The decision to sign up for Social Security is a big one. That's because your filing age will dictate how much of a monthly benefit you're entitled to throughout your retirement.

You can sign up for Social Security as early as age 62. But you can't claim your full monthly benefit based on your wage history until full retirement age, or FRA. FRA hinges on your year of birth, and it's either 66, 67, or 66 and a certain number of months.

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Meanwhile, Medicare eligibility begins at age 65. In fact, you can sign up for Medicare up to three months before the month of your 65th birthday. If you reach that point and you're not yet collecting Social Security, you may be wondering if it pays to delay your Medicare enrollment.

In some cases, it could. But in many cases, it doesn't.

Two separate programs

You might assume that you can't enroll in Medicare until you're signed up to receive benefits from Social Security. But actually, that's not true at all. Just as you can file for Social Security before Medicare, so too can you do the opposite -- enroll in Medicare at age 65 even if you want to wait until FRA or beyond to claim Social Security.

In fact, delaying Medicare simply because you're not on Social Security could end up being problematic for a couple of reasons. First, it could mean forgoing the health coverage you need. Secondly, it could mean facing costly penalties for Medicare Part B, which covers outpatient services.

For each year-long period you're eligible for Part B but don't enroll, you face a lifelong 10% surcharge on your premium costs. Now there's an exception to that rule, and it's if you're covered by a group health insurance plan. If so, that penalty is waived, and you'll get a special enrollment period to sign up for Medicare once you separate from your employer or your group coverage goes away.

But otherwise, be mindful of that penalty when deciding whether to delay Medicare. And don't let Social Security -- or the fact that you're not yet collecting benefits -- dictate that decision.

When it does pay to delay Medicare

For many seniors, enrolling in Medicare at age 65 makes sense. But if you're still working, have group health coverage you're happy with, and are contributing to a health savings account (HSA), it could pay to delay Medicare.

Once you enroll in Medicare, you're no longer eligible to fund an HSA. Now this doesn't mean you can't use your existing HSA to cover healthcare costs you incur as a Medicare beneficiary. But you can't put fresh funds into your account.

Aside from that, it often pays to at least enroll in Medicare Part A at age 65, even if you have a group health plan through an employer. Part A, which covers hospital care, is generally free for seniors. And it can serve as secondary insurance, picking up some of the costs that your primary insurance plan does not.