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The Affordable Care Act's health insurance exchanges opened for the second time on Saturday. According to the Department of Health and Human Services, more than 500,000 people visited the federal exchange, health, on the first day of open enrollment to compare plans offered by insurers such as UnitedHealth (NYSE: UNH), WellPoint (NYSE: WLP), and Aetna (NYSE: AET).

As the open enrollment period progresses, industry watchers expect millions more people will log onto the site. But some of those visitors might not want to buy insurance or might not be able to afford the health insurance plans being offered. For those people, forgoing insurance could pose a problem at tax time. That's because the Affordable Care Act includes a penalty payment for uninsured Americans who do not purchase health insurance. However, not everyone will be on the hook for this penalty.

First, a bit of background
Americans who didn't have health insurance this year could be penalized when they file their taxes next April. That fee is the higher of $95 per adult plus $47.50 per child under 18,  or 1% of household income above the tax filing threshold, up to a family maximum of $285. That penalty will jump in 2015 to the higher of $325 per adult plus $162.50 per child under 18, or 2% of household income above the tax filing threshold, up to a family maximum of $975.

Read on to learn who might be exempt.

The fee for not having insurance only applies to those who fail to have health insurance coverage for three months or longer in any year. So, for example, if you left one job and started another job, but had a two month interruption in your health insurance, you wouldn't have to pay the penalty.

Pricey payments
The ACA also exempts people from being penalized if the cost of the lowest-priced plan available exceeds 8% of household income. But be careful: Since the exemption is for household income, not individual income, don't forget to include income from a spouse when doing the calculation.

Those who do not earn enough during the year to have to file a tax return won't be responsible for paying the penalty. That means that people who have part-time jobs at which they earn less than the tax filing threshold, which is $10,150 for individuals and $20,300 for married couples filing jointly in 2015, wouldn't have to pay.

Source: IRS

Special interest groups
Those who are members of a federally recognized Native American tribe, or eligible for health services through a Native American provider, are exempt.

So are members of a recognized health care sharing ministry, which is a non-profit that shares the cost of members' medical care across its membershipBut that exemption doesn't mean people can just start up their own ministry. The exemption only applies to those ministries established prior to 1999. And health care sharing ministries may not be for everyone given that members must pledge to live their lives based on specific religious doctrines. 

Members of a recognized religious sect with religious objections to insurance, including Social Security and Medicare, aren't required to pay the penalty, either. However, that exemption is primarily for the Amish and Mennonites, who do not participate in the Social Security and Medicare systems. 

Incarceration or illegal immigrants
The penalty doesn't apply to those who are serving time in jail, including those being detained, and  since illegal immigrants can't qualify for health insurance through the exchanges, they won't pay, either.

Falling on tough times
If you've fallen on hard times, there's a chance you won't have to pay the penalty.

The ACA includes a hardship provision for people who are homeless, recently evicted, or foreclosed upon. The hardship exemption also applies if a utility has sent you a shutoff notice or if you're the victim of domestic violence. If a close family member has died or you have declared bankruptcy, you might receive an exemption as well.

Those aren't the only hardship exemptions available. For example, many low income earners may qualify for the hardship exemption that addresses the coverage gap. When the ACA was created, Medicaid expansion was expected to cover more low income earners, so insurance exchange subsidies don't kick in until an individual's income hits $11,670. Since Medicaid was made an opt-in provision by the Supreme Court in 2012 and only 27 states have adopted the expansion so far, many people won't qualify for either Medicaid or ACA subsidies. If that's the case, you can apply for an exemption.


Fool-worthy thoughts
Don't wait until the last minute to see if you qualify for an exemption. The second open enrollment period ends Feb. 15, and penalty payments will be due when taxes are filed on April 15. Preparation is key, so taking time up front to understand the exchanges, the fee, and whether you meet any exemption classifications could save you hundreds of dollars at tax time.