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Question: How many monthly payments of $5,000.00 do you get out of $150,000.00 maturing with 4% interest monthly.

To determine how many monthly payments of $5,000 you can get from an investment of $150,000 that accrues interest at a rate of 4% per month, we need to factor in the accumulating interest on the remaining balance each month and the monthly withdrawal. Here's the step-by-step method to solve this problem: 1. **Interest Calculation**: Calculate the balance at the beginning of each month after interest is applied. 2. **Payment Subtracted**: Subtract the $5,000 payment at the end of each month. 3. **Iterate**: Repeat the above steps until the balance is insufficient to cover the $5,000 payment. The formula to calculate the balance after one month, including the interest added and payment deducted, is: \[ \text{New Balance} = (\text{Previous Balance} \times 1.04) - 5000 \] Let's illustrate this with manual calculations for the first few months for clarity: 1. Initial balance: $150,000 \[ 150,000 \times 1.04 = 156,000 - 5,000 = 151,000 \] 2. Second month balance: \[ 151,000 \times 1.04 = 157,040 - 5,000 = 152,040 \] 3. Third month balance: \[ 152,040 \times 1.04 = 158,121.60 - 5,000 = 153,121.60 \] Notice the amount keeps increasing due to the high interest rate compared to the fixed withdrawal. It seems that with a 4% monthly interest rate, the principal actually grows every month even after the $5,000 withdrawal. Essentially, the investment could sustain indefinitely in this specific case because the interest earned each month exceeds the withdrawal amount. Therefore, theoretically, you are getting an infinite number of monthly payments because the account balance will continuously grow each month due to the high monthly interest rate. Note, however, that such a high monthly interest rate (48% annually when compounded) is unusually high and almost unrealistic in typical financial scenarios. In practical situations, investments usually have much lower monthly interest rates.

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