To calculate the maximum amount that can be withdrawn at the start of each quarter, we need to consider the contributions made, the interest accumulated, and the time periods involved.
1. Contributions: Each month, 324 is contributed to the account for 10 years, resulting in a total contribution of 10 * 12 * 324 = 38,880.
2. Accumulation period: After the final payment, the funds are allowed to accumulate interest for exactly 9 years. Since the interest is compounded quarterly, the total number of compounding periods is 9 * 4 = 36.
3. Withdrawal period: After the accumulation period, start of quarter withdrawals are made for 9 years. Again, since the interest is compounded quarterly, the total number of compounding periods for withdrawals is 9 * 4 = 36.
Now, let's calculate the maximum amount that can be withdrawn at the start of each quarter.
Step 1: Calculate the future value of the contributions during the accumulation period:
Future Value = Present Value * (1 + interest rate)^number of compounding periods
Future Value = $38,880 * (1 + 0.046/4)^36
Future Value = $38,880 * (1.0115)^36
Future Value = $38,880 * 1.53359
Future Value = $59,573.61
Step 2: Calculate the maximum amount that can be withdrawn at the start of each quarter during the withdrawal period:
Maximum Withdrawal Amount = Future Value / number of compounding periods for withdrawals
Maximum Withdrawal Amount = $59,573.61 / 36
Maximum Withdrawal Amount = $1,654.27 (rounded to two decimal places)
Therefore, the maximum amount that can be withdrawn at the start of each quarter is $1,654.27.
Please note that the calculations assume the interest rate remains constant over the entire 28-year period and that there are no additional contributions or withdrawals during the withdrawal period.