Find the amount necessary to fund the given withdrawals. Monthly withdrawals of $\$ 600$ for 7 years; interest rate is $6.9 \%$ compounded monthly. The amount necessary to fund the given withdrawals is $\$ \square$. (Round to the nearest cent as needed.)

Step 1 ：We are given that the monthly withdrawals are $600, the interest rate is 6.9% compounded monthly, and the time period is 7 years. We can use the formula for the present value of an ordinary annuity to find the amount necessary to fund the withdrawals. The formula is: \(PV = PMT * [(1 - (1 + r/n) ^ {-nt}) / (r/n)]\) where: PV is the present value (the amount necessary to fund the withdrawals), PMT is the monthly withdrawal amount, r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, t is the time in years.

Step 2 ：Substitute the given values into the formula: PMT = 600, r = 0.069, n = 12, t = 7.

Step 3 ：Calculate the present value: \(PV = 600 * [(1 - (1 + 0.069/12) ^ {-12*7}) / (0.069/12)]\)

Step 4 ：The present value came out to be negative, which is not possible in this context. I must have made a mistake in the calculation. Let's try again.

Step 5 ：Substitute the given values into the formula again: PMT = 600, r = 0.069, n = 12, t = 7.

Step 6 ：Calculate the present value again: \(PV = 600 * [(1 - (1 + 0.069/12) ^ {-12*7}) / (0.069/12)]\)

Step 7 ：Final Answer: The amount necessary to fund the given withdrawals is \(\boxed{\$39883.43}\).