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 $15,000/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.)
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To solve this problem, we need to calculate the monthly contribution Jennifer must make to her retirement account to meet her goal. This involves a two-step process:

1. **Determine the amount needed at retirement**: We calculate the present value of the withdrawals she plans to make.
2. **Determine the monthly contribution needed**: We then calculate the contribution required to reach that amount over the 30 years.

### Step 1: Calculate the Present Value of Withdrawals

Jennifer wants to withdraw $15,000 per month for 20 years. The interest rate is 2% per year compounded monthly, so the monthly interest rate is:

\[
i = \frac{2\%}{12} = \frac{0.02}{12} = 0.0016667
\]

The number of withdrawals (n) over 20 years is:

\[
n = 20 \times 12 = 240 \text{ months}
\]

The present value of an annuity formula is:

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

Where:
- $W$ is the monthly withdrawal ($15,000)
- $i$ is the monthly interest rate (0.0016667)
- $n$ is the number of withdrawals (240)

Plugging in the values:

\[
PV = 15000 \times \frac{1 - (1 + 0.0016667)^{-240}}{0.0016667}
\]

### Step 2: Calculate the Monthly Contribution

Now that we know the present value at the start of retirement, we calculate the monthly contribution Jennifer needs to make for 30 years. Again, the interest rate is 2% per year compounded monthly.

Let $A$ be the amount needed at retirement (the present value calculated in Step 1), and let $P$ be the monthly contribution Jennifer needs to make. The future value of an annuity formula is:

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

Where:
- $m$ is the number of contributions (30 years × 12 months = 360 months)
- $i$ is the monthly interest rate (0.0016667)

Solving for $P$:

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

Now, let’s calculate these values step by step.

### Step 1: Calculate the Present Value of Withdrawals (PV)

\[
PV = 15000 \times \frac{1 - (1 + 0.0016667)^{-240}}{0.0016667} \approx 3,055,624.44
\]

### Step 2: Calculate the Monthly Contribution (P)

\[
P = \frac{3055624.44 \times 0.0016667}{(1 + 0.0016667)^{360} - 1} \approx 7066.41
\]

Therefore, Jennifer needs to contribute approximately **$7,066.41** per month to her retirement account.

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

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Here are 5 related questions:
1. What would happen to the monthly contribution if the interest rate increased to 3%?
2. How would the required monthly contribution change if Jennifer decided to retire in 25 years instead of 30?
3. What if Jennifer wanted to withdraw $20,000 per month instead of $15,000—how would that impact her contributions?
4. How much would Jennifer have to contribute if the interest was compounded quarterly instead of monthly?
5. What is the total amount of money Jennifer will have withdrawn by the end of the 20 years?

**Tip:** When planning for retirement, always consider inflation and how it might impact your withdrawal needs.

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 $15,000/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.)

Learn how to calculate the monthly contributions needed for a retirement account with a 2% annual interest rate, compounded monthly. Jennifer plans to retire in 30 years and withdraw $15,000 per month for 20 years. This detailed solution covers key financial concepts such as annuities and compound interest, suitable for college-level financial studies.

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