Many people can't wait until their 65th birthday to arrive so they can obtain health coverage through Medicare. But then there are some people who don't sign up for Medicare when they're initially eligible to do so.

In some cases, failing to enroll in Medicare on time could negatively impact your finances for the remainder of your retirement, so it's important to not only know the rules, but follow them.

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How Medicare enrollment works

Your initial window to enroll in Medicare spans seven months. It begins three months before the month of your 65th birthday and it ends three months after that month. If you sign up for Medicare during that initial window, but after your 65th birthday, your coverage will be retroactive to your 65th birthday.

If you're covered by a qualifying group health plan through a job (yours or your spouse's) at the time of your initial Medicare enrollment window, you won't have to sign up during that time. Rather, you'll get a special enrollment period once your group health coverage comes to an end.

You technically don't have to sign up during your initial Medicare enrollment window even if you're not covered by a qualifying group health plan during that time. But failing to enroll in this situation could leave you paying more for Medicare throughout retirement.

You should also know that if you're collecting Social Security benefits prior to age 65, you'll automatically be enrolled in Medicare (Parts A and B) starting the first day of the month you turn 65. Social Security eligibility begins at age 62, so it's possible to collect benefits for several years before becoming eligible for Medicare coverage.

Don't risk a costly surcharge

Medicare enrollment is not obligatory. But if you don't sign up when you're supposed to and you're not entitled to a special enrollment period, you'll face a 10% surcharge on your Part B premiums for each 12-month period you were eligible for coverage but didn't sign up. And that surcharge will stay in effect for the remainder of your retirement. That could put a huge strain on your budget.

But that's not the only problem with failing to enroll in Medicare on time. Let's say that as of your 65th birthday, you don't have coverage through a group plan but you also delay your Medicare enrollment to avoid paying those premiums. What if you get hurt or sick to the point that you require a hospital stay? The costs you might face in that situation could be astronomical.

So Part B surcharges aside, it pays to enroll in Medicare when you're supposed to if you don't have a group health plan to fall back on. Failing to put coverage in place could end up being one of the worst financial mistakes you'll ever make.

Also, if you don't enroll in Medicare and also don't have group health coverage, you may be inclined to neglect health issues that should really be brought to the attention of a provider. That, too, could be hugely problematic -- not necessarily for financial reasons, but for the sake of your physical well-being.

As such, it pays to read up on Medicare so you know exactly when to enroll. And you should make an effort to sign up on time to avoid all manner of unwanted consequences.