What is your question about a 1099?
It would be in your best interest to make estimated quarterly tax payments to both the IRS and the State of California so as to avoid owing a lot of tax at the end of next year. The amount you should pay would only be based on the $10,000 you will be making as an independent contractor, as I assume your employer is already withholding taxes from your regular paycheck. The other factor you need to consider is whether or not you will have any deductions to take against that $10,000. As an independent contractor you might be able to deduct expenses that you incur such as using your own equipment, mileage, supplies you need to purchase, etc. Whatever you think your NET income will be after taking a deduction for any expenses, then I would say you should estimate that your federal taxes for next year will be 28% on that amount. Simply then divide that amount by 4 and make those 4 estimated tax payments each quarter.
Here is a link to the federal estimated tax form with instructions and filing date information
Here is the link for your California state estimated taxes
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