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Deductions & credits
Correct. The tax and penalty will be applied to the excess that was removed, but it will be removed from your tax history and no longer be subject to an annual 6% penalty.
However, it may not always be necessary to do this.
1. If you are eligible to make new contributions, you can "use up" the excess by contributing less than the maximum amount in the current year. When you consider income tax plus 20%, versus 6% per year, you can see that it might be cheaper in the long run to leave the excess in the account IF you think you might have HSA eligible insurance again some time in the next 5 years.
2. The penalty is 6% of the excess or 6% of the account balance, whichever is less. If you won't be eligible to make new contributions any time soon, but you think you might spend the account down to zero in the next 5 years, you may pay less tax in the long run by paying the annual 6% until you spend the account out, instead of the income tax plus 20% now.
3. If you are age 65 or older, you will pay income tax but not the penalty if you withdraw the excess for non-medical expenses. If you are 62 or older, it may be cheaper to leave the money in the account and pay 6% for a couple of years instead of 20% now.