Congratulations on your win! However, no one is going to be able to answer your question without a lot more information about other income you will likely have in 2015. You need to figure out what your total gross taxable income is likely to be, including the value of the car and any other prizes and also any wages, commissions, bonuses, interest, dividends, rents, and other income. You then need to figure out what your total deductions are likely to be for the year, and whether you may be able to itemize or will be stuck with the standard deduction. If you file jointly, your spouse's income and deductions will also need to be estimated. Then, you should be able to figure out the likely net income number and how much you will have withheld. The additional amount will be what you need to have set aside. You might also need to file quarterly estimated income returns and pay some of those taxes in advance, even if you have withholding from other income sources. Don't forget to look at both state and federal income, including the taxes that may be imposed by the state where you won the car, if that's not the same as your home state (i.e., if you won a game show that is filmed in California, California will likely want to tax the winnings as income from California, even if you live somewhere else).
It's probably a good idea to talk to a good income tax CPA or other experienced income tax preparer who can help you make the estimates and figure out what you need to set aside, and whether you should be filing the quarterly estimated returns. It's not the sort of question most tax attorneys will answer.
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