No.

Detailed instructions:

1. Repaying 1,000 yuan on a credit card every month will not lead to prosecution.

2. Banks usually do not immediately sue customers because their monthly repayments fall below a certain amount.

3. Usually, banks will take other measures to solve overdue repayment problems, such as collection calls or letter reminders.

4. Banks are more inclined to cooperate with customers and help them get out of trouble by providing deferred repayment, installment payment, etc.

5. Unless the debt is large and has not been repaid for a long time, or there are other special circumstances, the bank will consider taking legal measures to recover the debt.

Summary:

Under the given conditions, paying a credit card bill of $1,000 per month will not lead to prosecution. Banks often resolve late payment issues in other ways and work with customers to find solutions.

Extended information:

Each bank may have different policies and practices when dealing with overdue credit card repayments. It is recommended to contact the bank in time to understand the specific repayment arrangements and solutions. Additionally, a good credit history is important to maintain a good credit rating and avoid legal troubles. If necessary, you can consult a professional financial advisor or legal agency for more detailed advice.

Note: The above answers are based on general situations only. Specific situations may vary due to changes in personal credit records, bank policies, laws and regulations. Please take appropriate measures and consult relevant professionals based on the actual situation.