.0016667),
- $n$ is the number of months Jennifer will contribute (30 years = 360 months).

Solve for $P$ (monthly contribution) after finding the future value in Step 1.

Let me compute the solution.Jennifer must contribute approximately **$4,011.85** each month for 30 years into her retirement account to meet her retirement goal of withdrawing $10,000 per month for 20 years, assuming the account earns 2% interest compounded monthly.

Would you like further details or have any questions about the steps involved?

Here are 5 related questions to explore this topic further:
1. How would the required monthly contribution change if the interest rate were higher?
2. What happens if Jennifer wants to retire sooner, say in 25 years instead of 30?
3. How does the frequency of compounding (e.g., quarterly or annually) affect the required contributions?
4. What if Jennifer wants to withdraw $12,000 per month instead of $10,000?
5. How much more would Jennifer need to save if the interest rate drops to 1.5%?

**Tip**: Small changes in the interest rate can significantly impact long-term savings and withdrawals, especially when compounded monthly.

Jennifer is the owner of a video game and entertainment software retail store. She is currently planning to retire in 30 years and wishes to withdraw $10,000/month for 20 years from her retirement account starting at that time. How much must she contribute each month for 30 years into a retirement account earning interest at the rate of 2%/year compounded monthly to meet her retirement goal? (Round your answer to the nearest cent.)

Discover how to calculate the monthly contributions Jennifer must make to her retirement account to meet her goal of withdrawing $10,000 per month for 20 years. This financial problem involves annuity and compound interest calculations with a 2% interest rate compounded monthly. Detailed step-by-step solution provided.

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