To solve this problem, we need to calculate the monthly contributions Jennifer must make to her retirement account to ensure she can withdraw $15,000 per month for 20 years after 30 years of contributions. Here’s a step-by-step breakdown of the solution:

Step 1: Calculate the Present Value of the Retirement Withdrawals

Jennifer wants to withdraw $15,000 per month for 20 years (240 months), starting 30 years from now. First, we need to calculate the present value of these withdrawals at the time she starts withdrawing (30 years from now).

The formula for the present value of an annuity is:

$PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}$

where:

• $PMT = 15,000$ (monthly withdrawal amount)
• $r = \frac{0.02}{12} = 0.0016667$ (monthly interest rate)
• $n = 20 \times 12 = 240$ (total number of withdrawals)

Now, let's calculate the present value (PV):

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

Step 2: Calculate the Future Value of the Present Value

The present value calculated above is at the start of the withdrawal period, 30 years from now. To find the future value of this amount at the time Jennifer starts making her withdrawals, we use the future value formula:

$FV = PV \times (1 + r)^n$

where:

• $PV$ is the present value found in step 1,
• $r = 0.0016667$ (monthly interest rate),
• $n = 30 \times 12 = 360$ (total number of months until retirement).