If it's a Traditional IRA, and you received a tax deduction for your contributions, closing it will result in a fully taxable distribution. You'll receive a Form 1099-R for the value of the IRA that you received. And it will be taxed at your ordinary income tax rate.
If it's a ROTH IRA, contributions are made with after tax dollars. This means, at worst, only your growth (earnings) on the funds you contributed would be taxed. However, if you've had the account for over five years, there is no tax on the growth either. You will still receive a Form 1099-R for your full distribution and a taxable portion which will either be the growth or $0 if you've had the account for longer than the five year period.
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